DeRhamComputation/sage/.run.term-0.term

sage: ((C.y)^(-1)*(C.x)^(-2)*C.dx).jth_component(0)
0
[6nsage: ((C.y)^(-1)*(C.x)^(-2)*C.dx).jth_component(1)
1/x^2
[6nsage: ((C.y)^(-1)*(C.x)^(-2)*C.dx).jth_component(2)
0
[6nsage: ((C.y)^(-2)*(C.x)^(-2)*C.dx).jth_component(0)
1/(x^5 + 2*x^3)
[6nsage: decomposition_omega0_omega8((C.x)^(-2)*C.dx)
component, q, r 1/x^2 0 1
component, q, r 0 0 0
(0 dx, ((-1)/x^2) dx)
[6nsage: load('init.sage')
aux.h2, decomposition_g0_g8(aux.h2, prec=prec) ((x^4 + x^2 + 1)/x^3)*y (x*y, 2/x^3*y, 1/x*y) ((x^4 + 1)/x^3)*y
aux.h2, decomposition_g0_g8(aux.h2, prec=prec) (x^6/(x^2 + 2))*y ((x^6/(x^2 + 2))*y, 0, 0) (x^6/(x^2 + 2))*y
(1, 0)
aux before reduce (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([((2*x^2 + 2*x + 2)/(x^2 + x))*y]), V((2/(x^2 + x))*y), V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([2*y]))
aux V(smth) (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx), [0], V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx))
aux.omega0.omega.cartier() ((-x + 1)/y) dx
---------------------------------------------------------------------------
KeyError Traceback (most recent call last)
Input In [84], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:28, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:17, in <module>
 
File <string>:340, in coordinates(self, basis)
 
File <string>:66, in coordinates(self)
 
KeyError: (1, 1)
[6nsage: b[0]
([(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([((2*x^3 + 2*x)/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([((2*x^4 + x^2 + 1)/(x^3 + 2*x))*y]))
[6nsasage: autom(b[0]) - 4*b[0]-6*b[0]
(V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([((2*x^2 + 2*x + 2)/(x^2 + x))*y]), V((2/(x^2 + x))*y), V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([2*y]))
[6nsage: load('init.sage')
(0, 1)
(0, 1)
aux.h2, decomposition_g0_g8(aux.h2, prec=prec) ((x^4 + x^2 + 1)/x^3)*y (x*y, 2/x^3*y, 1/x*y) ((x^4 + 1)/x^3)*y
(0, x)
(0, 2/x)
aux.h2, decomposition_g0_g8(aux.h2, prec=prec) (x^6/(x^2 + 2))*y ((x^6/(x^2 + 2))*y, 0, 0) (x^6/(x^2 + 2))*y
(1, 0)
aux before reduce (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([((2*x^2 + 2*x + 2)/(x^2 + x))*y]), V((2/(x^2 + x))*y), V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([2*y]))
aux V(smth) (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx), [0], V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx))
aux.omega0.omega.cartier() ((-x + 1)/y) dx
---------------------------------------------------------------------------
KeyError Traceback (most recent call last)
Input In [87], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:28, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:17, in <module>
 
File <string>:340, in coordinates(self, basis)
 
File <string>:66, in coordinates(self)
 
KeyError: (1, 1)
[6nsage: b[0].omega0.frobenius()
((-x^3 - x)/y) dx
[6nsage: b[0].omega8.frobenius()
((-x^4 + 1)/(x*y)) dx
[6nsage: b[0].omega8.frobenius().valuation()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [90], in <cell line: 1>()
----> 1 b[Integer(0)].omega8.frobenius().valuation()
 
AttributeError: 'superelliptic_form' object has no attribute 'valuation'
[6nsage: b[0].omega8.frobenius().expansion_at_infty()
2*t^-6 + t^-2 + t^2 + O(t^4)
[6nsage: load('init.sage')
(0, 1)
t^2 + t^10 + O(t^12)
(0, x)
t^-4 + t^4 + O(t^6)
(1, 0)
aux before reduce (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([((2*x^2 + 2*x + 2)/(x^2 + x))*y]), V((2/(x^2 + x))*y), V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([2*y]))
aux V(smth) (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx), [0], V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx))
aux.omega0.omega.cartier() ((-x + 1)/y) dx
---------------------------------------------------------------------------
KeyError Traceback (most recent call last)
Input In [92], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:28, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:17, in <module>
 
File <string>:340, in coordinates(self, basis)
 
File <string>:66, in coordinates(self)
 
KeyError: (1, 1)
[6nsage: load('init.sage')
(0, 1)
t^2 + t^10 + O(t^12)
(0, x)
2*t^8 + 2*t^16 + O(t^18)
(1, 0)
aux before reduce (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([((2*x^2 + 2*x + 2)/(x^2 + x))*y]), V((2/(x^2 + x))*y), V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([2*y]))
aux V(smth) (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx), [0], V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx))
aux.omega0.omega.cartier() ((-x + 1)/y) dx
---------------------------------------------------------------------------
KeyError Traceback (most recent call last)
Input In [93], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:28, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:17, in <module>
 
File <string>:340, in coordinates(self, basis)
 
File <string>:66, in coordinates(self)
 
KeyError: (1, 1)
[6nsage: b[0].omega8.frobenius().expansion_at_infty()
2*t^-6 + t^-2 + t^2 + O(t^4)
[6nsage: load('init.sage')
(0, 1)
t^2 + t^10 + O(t^12)
aux (is h1 = 0?) V(((-x^6 - x^4 + 1)/(x*y)) dx) + dV([((x^4 + x^2 + 1)/x^3)*y])
(0, x)
2*t^8 + 2*t^16 + O(t^18)
aux (is h1 = 0?) V(((-x^16 - x^14 - x^12 + x^10 - x^8 - x^6 + x^4 - x^2 - 1)/(x^8*y - x^6*y)) dx) + dV([((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y])
(1, 0)
aux before reduce (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([((2*x^2 + 2*x + 2)/(x^2 + x))*y]), V((2/(x^2 + x))*y), V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([2*y]))
aux V(smth) (V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx), [0], V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx))
aux.omega0.omega.cartier() ((-x + 1)/y) dx
---------------------------------------------------------------------------
KeyError Traceback (most recent call last)
Input In [95], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:28, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:17, in <module>
 
File <string>:340, in coordinates(self, basis)
 
File <string>:66, in coordinates(self)
 
KeyError: (1, 1)
[6nsage: load('init.sage')
(0, 1)
t^2 + t^10 + O(t^12)
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [96], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:28, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:16, in <module>
 
File <string>:375, in crystalline_cohomology_basis(self, prec)
 
File <string>:363, in de_rham_witt_lift(cech_class, prec)
 
File <string>:18, in __eq__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
493 """
--> 494 return self.getattr_from_category(name)
495
496 cdef getattr_from_category(self, name):
 
File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
505 else:
506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
508
509 def __dir__(self):
 
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
359 dummy_error_message.cls = type(self)
360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
362 attribute = <object>attr
363 # Check for a descriptor (__get__ in Python)
 
AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function'
[6nsage: load('init.sage')
(0, 1)
t^2 + t^10 + O(t^12)
(0, x)
2*t^8 + 2*t^16 + O(t^18)
(1, 0)
aux before reduce (V((1/(x^2*y + x*y)) dx) + dV([(2/(x^2 + x))*y]), V((2/(x^2 + x))*y), V((1/(x^2*y + x*y)) dx))
aux V(smth) (V((1/(x^2*y + x*y)) dx), [0], V((1/(x^2*y + x*y)) dx))
aux.omega0.omega.cartier() 0 dx
[1, 0]
[6nsage: sage: autom(b[0]) - 4*b[0]-6*b[0]
(V((1/(x^2*y + x*y)) dx) + dV([(2/(x^2 + x))*y]), V((2/(x^2 + x))*y), V((1/(x^2*y + x*y)) dx))
[6nsage: (autom(b[0]) - 4*b[0]-6*b[0]).reduce()
(V((1/(x^2*y + x*y)) dx) + dV([(2/(x^2 + x))*y]), [0], V((1/(x^2*y + x*y)) dx) + dV([(2/(x^2 + x))*y]))
[6nsage: autom(b[0]).coordinates(basis = b)
(1, 0)
aux before reduce (V((1/(x^2*y + x*y)) dx) + dV([(2/(x^2 + x))*y]), V((2/(x^2 + x))*y), V((1/(x^2*y + x*y)) dx))
aux V(smth) (V((1/(x^2*y + x*y)) dx), [0], V((1/(x^2*y + x*y)) dx))
aux.omega0.omega.cartier() 0 dx
[1, 0]
[6nsage: (C.one/(C.x^2*C.y + C.x*C.y)) C.dx
Input In [101]
(C.one/(C.x**Integer(2)*C.y + C.x*C.y)) C.dx
^
SyntaxError: invalid syntax
 
[6nsage: (C.one/(C.x^2*C.y + C.x*C.y))* C.dx
(1/(x^2*y + x*y)) dx
[6nsage: ((C.one/(C.x^2*C.y + C.x*C.y))* C.dx).cartier()
0 dx
[6nsage: sage:
[6nsage:
[6nsage: ((C.one/(C.x^2*C.y + C.x*C.y))* C.dx).expansion_at_infty()
t^4 + 2*t^6 + t^8 + O(t^14)
[6nsage: load('init.sage')
(0, 1)
omega8_lift.frobenius().expansion_at_infty() t^2 + t^10 + O(t^12)
(0, x)
omega8_lift.frobenius().expansion_at_infty() 2*t^8 + 2*t^16 + O(t^18)
(1, 0)
aux before reduce (V((1/(x^2*y + x*y)) dx) + dV([(2/(x^2 + x))*y]), V((2/(x^2 + x))*y), V((1/(x^2*y + x*y)) dx))
aux V(smth) (V((1/(x^2*y + x*y)) dx), [0], V((1/(x^2*y + x*y)) dx))
aux.omega0.omega.cartier() 0 dx
[1, 0]
[6nsage: b[0]
([(1/(x^3 + 2*x))*y] d[x] + V(((-x)/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V(((-x)/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[6nsage: b[0].omega0.r()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [107], in <cell line: 1>()
----> 1 b[Integer(0)].omega0.r()
 
AttributeError: 'superelliptic_drw_form' object has no attribute 'r'
[6nsage: b[0].omega0.R()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [108], in <cell line: 1>()
----> 1 b[Integer(0)].omega0.R()
 
AttributeError: 'superelliptic_drw_form' object has no attribute 'R'
[6nsage: sage: load('init.sage')
(0, 1)
omega8_lift.frobenius().expansion_at_infty() t^2 + t^10 + O(t^12)
(0, x)
omega8_lift.frobenius().expansion_at_infty() 2*t^8 + 2*t^16 + O(t^18)
(1, 0)
aux before reduce (V((1/(x^2*y + x*y)) dx) + dV([(2/(x^2 + x))*y]), V((2/(x^2 + x))*y), V((1/(x^2*y + x*y)) dx))
aux V(smth) (V((1/(x^2*y + x*y)) dx), [0], V((1/(x^2*y + x*y)) dx))
aux.omega0.omega.cartier() 0 dx
[1, 0]
[6nsage: b[0].omega0.r()
(1/y) dx
[6nsage: b[0].omega0.frobenius()
((-x)/y) dx
[6nsage: bsage: b[0].omega8.r()
(1/y) dx
[6nsage: b[0].omega8.frobenius()
(1/(x*y)) dx
[6nsage: b[0].omega8.frobenius().expansion_at_infty()
t^2 + t^6 + O(t^12)
[6nsage: b[0]
([(1/(x^3 + 2*x))*y] d[x] + V(((-x)/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V(((-x)/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[6nsage: 3*b[0]
(V((x/(x^2*y - y)) dx), [0], V((x/(x^2*y - y)) dx))
[6nsage: b[0].coordinates()
(1, 0)
(0, 1)
omega8_lift.frobenius().expansion_at_infty() t^2 + t^10 + O(t^12)
(0, x)
omega8_lift.frobenius().expansion_at_infty() 2*t^8 + 2*t^16 + O(t^18)
aux before reduce (0, [0], 0)
aux V(smth) (0, [0], 0)
aux.omega0.omega.cartier() 0 dx
[1, 0]
[6nsage: autom(b[0]).coordinates()
(1, 0)
(0, 1)
omega8_lift.frobenius().expansion_at_infty() t^2 + t^10 + O(t^12)
(0, x)
omega8_lift.frobenius().expansion_at_infty() 2*t^8 + 2*t^16 + O(t^18)
aux before reduce (V((1/(x^2*y + x*y)) dx) + dV([(2/(x^2 + x))*y]), V((2/(x^2 + x))*y), V((1/(x^2*y + x*y)) dx))
aux V(smth) (V((1/(x^2*y + x*y)) dx), [0], V((1/(x^2*y + x*y)) dx))
aux.omega0.omega.cartier() 0 dx
[1, 0]
[6nsage: ((C.one/(C.x^2*C.y + C.x*C.y))* C.dx).is_regular_on_U0()
0
[6nsage: (2*C.one/(C.x^2 + C.x))*C.y
(2/(x^2 + x))*y
[6nsage: decomposition_into_go_g8((2*C.one/(C.x^2 + C.x))*C.y)
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [121], in <cell line: 1>()
----> 1 decomposition_into_go_g8((Integer(2)*C.one/(C.x**Integer(2) + C.x))*C.y)
 
NameError: name 'decomposition_into_go_g8' is not defined
[6nsage: decomposition_into_g0_g8((2*C.one/(C.x^2 + C.x))*C.y)
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [122], in <cell line: 1>()
----> 1 decomposition_into_g0_g8((Integer(2)*C.one/(C.x**Integer(2) + C.x))*C.y)
 
NameError: name 'decomposition_into_g0_g8' is not defined
[6nsage: decomposition_g0_g8((2*C.one/(C.x^2 + C.x))*C.y)
(0, (1/(x^2 + x))*y, 0)
[6nsage: sage: quit()
[23;0t
~/Research/2021 De Rham/DeRhamComputation/sage$ cd ..
~/Research/2021 De Rham/DeRhamComputation$ git add -u
~/Research/2021 De Rham/DeRhamComputation$ git commit -m "nieudane proby coordinates dla cech_drw"
[master 5f82d7d] nieudane proby coordinates dla cech_drw
10 files changed, 28539 insertions(+), 40853 deletions(-)
rewrite sage/drafty/draft.sage (63%)
~/Research/2021 De Rham/DeRhamComputation$ git push
Username for 'https://git.wmi.amu.edu.pl': jgarnek
Password for 'https://jgarnek@git.wmi.amu.edu.pl':
Enumerating objects: 28, done.
Counting objects: 100% (28/28), done.
Delta compression using up to 4 threads
Compressing objects: 100% (16/16), done.
Writing objects: 100% (16/16), 200.65 KiB | 1.44 MiB/s, done.
Total 16 (delta 12), reused 0 (delta 0)
remote: . Processing 1 references
remote: Processed 1 references in total
To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git
b79484b..5f82d7d master -> master
~/Research/2021 De Rham/DeRhamComputation$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
[22;0t[6nsage: load('init.sage')
---------------------------------------------------------------------------
OSError Traceback (most recent call last)
Input In [1], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:244, in load(filename, globals, attach)
242 break
243 else:
--> 244 raise IOError('did not find file %r to load or attach' % filename)
246 ext = os.path.splitext(fpath)[1].lower()
247 if ext == '.py':
 
OSError: did not find file 'init.sage' to load or attach
[6nsage: quit()
[23;0t~/Research/2021 De Rham/DeRhamComputation$ cd sage
~/Research/2021 De Rham/DeRhamComputation/sage$ [3Psage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
[22;0t[6nsage: load('init.sage')
(0, 1)
omega8_lift.frobenius().expansion_at_infty() t^2 + t^10 + O(t^12)
(0, x)
omega8_lift.frobenius().expansion_at_infty() 2*t^8 + 2*t^16 + O(t^18)
(1, 0)
aux before reduce (V((1/(x^2*y + x*y)) dx) + dV([(2/(x^2 + x))*y]), V((2/(x^2 + x))*y), V((1/(x^2*y + x*y)) dx))
aux V(smth) (V((1/(x^2*y + x*y)) dx) + dV([(2/(x^2 + x))*y]), V((2/(x^2 + x))*y), V((1/(x^2*y + x*y)) dx))
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [1], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:28, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:17, in <module>
 
File <string>:340, in coordinates(self, basis)
 
File <string>:168, in pth_root(self)
 
ValueError: Function is not a p-th power.
[6nsage: C
Superelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
[6nsage: C.frobenius_matrix()
[0]
[6nsage: b[0] - 4*b[0] - 6*b[1]
(V(((x^3 + x^2 + x)/(x*y + y)) dx), V(((2*x^2 + 1)/x^2)*y), V(((x^3 + x^2 + x)/(x*y + y)) dx) + dV([((x^2 + 2)/x^2)*y]))
[6nsage: (b[0] - 4*b[0] - 6*b[1]).reduce()
(V(((x^3 + x^2 + x)/(x*y + y)) dx) + dV([y]), [0], V(((x^3 + x^2 + x)/(x*y + y)) dx) + dV([y]))
[6nsage: (b[0] - 4*b[0] - 6*b[1]).reduce().omega0.frobenius()
(1/y) dx
[6nsage: autom(b[0]) - 4*b[0] - 6*b[1]
(V(((x^4 + x^3 + x^2 + 1)/(x^2*y + x*y)) dx) + dV([(2/(x^2 + x))*y]), V(((2*x^3 + 2*x^2 + 1)/(x^3 + x^2))*y), V(((x^4 + x^3 + x^2 + 1)/(x^2*y + x*y)) dx) + dV([((x^2 + 2)/x^2)*y]))
[6nsage: (autom(b[0]) - 4*b[0] - 6*b[1]).reduce()
(V(((x^4 + x^3 + x^2 + 1)/(x^2*y + x*y)) dx) + dV([((x^2 + x + 2)/(x^2 + x))*y]), [0], V(((x^4 + x^3 + x^2 + 1)/(x^2*y + x*y)) dx) + dV([((x^2 + x + 2)/(x^2 + x))*y]))
[6nsage: (autom(b[0]) - 4*b[0] - 6*b[1]).reduce().frobenius()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [9], in <cell line: 1>()
----> 1 (autom(b[Integer(0)]) - Integer(4)*b[Integer(0)] - Integer(6)*b[Integer(1)]).reduce().frobenius()
 
AttributeError: 'superelliptic_drw_cech' object has no attribute 'frobenius'
[6nsage: (autom(b[0]) - 4*b[0] - 6*b[1]).reduce().omega0.frobenius()
(1/(x^2*y + x*y)) dx
[6nsage: (autom(b[0]) - 4*b[0] - 6*b[1]).reduce().f
[0]
[6nsage: (autom(b[0]) - 4*b[0] - 6*b[1]).omega0.frobenius()
((-x^2 - x + 1)/(x^2*y + x*y)) dx
[6nsage: True == 1
True
[6nsage: load('init.sage')
(0, 1)
omega8_lift.frobenius().expansion_at_infty() t^2 + t^10 + O(t^12)
(0, x)
omega8_lift.frobenius().expansion_at_infty() 2*t^8 + 2*t^16 + O(t^18)
(1, 0)
aux before reduce (V((1/(x^2*y + x*y)) dx) + dV([(2/(x^2 + x))*y]), V((2/(x^2 + x))*y), V((1/(x^2*y + x*y)) dx))
aux V(smth) (V((1/(x^2*y + x*y)) dx) + dV([(2/(x^2 + x))*y]), V((2/(x^2 + x))*y), V((1/(x^2*y + x*y)) dx))
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [14], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:28, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:17, in <module>
 
File <string>:340, in coordinates(self, basis)
 
File <string>:168, in pth_root(self)
 
ValueError: Function is not a p-th power.
[6nsage: b[0].is_regular()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [15], in <cell line: 1>()
----> 1 b[Integer(0)].is_regular()
 
File <string>:348, in is_regular(self)
 
AttributeError: 'superelliptic_form' object has no attribute 'is_regular_on_U8'
[6nsage: load('init.sage')
(0, 1)
omega8_lift.frobenius().expansion_at_infty() t^2 + t^10 + O(t^12)
(0, x)
omega8_lift.frobenius().expansion_at_infty() 2*t^8 + 2*t^16 + O(t^18)
(1, 0)
aux before reduce (V((1/(x^2*y + x*y)) dx) + dV([(2/(x^2 + x))*y]), V((2/(x^2 + x))*y), V((1/(x^2*y + x*y)) dx))
aux V(smth) (V((1/(x^2*y + x*y)) dx) + dV([(2/(x^2 + x))*y]), V((2/(x^2 + x))*y), V((1/(x^2*y + x*y)) dx))
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [16], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:28, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:17, in <module>
 
File <string>:340, in coordinates(self, basis)
 
File <string>:168, in pth_root(self)
 
ValueError: Function is not a p-th power.
[6nsage: b[0].is_regular()
1
[6nsage: b[1].is_regular()
1
[6nsage: autom(b[1]) - 4*b[0] - 4*b[1]
(V(((-x^3 + x + 1)/(x*y)) dx) + dV([2/x*y]), [(1/(x^2 + x))*y] + V(((x^3 + x^2 + 2)/(x^3 + x^2))*y), [((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^8 - x^6 - x^5 - x^4 - x^2 - x + 1)/(x^6*y - x^4*y + x^3*y - x*y)) dx) + dV([((2*x^7 + 2*x^6 + x^5 + x^4 + 2*x^3 + x^2 + 2)/(x^7 + 2*x^5 + x^4 + 2*x^2))*y]))
[6nsage: autom(b[1]).is_regular()
0
[6nsage: autom(b[0]).is_regular()
0
[6nsage: sage: b[0].is_regular()
1
[6nsage: b[0]
([(1/(x^3 + 2*x))*y] d[x] + V(((-x)/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V(((-x)/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[6nsage: autom(b[0])
([(1/(x^3 + 2*x))*y] d[x] + V(((-x - 1)/(x^2*y - x*y)) dx) + dV([((x + 1)/(x^2 + 2*x))*y]), V((1/(x + 1))*y), [(1/(x^3 + 2*x))*y] d[x] + V(((-x - 1)/(x^2*y - x*y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[6nsage: load('init.sage')
(0, 1)
omega8_lift.frobenius().expansion_at_infty() t^2 + t^10 + O(t^12)
(0, x)
omega8_lift.frobenius().expansion_at_infty() 2*t^8 + 2*t^16 + O(t^18)
(1, 0)
aux before reduce (V((1/(x^2*y + x*y)) dx) + dV([(2/(x^2 + x))*y]), V((2/(x^2 + x))*y), V((1/(x^2*y + x*y)) dx))
aux V(smth) (V((1/(x^2*y + x*y)) dx) + dV([(2/(x^2 + x))*y]), V((2/(x^2 + x))*y), V((1/(x^2*y + x*y)) dx))
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [25], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:28, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:17, in <module>
 
File <string>:340, in coordinates(self, basis)
 
File <string>:168, in pth_root(self)
 
ValueError: Function is not a p-th power.
[6nsage: autom(b[0])
([(1/(x^3 + 2*x))*y] d[x] + V(((-x - 1)/(x^2*y - x*y)) dx) + dV([((x + 1)/(x^2 + 2*x))*y]), V((1/(x + 1))*y), [(1/(x^3 + 2*x))*y] d[x] + V(((-x - 1)/(x^2*y - x*y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[6nsage: load('init.sage')
(0, 1)
omega8, omega8_lift.r() (1/y) dx (1/y) dx
(0, x)
omega8, omega8_lift.r() ((-1)/(x*y)) dx ((-1)/(x*y)) dx
[6nsage: autom(b[0]).is_regular()
1 1 0 1
0
[6nsage: autom(b[0]).r()
((1/y) dx, 0, (1/y) dx)
[6nsage: autom(b[0])
([(1/(x^3 + 2*x))*y] d[x] + V(((-x - 1)/(x^2*y - x*y)) dx) + dV([((x + 1)/(x^2 + 2*x))*y]), V((1/(x + 1))*y), [(1/(x^3 + 2*x))*y] d[x] + V(((-x - 1)/(x^2*y - x*y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[6nsage: b[0]
([(1/(x^3 + 2*x))*y] d[x] + V(((-x)/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V(((-x)/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[6nsage: sage: om1 = C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*(C.y).diffn())
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [32], in <cell line: 1>()
----> 1 om1 = C.y.teichmuller().diffn() + (Integer(2)*C.x*C.y).verschiebung().diffn() + (C.x**Integer(5)*(C.y).diffn())
 
File <string>:231, in __add__(self, other)
 
AttributeError: 'superelliptic_form' object has no attribute 'h1'
[6nsage: om1 = C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*(C.y).diffn()).verschiebung()
[6nsasage: xi = superelliptic_drw_cech(om1, ((C.y)/(C.x)).teichmuller())
[6nsage: xi.is_regular()
1 0 1 0
0
[6nsage: xi.r()
((1/y) dx, 1/x*y, ((x^2 + x + 1)/(x*y)) dx)
[6nsage: C.de_rham_basis()
[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
[6nsage: xi = superelliptic_drw_cech(om1, ((C.y)/(C.x)).verschiebung())
[6nsage: xi.is_regular()
1 1 1 1
1
[6nsage: autom(xi).is_regular()
1 1 0 1
0
[6nsage: autom(xi).omega0.frobenius()
((-x^3 + x^2 - x + 1)/(x^2*y + x*y)) dx
[6nsage: x
x
[6nsage: Rx
Univariate Polynomial Ring in x over Finite Field of size 3
[6nsasage: (-x^3 + x^2 - x + 1).quo_rem(x^2 + x)
(2*x + 2, 1)
[6nsage: autom(x)
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [45], in <cell line: 1>()
----> 1 autom(x)
 
File <string>:389, in autom(self)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
493 """
--> 494 return self.getattr_from_category(name)
495
496 cdef getattr_from_category(self, name):
 
File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
505 else:
506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
508
509 def __dir__(self):
 
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
359 dummy_error_message.cls = type(self)
360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
362 attribute = <object>attr
363 # Check for a descriptor (__get__ in Python)
 
AttributeError: 'sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint' object has no attribute 'curve'
[6nsage: autom(xi).omega0.frobenius()
((-x^3 + x^2 - x + 1)/(x^2*y + x*y)) dx
[6nsage: autom(xi)
([(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^4 - x^2 - 1)/(x^2*y - x*y)) dx) + dV([((x + 1)/(x^2 + 2*x))*y]), V((1/(x + 1))*y), [(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^4 - x^2 - 1)/(x^2*y - x*y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[6nsage: xi
([(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^3 - x)/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^3 - x)/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[6nsage: C.y.teichmuller().diffn()
[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[6nsage: load('init.sage')
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[6nsage: C.y.teichmuller().diffn()
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[6nsasage: (-1/2)%9
4
[6nsage: C.x.teichmuller().diffn()
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[1] d[x]
[6nsage: 1/2*C.x.teichmuller().diffn()
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[2] d[x] + V((x^2) dx)
[6nsage: (1/2^3)%9
8
[6nsage: (2^3)%9
8
[6nsage: teichmuller_lift(2, 3)
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [57], in <cell line: 1>()
----> 1 teichmuller_lift(Integer(2), Integer(3))
 
NameError: name 'teichmuller_lift' is not defined
[6nsasage: -C.x.teichmuller().diffn()
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[2] d[x]
[6nsage: 2*C.x.teichmuller().diffn()
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[2] d[x] + V((x^2) dx)
[6nsage: (-1/2)*C.x.teichmuller().diffn()
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[1] d[x] + V((-x^2) dx)
[6nsage: 1/2*C.x.teichmuller().diffn()
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[2] d[x] + V((x^2) dx)
[6nsagsage: (1/2)%9
5
[6nsage: 5^3-5
120
[6nsage: load('init.sage')
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[6nsage: 1/2*C.x.teichmuller().diffn()
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[2] d[x] + V((-x^2) dx)
[6nsasage: 5*C.x.teichmuller().diffn()
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[2] d[x] + V((-x^2) dx)
[6nsage: b[0]
([(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[6nsage: autom(b[0]).is_regular()
1 1 0 1
0
[6nsage: om1 = C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*(C.y).diffn()).verschiebung()
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[6nsage: xi = superelliptic_drw_cech(om1, ((C.y)/(C.x)).verschiebung())
[6nsage: xi.is_regular()
1 1 1 1
1
[6nsage: autom(xi).is_regular()
1 1 0 1
0
[6nsage: auxilliary_derivative(x^3 - x)
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [73], in <cell line: 1>()
----> 1 auxilliary_derivative(x**Integer(3) - x)
 
File <string>:136, in auxilliary_derivative(P)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
493 """
--> 494 return self.getattr_from_category(name)
495
496 cdef getattr_from_category(self, name):
 
File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
505 else:
506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
508
509 def __dir__(self):
 
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
359 dummy_error_message.cls = type(self)
360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
362 attribute = <object>attr
363 # Check for a descriptor (__get__ in Python)
 
AttributeError: 'sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint' object has no attribute 't'
[6nsage: auxilliary_derivative((C.x^3 - C.x).teichmuller())
[2] d[x] + V((x^8) dx) + dV([2*x^7 + x^5])
[6nsage: sage: (C.x^3 - C.x).teichmuller()
[x^3 + 2*x]
[6nsage: C.y.teichmuller().diffn()
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[6nsage: (-(C.y).teichmuller())^(-1)* auxilliary_derivative((C.x^3 - C.x).teichmuller())
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [77], in <cell line: 1>()
----> 1 (-(C.y).teichmuller())**(-Integer(1))* auxilliary_derivative((C.x**Integer(3) - C.x).teichmuller())
 
File /ext/sage/9.7/src/sage/rings/integer.pyx:2195, in sage.rings.integer.Integer.__pow__()
2193 return coercion_model.bin_op(left, right, operator.pow)
2194 # left is a non-Element: do the powering with a Python int
-> 2195 return left ** int(right)
2196
2197 cpdef _pow_(self, other):
 
TypeError: unsupported operand type(s) for ** or pow(): 'superelliptic_witt' and 'int'
[6nsage: (-((C.y)^(-1)).teichmuller())* auxilliary_derivative((C.x^3 - C.x).teichmuller())
[(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 - x^3)/y) dx) + dV([(x^3/(x^2 + 2))*y])
[6nsage: ((-((C.y)^(-1)).teichmuller())* auxilliary_derivative((C.x^3 - C.x).teichmuller())).frobenius()
((x^3 - x)/y) dx
[6nsage: C.y.diffn()
(1/y) dx
[6nsage: (C.y^2).teichmuller().diffn() == (C.x^3 - C.x).teichmuller().diffn()
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [81], in <cell line: 1>()
----> 1 (C.y**Integer(2)).teichmuller().diffn() == (C.x**Integer(3) - C.x).teichmuller().diffn()
 
File <string>:172, in __eq__(self, other)
 
File <string>:42, in __eq__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
493 """
--> 494 return self.getattr_from_category(name)
495
496 cdef getattr_from_category(self, name):
 
File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
505 else:
506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
508
509 def __dir__(self):
 
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
359 dummy_error_message.cls = type(self)
360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
362 attribute = <object>attr
363 # Check for a descriptor (__get__ in Python)
 
AttributeError: 'sage.rings.integer.Integer' object has no attribute 'form'
[6nsage: C.y^2
x^3 + 2*x
[6nsage: load('init.sage')
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[6nsage: (C.y^2).teichmuller().diffn() == (C.x^3 - C.x).teichmuller().diffn()
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[2] d[x] + V((x^8) dx) + dV([2*x^7 + x^5]) [2] d[x] + V((x^8) dx) + dV([2*x^7 + x^5])
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [84], in <cell line: 1>()
----> 1 (C.y**Integer(2)).teichmuller().diffn() == (C.x**Integer(3) - C.x).teichmuller().diffn()
 
File <string>:174, in __eq__(self, other)
 
File <string>:42, in __eq__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
493 """
--> 494 return self.getattr_from_category(name)
495
496 cdef getattr_from_category(self, name):
 
File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
505 else:
506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
508
509 def __dir__(self):
 
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
359 dummy_error_message.cls = type(self)
360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
362 attribute = <object>attr
363 # Check for a descriptor (__get__ in Python)
 
AttributeError: 'sage.rings.integer.Integer' object has no attribute 'form'
[6nsage: load('init.sage')
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[6nsage: (C.y^2).teichmuller().diffn() == (C.x^3 - C.x).teichmuller().diffn()
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
True
[6nsage: 2*(C.y).teichmuller().diffn() == (C.x^3 - C.x).teichmuller().diffn()
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
False
[6nsage: 2*(C.y).teichmuller() * (C.y).teichmuller().diffn() == (C.x^3 - C.x).teichmuller().diffn()
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
dy_w [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
True
[6nsage: load('init.sage')
[6nsage: 2*(C.y).teichmuller() * (C.y).teichmuller().diffn() == (C.x^3 - C.x).teichmuller().diffn()
True
[6nsage: 2*(C.y).teichmuller() * (C.y).teichmuller().diffn(dy_w = C.dy_w) == (C.x^3 - C.x).teichmuller().diffn(dy_w = C.dy_w)
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [91], in <cell line: 1>()
----> 1 Integer(2)*(C.y).teichmuller() * (C.y).teichmuller().diffn(dy_w = C.dy_w) == (C.x**Integer(3) - C.x).teichmuller().diffn(dy_w = C.dy_w)
 
File <string>:99, in diffn(self, dy_w)
 
File <string>:230, in __add__(self, other)
 
AttributeError: 'NoneType' object has no attribute 'h1'
[6nsage: C.dy_w
<bound method dy_w of Superelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3>
[6nsage: C.dy_w()
[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[6nsage: 2*(C.y).teichmuller() * (C.y).teichmuller().diffn(dy_w = C.dy_w()) == (C.x^3 - C.x).teichmuller().diffn(dy_w = C.dy_w())
True
[6nsage: C.y.teichmuller().diffn()
[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[6nsage:
sage:
sage:
sage: om1 = C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*(C.y).diffn()).verschiebung()
[sage: autom(om1)
[(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^4 - x^2 - x + 1)/(x^2*y - x*y)) dx) + dV([((x + 1)/(x^2 + 2*x))*y])
[6nsage: autom(om1).frobenius()]
Input In [98]
autom(om1).frobenius()]
^
SyntaxError: unmatched ']'
 
[6nsage: autom(om1).frobenius()
((-x^3 + x^2 - x + 1)/(x^2*y + x*y)) dx
[6nsage: C.y.teichmuller().diffn().frobenius()
((x^3 - x)/y) dx
[6nsage: C.y.teichmuller().diffn().frobenius() == (C.y)^2 * C.y.diffn()
True
[6nsage: (2*C.x*C.y).verschiebung().diffn().frobenius()
((-x^3)/y) dx
[6nsage: (C.x^5*(C.y).diffn()).verschiebung().frobenius()
0 dx
[6nsage: om1.frobenius()
((-x)/y) dx
[6nsage: autom(om1).frobenius()
((-x^3 + x^2 - x + 1)/(x^2*y + x*y)) dx
[6nsage: om1
[(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^3 + x)/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y])
[6nsage: autom((C.x^5*(C.y).diffn()).verschiebung()).frobenius()
0 dx
[6nsage: autom((C.y).teichmuller().diffn()).frobenius()
((x^5 + x^4 - x^3 - x^2 + 1)/(x^2*y + x*y)) dx
[6nsage: autom(C.y.teichmuller().diffn())
[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 - x^6 + x^4 - x^3 + 1)/(x^2*y - x*y)) dx) + dV([((x^3 + 1)/(x^2 + 2*x))*y])
[6nsage: autom(C.y.teichmuller().diffn()) - C.y.teichmuller().diffn()
V(((x^6 + x^4 - x^2 + x - 1)/(x^2*y + x*y)) dx) + dV([((x^2 + x + 2)/(x^2 + x))*y])
[6nsage: load('init.sage')
[6nsage: om1 = C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*(C.y).diffn()).verschiebung()
[6nsage: om1.is_regular()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [113], in <cell line: 1>()
----> 1 om1.is_regular()
 
AttributeError: 'superelliptic_drw_form' object has no attribute 'is_regular'
[6nsage: om1.frobenius()
((-x)/y) dx
[6nsage: autom(om1).frobenius()
((-x - 1)/y) dx
[6nsage: b[0]
([(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[6nsage: autom(b[0]).is_regular()
1 1 1 1
1
[6nsage: autom(b[0]).coordinates()
(1, 0)
aux before reduce (V(((-1)/(x^2*y + x*y + y)) dx) + dV([(2/(x^2 + x + 1))*y]), V((2/(x^2 + x))*y), V(((-1)/(x^2*y + x*y + y)) dx) + dV([(1/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
aux V(smth) (V(((-1)/(x^2*y + x*y + y)) dx) + dV([(2/(x^2 + x + 1))*y]), V((2/(x^2 + x))*y), V(((-1)/(x^2*y + x*y + y)) dx) + dV([(1/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [118], in <cell line: 1>()
----> 1 autom(b[Integer(0)]).coordinates()
 
File <string>:339, in coordinates(self, basis)
 
File <string>:168, in pth_root(self)
 
ValueError: Function is not a p-th power.
[6nsage: quit()
[23;0t~/Research/2021 De Rham/DeRhamComputation/sage$ cd ..
~/Research/2021 De Rham/DeRhamComputation$ git add -u
~/Research/2021 De Rham/DeRhamComputation$ git commit -m "Poprawiony [1@[1@ia[1@[1@s[1@p[1@r[1@a[1@d[1@[1[1P[1@w[1@d[1@z[1@o[1@n[1@y autom."
[master cc45757] Poprawiony i sprawdzony dy_w oraz autom.
4 files changed, 800 insertions(+), 17 deletions(-)
~/Research/2021 De Rham/DeRhamComputation$ git push
Username for 'https://git.wmi.amu.edu.pl': jgarnek
Password for 'https://jgarnek@git.wmi.amu.edu.pl':
Enumerating objects: 17, done.
Counting objects: 100% (17/17), done.
Delta compression using up to 4 threads
Compressing objects: 100% (9/9), done.
Writing objects: 100% (9/9), 15.99 KiB | 207.00 KiB/s, done.
Total 9 (delta 8), reused 0 (delta 0)
remote: . Processing 1 references
remote: Processed 1 references in total
To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git
5f82d7d..cc45757 master -> master
~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
[22;0t[6nsage: load('init.sage')
[6nsage: b
[([(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y])),
([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))]
[6nsage: load('init.sage')
[6nsage: eta1
([(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^3 + x)/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y]), [1/x*y], [((x + 2)/(x^3 + x^2))*y] d[x] + V(((-x^5 + x^4 - x^3 + x - 1)/(x^2*y)) dx) + dV([(1/(x + 1))*y]))
[6nsage: eta1.is_regular()
1 0 1 0
0
[6nsage: load('init.sage')
[6nsage: eta1.is_regular()
1 1 1 1
1
[6nsage: eta2.is_regular()
1 1 1 1
1
[6nsage: b[0]-eta1
(V((x^3/y) dx), [0], V((x^3/y) dx))
[6nsage: b[0] == eta1
False
[6nsage: b[0].omega0 == eta1.omega0
True
[6nsage: b[0].omega8 == eta1.omega8
True
[6nsage: b[1].omega8 == eta2.omega8
False
[6nsage: sage: b[1] - eta2
(V(((x^8 - x^6 + 1)/y) dx), [0], V(((x^8 - x^6 + 1)/y) dx))
[6nsage: sage: (b[1] - eta2).omega0.omega.cartier()
(x^3/y) dx
sage: om3 = C.y.verschiebung().diffn() + mult_by_p(C.x*(C.y).diffn())
sage: ome3
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [17], in <cell line: 1>()
----> 1 ome3
 
NameError: name 'ome3' is not defined
[6nsage: om3
V((x^4/(x^2*y - y)) dx) + dV([y])
[6nsage: om3.reduce()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [19], in <cell line: 1>()
----> 1 om3.reduce()
 
AttributeError: 'superelliptic_drw_form' object has no attribute 'reduce'
[6nsage: (b[1] - eta2).omega0 - om3
V(((x^10 + x^8 + x^6 - x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([2*y])
[6nsage: ((b[1] - eta2).omega0 - om3).frobenius()
((-1)/y) dx
[6nsage: (b[1] - eta2).omega0 + om3
V(((x^10 + x^8 + x^6 + x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([y])
[6nsage: (b[1] - eta2).omega0.frobenius()
0 dx
[6nsage: (b[1] - eta2)
(V(((x^8 - x^6 + 1)/y) dx), [0], V(((x^8 - x^6 + 1)/y) dx))
[6nsage: (b[1] - eta2).omega0.cartier()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [25], in <cell line: 1>()
----> 1 (b[Integer(1)] - eta2).omega0.cartier()
 
AttributeError: 'superelliptic_drw_form' object has no attribute 'cartier'
[6nsage: (b[1] - eta2).omega0.omega.cartier()
(x^3/y) dx
[6nsage: C.de_rham_basis()
[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
[6nsage: load('init.sage')
omega0_regular (0, 1)
omega8_regular (0, 1)
omega0_regular (0, x)
omega8_regular (0, 2/x)
[6nsasage: ((C.x*C.y)^(-1)*C.dx).expansion_at_infty()
t^2 + t^6 + O(t^12)
[6nsage: second_patch((C.x*C.y)^(-1)*C.dx))
Input In [30]
second_patch((C.x*C.y)**(-Integer(1))*C.dx))
^
SyntaxError: unmatched ')'
 
[6nsage: second_patch((C.x*C.y)^(-1)*C.dx)
((-x)/y) dx
[6nsage: b[0]
([(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[6nsage: b[1]
([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[6nsage: b[1].is_regular()
1 1 1 1
1
[6nsage: load('init.sage')
omega0_regular (0, 1)
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[6nsage: load('init.sage')
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[6nsage: C.de_rham_basis()[1]
((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
[6nsage: load('init.sage')
[6nsage: aux = de_rham_witt_lift(C.de_rham_basis()[1])
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[6nsage: aux1 = C.xsage: aux1 = C.x.teichmuller()*(C.y.teichmuller().diffn()) - (2*(C.x)^(-1)).teichmuller()*(C.y/C.x^2).teichmuller().diffn() + (C.y/C.x).diffn()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [40], in <cell line: 1>()
----> 1 aux1 = C.x.teichmuller()*(C.y.teichmuller().diffn()) - (Integer(2)*(C.x)**(-Integer(1))).teichmuller()*(C.y/C.x**Integer(2)).teichmuller().diffn() + (C.y/C.x).diffn()
 
File <string>:230, in __add__(self, other)
 
AttributeError: 'superelliptic_form' object has no attribute 'h1'
[6nsage: aux1 = C.x.teichmuller()sage: aux1 = C.x.teichmuller()*(C.y.teichmuller().diffn()) - (2*(C.x)^(-1)).teichmuller()*(C.y/C.x^2).teichmuller().diffn() + (C.y/C.x).teichmuller().diffn()
[6nsage: aux1 = C.x.teichmsage: aux == aux1
True
[6nsage: aux
V(((-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV([((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y])
~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
[22;0t[6nsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
V(((-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV([((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y])
[6nsage: quit()
[23;0t~/Research/2021 De Rham/DeRhamComputation/sage$ cd ..
~/Research/2021 De Rham/DeRhamComputation$ [1add dra -u
~/Research/2021 De Rham/DeRhamComputation$ git commit -m "przeniesione pliki"
[master 7bcfa5d] przeniesione pliki
6 files changed, 208 insertions(+), 516 deletions(-)
delete mode 100644 sage/drafty/second_patch.sage
delete mode 100644 sage/drafty/superelliptic_drw.sage
delete mode 100644 sage/superelliptic/decomposition_into_g0_g8.sage
~/Research/2021 De Rham/DeRhamComputation$ git add sage/superelliptic_drw/superelliptic_drw.sage
~/Research/2021 De Rham/DeRhamComputation$ git add sage/superelliptic_drw/second_patch.sage sage/superelliptic_drw/decomposition_into_g0_g8.sage
~/Research/2021 De Rham/DeRhamComputation$ git [19Pcommit -m "przeniesione pliki 2"ptic_drw.sage
[master b03c679] przeniesione pliki 2
3 files changed, 515 insertions(+)
create mode 100644 sage/superelliptic_drw/decomposition_into_g0_g8.sage
create mode 100644 sage/superelliptic_drw/second_patch.sage
create mode 100644 sage/superelliptic_drw/superelliptic_drw.sage
~/Research/2021 De Rham/DeRhamComputation$ git add sage/superelliptic_drw/superelliptic_witt.sage sage/superelliptic_drw/superelliptic_drw_cech.sage sage/superelliptic_drw/superelliptic_drw_
superelliptic_drw_cech.sage superelliptic_drw_form.sage superelliptic_drw_tests/
~/Research/2021 De Rham/DeRhamComputation$ git add sage/superelliptic_drw/superelliptic_witt.sage sage/superelliptic_drw/superelliptic_drw_cech.sage sage/superelliptic_drw/superelliptic_drw_
superelliptic_drw_cech.sage superelliptic_drw_form.sage superelliptic_drw_tests/
~/Research/2021 De Rham/DeRhamComputation$ git add sage/superelliptic_drw/superelliptic_witt.sage sage/superelliptic_drw/superelliptic_drw_cech.sage sage/superelliptic_drw/superelliptic_drw_form.sage sage/superelliptic_drw/de_rham_witt_lift.sage sage/superelliptic_drw/automorphism.sage
~/Research/2021 De Rham/DeRhamComputation$ git add -u
~/Research/2021 De Rham/DeRhamComputation$ git commit -m "superelliptic drw podzielone na wiecej plikow"
[master ce0ac0d] superelliptic drw podzielone na wiecej plikow
8 files changed, 442 insertions(+), 421 deletions(-)
create mode 100644 sage/superelliptic_drw/automorphism.sage
create mode 100644 sage/superelliptic_drw/de_rham_witt_lift.sage
delete mode 100644 sage/superelliptic_drw/superelliptic_drw.sage
create mode 100644 sage/superelliptic_drw/superelliptic_drw_cech.sage
create mode 100644 sage/superelliptic_drw/superelliptic_drw_form.sage
create mode 100644 sage/superelliptic_drw/superelliptic_witt.sage
~/Research/2021 De Rham/DeRhamComputation$ git push
Username for 'https://git.wmi.amu.edu.pl': jgarnek
Password for 'https://jgarnek@git.wmi.amu.edu.pl':
Enumerating objects: 31, done.
Counting objects: 100% (31/31), done.
Delta compression using up to 4 threads
Compressing objects: 100% (24/24), done.
Writing objects: 100% (24/24), 11.54 KiB | 168.00 KiB/s, done.
Total 24 (delta 17), reused 0 (delta 0)
remote: . Processing 1 references
remote: Processed 1 references in total
To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git
cc45757..ce0ac0d master -> master
~/Research/2021 De Rham/DeRhamComputation$ cd sage/
~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
[22;0t[6nsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
V(((-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV([((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y])
[6nsage: aux
V(((-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV([((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y])
[6nsage: aux.omega
'((-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx
[6nsagsage: decomposition_omega0_omega8(aux.omega)
(((-x^8 + x^6 - 1)/y) dx, ((-x^8 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx)
[6nsage: decomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1] == aux.omega
False
[6nsage: decomposition_omega0_omega8(aux.omega)[0] + decomposition_omega0_omega8(aux.omega)[1] == aux.omega
False
[6nsage: decomposition_omega0_omega8(aux.omega)[0] + decomposition_omega0_omega8(aux.omega)[1] - aux.omega
((x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx
[6nsage: decomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]- aux.omega
0 dx
[6nsage: decomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega
False
[6nsasage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
V(((-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV([((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y])
[6nsage: decomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega
False
[6nsage: (decomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]).reduce().form
(-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)
[6nsage: aux.omega.reduce().form
(-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)
[6nsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
V(((-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV([((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y])
[6nsage: decomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega
False
[6nsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
V(((-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV([((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y])
[6nsage: decomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega
False
[6nsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
V(((-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV([((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y])
[6nsage: decomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega
(-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y) (-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)
True
[6nsage: sage: decomposition_omega0_omega8(aux.omega)[1].expansion_at_infty()
2*t^4 + 2*t^8 + t^12 + O(t^14)
[6nsage: decomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega
(-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y) (-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)
True
[6nsage: decomposition_omega0_omega8(aux.omega)[0]
((-x^8 + x^6 - 1)/y) dx
[6nsage: aux
V((((2*x^18 + 2*x^16 + 2*x^14 + 2*x^10 + 2*x^8 + 2*x^4 + 2*x^2 + 2)/(x^13 + x^11 + x^9))*y) dx) + dV([((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y])
[6nsage: aux.h2
((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y
sage: decomposition_g0_g8(aux.h2)
((x^4 + x^2 + 1)*y, ((x^4 + x^2 + 1)/x^6)*y, 0)
sage: decomposition_g0_g8(aux.h2)[0] - decomposition_g0_g8(aux.h2)[1] == aux.h2
True
[6nsagsage: decomposition_g0_g8(aux.h2)[1].expansion_at_infty()
t + t^5 + 2*t^9 + t^13 + O(t^21)
[6nsage: aux.omega
(((2*x^18 + 2*x^16 + 2*x^14 + 2*x^10 + 2*x^8 + 2*x^4 + 2*x^2 + 2)/(x^13 + x^11 + x^9))*y) dx
sage: load('superelliptic_drw/tests/decomposition_into_g0_g8_tests.sage')
(-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y) (-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)
1
True
sage: load('superelliptic_drw/tests/decomposition_into_g0_g8_tests.sage')
(-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y) (-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)
1
True
[6nsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[6nsage: eta2
([(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^10 + x^8 - x^2 + 1)/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[6nsage: eta2.r()
((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
[6nsage: aux.r()
((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
[6nssage: eta2 - aux
(V(((-x^8 + x^6 - 1)/y) dx), [0], V(((-x^8 + x^6 - 1)/y) dx))
[6nsage: (eta2 - aux).omega0.frobenius()
0 dx
[6nsage: (x^8 - x^6).quo_rem(x^3 - x)
(x^5, 0)
[6nsage: (eta2 - aux).omega0.omega.cartier()
((-x^3)/y) dx
[6nsage: (-C.x^8 + C.x^6 - C.one)/C.y)*C.dx
Input In [39]
(-C.x**Integer(8) + C.x**Integer(6) - C.one)/C.y)*C.dx
^
SyntaxError: unmatched ')'
 
[6nsage: (-C.x^8 + C.x^6 - C.one)/C.y*C.dx
((-x^8 + x^6 - 1)/y) dx
[6nsage: ((-C.x^8 + C.x^6 - C.one)/C.y*C.dx).cartier()
((-x^3)/y) dx
[6nsage: ((C.x^6 - C.one)/C.y*C.dx).cartier()
0 dx
[6nsage: aux
([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[6nsage: aux.reduce()
([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[6nsage: eta2
([(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^10 + x^8 - x^2 + 1)/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[6nsage: eta2 - aux
(V(((-x^8 + x^6 - 1)/y) dx), [0], V(((-x^8 + x^6 - 1)/y) dx))
[6nsage: eta2.omega0.cartier()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [47], in <cell line: 1>()
----> 1 eta2.omega0.cartier()
 
AttributeError: 'superelliptic_drw_form' object has no attribute 'cartier'
[6nsage: eta2.omega0.omega.cartier()
((-x^3 + x)/y) dx
[6nsage: autom(eta2).coordinates()
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [49], in <cell line: 1>()
----> 1 autom(eta2).coordinates()
 
File <string>:63, in coordinates(self, basis)
 
File <string>:81, in coordinates(self)
 
File <string>:87, in coordinates(self)
 
File <string>:87, in coordinates(self)
 
[... skipping similar frames: coordinates at line 87 (1097 times)]
 
File <string>:87, in coordinates(self)
 
File <string>:86, in coordinates(self)
 
File <string>:5, in __init__(self, C, omega, fct)
 
File <string>:28, in __sub__(self, other)
 
File <string>:7, in __init__(self, C, g)
 
File <string>:245, in reduction_form(C, g)
 
File <string>:216, in reduction(C, g)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:711, in FractionField_generic._element_constructor_(self, x, y, coerce)
708 raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
709 x0, y0, self))
710 try:
--> 711 return self._element_class(self, x, y, coerce=coerce)
712 except TypeError:
713 if parent(x) is parent(x0):
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:115, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
113 if coerce:
114 self.__numerator = parent.ring()(numerator)
--> 115 self.__denominator = parent.ring()(denominator)
116 else:
117 self.__numerator = numerator
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:506, in FractionField_generic.ring(self)
503 s = 'FieldOfFractions(%s)' % self.ring()._magma_init_(magma)
504 return magma._with_names(s, self.variable_names())
--> 506 def ring(self):
507 """
508 Return the ring that this is the fraction field of.
509
(...)
516 Multivariate Polynomial Ring in x, y over Rational Field
517 """
518 return self._R
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: autom(eta2).coordinates()
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
File <string>:59, in __mul__(self, other)
 
File <string>:226, in reduction(C, g)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
1002 try:
-> 1003 return self(str(element))
1004 except TypeError:
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:991, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
990 element = element.replace("^","**")
--> 991 element = eval(element, d, {})
992 except (SyntaxError, NameError):
 
File <string>:1, in <module>
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
 
During handling of the above exception, another exception occurred:
 
AttributeError Traceback (most recent call last)
Input In [50], in <cell line: 1>()
----> 1 autom(eta2).coordinates()
 
File <string>:23, in autom(self)
 
File <string>:6, in __init__(self, omega0, f)
 
File <string>:90, in diffn(self, dy_w)
 
File <string>:99, in diffn(self, dy_w)
 
File <string>:84, in __add__(self, other)
 
File <string>:31, in __add__(self, other)
 
File <string>:63, in __mul__(self, other)
 
AttributeError: 'superelliptic_function' object has no attribute 'form'
[6nsage: autom(eta2)
^C---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:380, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
379 try:
--> 380 z = integer_ring.Z(value)
381 except (TypeError, ValueError):
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
286 cdef Map m
--> 287 cdef Element e = method(C)
288 if e is None:
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:832, in sage.rings.fraction_field_element.FractionFieldElement._conversion()
831 self.reduce()
--> 832 num = R(self.__numerator)
833 inv_den = R(self.__denominator).inverse_of_unit()
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
 
File /ext/sage/9.7/src/sage/categories/map.pyx:1692, in sage.categories.map.FormalCompositeMap._call_()
1691 for f in self.__list:
-> 1692 x = f._call_(x)
1693 return x
 
File /ext/sage/9.7/src/sage/categories/map.pyx:1677, in sage.categories.map.FormalCompositeMap._call_()
1676
-> 1677 cpdef Element _call_(self, x):
1678 """
 
File /ext/sage/9.7/src/sage/categories/map.pyx:1692, in sage.categories.map.FormalCompositeMap._call_()
1691 for f in self.__list:
-> 1692 x = f._call_(x)
1693 return x
 
File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1620, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
1619
-> 1620 cpdef Element _call_(self, _x):
1621 """
 
File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1652, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
1651 if nmod_poly_degree(x._denom) != 0:
-> 1652 raise ValueError("not integral")
1653 if nmod_poly_degree(x._numer) > 0:
 
ValueError: not integral
 
During handling of the above exception, another exception occurred:
 
KeyboardInterrupt Traceback (most recent call last)
Input In [51], in <cell line: 1>()
----> 1 autom(eta2)
 
File <string>:23, in autom(self)
 
File <string>:19, in autom(self)
 
File <string>:13, in autom(self)
 
File <string>:7, in __init__(self, C, g)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
636 ring_one = self.ring().one()
637 try:
--> 638 return self._element_class(self, x, ring_one, coerce=coerce)
639 except (TypeError, ValueError):
640 pass
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
112 FieldElement.__init__(self, parent)
113 if coerce:
--> 114 self.__numerator = parent.ring()(numerator)
115 self.__denominator = parent.ring()(denominator)
116 else:
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1009, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
1007 try:
1008 # now try calling the base ring's __call__ methods
-> 1009 element = self.base_ring()(element)
1010 _p = p_NSet(sa2si(element,_ring), _ring)
1011 return new_MP(self,_p)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x)
1143 """
1144 TESTS::
1145
(...)
1182 True
1183 """
1184 try:
-> 1185 return integer_mod.IntegerMod(self, x)
1186 except (NotImplementedError, PariError):
1187 raise TypeError("error coercing to finite field")
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod()
199 return a
200 t = modulus.element_class()
--> 201 return t(parent, value)
202
203
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:388, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
386 value = py_scalar_to_element(value)
387 if isinstance(value, Element) and value.parent().is_exact():
--> 388 value = sage.rings.rational_field.QQ(value)
389 z = value % self.__modulus.sageInteger
390 else:
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__()
536 """
537 if x is not None:
--> 538 self.__set_value(x, base)
539
540 def __reduce__(self):
 
File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value()
624
625 elif hasattr(x, "_rational_"):
--> 626 set_from_Rational(self, x._rational_())
627
628 elif isinstance(x, tuple) and len(x) == 2:
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:784, in sage.rings.fraction_field_element.FractionFieldElement._rational_()
782 1/2
783 """
--> 784 return self._conversion(QQ)
785
786 def _conversion(self, R):
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:832, in sage.rings.fraction_field_element.FractionFieldElement._conversion()
830 else:
831 self.reduce()
--> 832 num = R(self.__numerator)
833 inv_den = R(self.__denominator).inverse_of_unit()
834 return num * inv_den
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__()
536 """
537 if x is not None:
--> 538 self.__set_value(x, base)
539
540 def __reduce__(self):
 
File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value()
624
625 elif hasattr(x, "_rational_"):
--> 626 set_from_Rational(self, x._rational_())
627
628 elif isinstance(x, tuple) and len(x) == 2:
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:1446, in sage.rings.polynomial.polynomial_element.Polynomial._rational_()
1444 TypeError: not a constant polynomial
1445 """
-> 1446 return self._scalar_conversion(sage.rings.rational.Rational)
1447
1448 def _symbolic_(self, R):
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:1391, in sage.rings.polynomial.polynomial_element.Polynomial._scalar_conversion()
1389 if self.degree() > 0:
1390 raise TypeError("cannot convert nonconstant polynomial")
-> 1391 return R(self.get_coeff_c(0))
1392
1393 _real_double_ = _scalar_conversion
 
File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__()
536 """
537 if x is not None:
--> 538 self.__set_value(x, base)
539
540 def __reduce__(self):
 
File /ext/sage/9.7/src/sage/rings/rational.pyx:691, in sage.rings.rational.Rational.__set_value()
689
690 else:
--> 691 raise TypeError("unable to convert {!r} to a rational".format(x))
692
693 cdef void set_from_mpq(Rational self, mpq_t value):
 
File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
192 except AttributeError:
193 return super().__repr__()
--> 194 result = reprfunc()
195 if isinstance(result, str):
196 return result
 
File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:340, in sage.rings.fraction_field_FpT.FpTElement._repr_()
338 return repr(self.numer())
339 else:
--> 340 numer_s = repr(self.numer())
341 denom_s = repr(self.denom())
342 if '-' in numer_s or '+' in numer_s:
 
File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
192 except AttributeError:
193 return super().__repr__()
--> 194 result = reprfunc()
195 if isinstance(result, str):
196 return result
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_()
2688 NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3
2689 """
-> 2690 return self._repr()
2691
2692 def _latex_(self, name=None):
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2656, in sage.rings.polynomial.polynomial_element.Polynomial._repr()
2654 if n != m-1:
2655 s += " + "
-> 2656 x = y = repr(x)
2657 if y.find("-") == 0:
2658 y = y[1:]
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: eta2
([(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^10 + x^8 - x^2 + 1)/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
sage: load('superelliptic_drw/automorphism.sage')
sage: autom(eta2)
([(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^10 + x^8 - x^2 + 1)/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])) drw cech
[(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]) drw form
((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx form
(1/(x^2 + 2))*y function
(1/(x^2 + 2))*y function
[2/x*y] witt
2/x*y function
0 function
([(1/(x^2 + 2*x))*y] d[x] + V(((-x^10 - x^7 - x^4 - x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(x/(x^2 + x + 1))*y]), [(2/(x + 1))*y], [(2/(x^4 + x^3 + 2*x^2 + 2*x))*y] d[x] + V(((-x^14 - x^13 + x^11 + x^10 - x^7 + x^6 + x^4 + x^2 - x)/(x^6*y - x^5*y - x^4*y - x^3*y - x^2*y - x*y + y)) dx) + dV([((2*x^4 + 2*x^3 + 2*x^2 + x)/(x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 1))*y]))
[6nsage: autom(eta2).coordinates()
([(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^10 + x^8 - x^2 + 1)/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])) drw cech
[(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]) drw form
((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx form
(1/(x^2 + 2))*y function
(1/(x^2 + 2))*y function
[2/x*y] witt
2/x*y function
0 function
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [55], in <cell line: 1>()
----> 1 autom(eta2).coordinates()
 
File <string>:63, in coordinates(self, basis)
 
File <string>:81, in coordinates(self)
 
File <string>:87, in coordinates(self)
 
File <string>:87, in coordinates(self)
 
[... skipping similar frames: coordinates at line 87 (64 times)]
 
File <string>:87, in coordinates(self)
 
File <string>:52, in coordinates(self)
 
File <string>:102, in degrees_de_rham0(self)
 
File <string>:80, in basis_de_rham_degrees(self)
 
File <string>:5, in __init__(self, C, omega, fct)
 
File <string>:95, in diffn(self)
 
File <string>:7, in __init__(self, C, g)
 
File <string>:245, in reduction_form(C, g)
 
File <string>:222, in reduction(C, g)
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:632, in PolynomialRing(base_ring, *args, **kwds)
629 except KeyError:
630 raise TypeError("you must specify the names of the variables")
--> 632 names = normalize_names(n, names)
634 # At this point, we have only handled the "names" keyword if it was
635 # needed. Since we know the variable names, it would logically be
636 # an error to specify an additional "names" keyword. However,
(...)
639 # and we allow this for historical reasons. However, the names
640 # must be consistent!
641 if "names" in kwds:
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: a = autom(eta1)
([(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^3 + x)/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^3 + x)/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y])) drw cech
[(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^3 + x)/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y]) drw form
((-x^5 + x^3 + x)/(x^2*y - y)) dx form
(x/(x^2 + 2))*y function
(1/(x^3 + 2*x))*y function
V(1/x*y) witt
0 function
1/x*y function
[6nsage: a.coordinates()
(1, 0)
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
aux before reduce (V(((-x^5 - x^4 - x^3 - x^2 - x + 1)/(x^2*y + x*y + y)) dx) + dV([(2/(x^2 + x + 1))*y]), V((2/(x^2 + x))*y), V(((-x^5 - x^4 - x^3 - x^2 - x + 1)/(x^2*y + x*y + y)) dx) + dV([(1/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
aux V(smth) (V(((-x^5 - x^4 - x^3 - x^2 - x + 1)/(x^2*y + x*y + y)) dx) + dV([(2/(x^2 + x + 1))*y]), V((2/(x^2 + x))*y), V(((-x^5 - x^4 - x^3 - x^2 - x + 1)/(x^2*y + x*y + y)) dx) + dV([(1/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [57], in <cell line: 1>()
----> 1 a.coordinates()
 
File <string>:75, in coordinates(self, basis)
 
File <string>:168, in pth_root(self)
 
ValueError: Function is not a p-th power.
~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
[22;0t[6nsage: load('superelliptic_drw/automorphism.sage')
[6nsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[6nsage: quit()
~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
[22;0t[6nsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[6nsage: eta2 - aux
(V(((-x^8 + x^6 - 1)/y) dx), [0], V(((-x^8 + x^6 - 1)/y) dx))
[6nsage: (eta2 - aux).omega0.omega.cartier()
((-x^3)/y) dx
[6nsage: eta1.r()
((1/y) dx, 0, (1/y) dx)
[6nsage: eta2.r()
((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
[6nsage: C.de_rham_basis()[1]
((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
[6nsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [7], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:31, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:22, in <module>
 
File <string>:29, in de_rham_witt_lift(cech_class, prec)
 
File <string>:74, in __sub__(self, other)
 
File <string>:81, in __add__(self, other)
 
AttributeError: 'superelliptic_form' object has no attribute 'h1'
[6nsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]) V(((x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx)
([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[6nsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])
 
V(((x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx)
([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[6nsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])
 
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
 

([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[6nsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])
 
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
 

dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
[6nsage: aux
dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
[6nsage: aux.frobenius(*)
Input In [13]
aux.frobenius(*)
^
SyntaxError: invalid syntax
 
[6nsage: aux.frobenius()
((-x^6 + x^4 + x^2 - 1)/(x^6*y)) dx
[6nsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])
 
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
 
0
 

dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
[6nsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y
[6nsage: aux
((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y
[6nsage: aux.coordinates()
[0]
[6nsage: decomposition_g0_g8(aux)
((x^4 + x^2 + 1)*y, ((x^4 + x^2 + 1)/x^6)*y, 0)
[6nsage: decomposition_g0_g8(aux)[1].expansion_at_infty()
t + t^5 + 2*t^9 + t^13 + O(t^21)
[6nsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])
 
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
 
0
 

dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
[6nsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])
 
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
 
0
 

[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[6nsage: aux
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[6nsage: eta2.omega8 - aux
V(((-x^8 + x^6 - 1)/y) dx) + dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
[6nsage: (eta2.omega8 - aux).frobenius()
((-x^6 + x^4 + x^2 - 1)/(x^6*y)) dx
[6nsage: (eta2.omega8 - aux).frobenius().expansion_at_infty()
2 + 2*t^4 + t^8 + O(t^10)
[6nsage: aux.frobenius()
((-x^2 + 1)/(x^6*y)) dx
[6nsage: aux.frobenius().expansion_at_infty()
2*t^8 + 2*t^16 + O(t^18)
[6nsage: aux
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[6nsage: aux.r()
((-1)/(x*y)) dx
[6nsasage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])
 
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
 
0
 

[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[6nsage: compare
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [32], in <cell line: 1>()
----> 1 compare
 
NameError: name 'compare' is not defined
[6nsage: eta2
([(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^10 + x^8 - x^2 + 1)/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[6nsage: eta.omega8
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [34], in <cell line: 1>()
----> 1 eta.omega8
 
AttributeError: 'function' object has no attribute 'omega8'
[6nsage: eta2.omega8
[(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^10 + x^8 - x^2 + 1)/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])
[6nsage: eta2.omega8.frobenius()
((-x^2 + 1)/(x^2*y)) dx
[6nsage: eta2.omega8.frobenius().expansion_at_infty()
2 + 2*t^4 + O(t^10)
[6nsage: lift2.omega8.frobenius().expansion_at_infty()
2 + 2*t^4 + O(t^10)
[6nsage: sage: eta2.r()
((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
[6nsage: eta2
([(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^10 + x^8 - x^2 + 1)/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[6nsage: (lift2 - eta2)
(V(((x^8 - x^6 + 1)/y) dx), [0], V(((x^8 - x^6 + 1)/y) dx))
[6nsage: (lift2 - eta2).omega8.frobenius()
0 dx
[6nsage: sage: (lift2 - eta2).omega
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [43], in <cell line: 1>()
----> 1 (lift2 - eta2).omega
 
AttributeError: 'superelliptic_drw_cech' object has no attribute 'omega'
[6nsage: (lift2 - eta2).omega0.omega
((x^8 - x^6 + 1)/y) dx
~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
[22;0t[6nsage: load('init.sage')
fomega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])
 
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
 
0
 

[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[6nsage:sage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])
 
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
 
0
 

[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[6nsage: C.x.teichmuller()*C.y.teichmuller().diffn()
[(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y])
[6nsage: C.de_rham_basis()[1]
((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
[6nsage: second_patch(C.de_rham_basis()[1].omega8)
(x/y) dx
[6nsage: second_patch(C.y)
1/x^2*y
[6nsasage: patch(C)
Superelliptic curve with the equation y^2 = 2*x^3 + x over Finite Field of size 3
[6nsage: -(C.x^3).teichmuller()*C.y.teichmuller.diffn()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [8], in <cell line: 1>()
----> 1 -(C.x**Integer(3)).teichmuller()*C.y.teichmuller.diffn()
 
AttributeError: 'function' object has no attribute 'diffn'
[6nsage: -(C.x^3).teichmuller()*C.y.teichmuller().diffn()
[(2*x^2/(x^2 + 2))*y] d[x] + V(((x^16 - x^12 - x^10)/(x^2*y - y)) dx) + dV([(2*x^12/(x^2 + 2))*y])
[6nsage: -(C.x^3).teichmuller()*C.y.teichmuller().diffn() + 2*C.y.teichmuller()*(C.x^(-4)).teichmuller()*C.x.teichmuller().diffn()
[((2*x^6 + 2*x^2 + 1)/(x^6 + 2*x^4))*y] d[x] + V(((x^24 - x^20 - x^18 + x^14 - x^12 + x^10 + x^8 - x^6 - 1)/(x^10*y - x^8*y)) dx) + dV([(2*x^12/(x^2 + 2))*y])
[6nsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[6nsage: lift == omega8_lift
False
[6nsage: lift - omega8_lift
[((x^4 + x^2 + 1)/x^4)*y] d[x] + V(((-x^22 - x^20 + x^16 + x^14 + x^12 - x^10 - x^8 - x^6 - x^4 - x^2 + 1)/(x^8*y)) dx) + dV([((x^16 + x^14 + x^12 + x^10 + x^8 + x^6 + x^4 + x^2 + 1)/x^6)*y])
[6nsage: lift.r()
((-1)/(x*y)) dx
[6nsage: omega8_lift.r()
((-x^6 - x^2 + 1)/(x^3*y)) dx
[6nsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
omega8_lift.r() ((-1)/(x*y)) dx
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[6nsage: lift.r()
((-1)/(x*y)) dx
[6nsage: omega8_lift.r()
((-x^6 - x^2 + 1)/(x^3*y)) dx
[6nsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
omega8_lift.r() ((-1)/(x*y)) dx
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[6nsage: omega8_lift0.r()
((-1)/(x*y)) dx
[6nsage: omega8_lift0 - omega8_lift
[((x^4 + x^2 + 1)/x^4)*y] d[x] + V(((-x^22 - x^20 + x^16 + x^14 + x^12 - x^10 - x^8 - x^6 - x^4 - x^2 + 1)/(x^8*y)) dx) + dV([((x^16 + x^14 + x^12 + x^10 + x^8 + x^6 + x^4 + x^2 + 1)/x^6)*y])
[6nsage: -(C.x^3)*C.y.diffn() + 2*C.y*(C.x^(-4))*C.x.diffn()
((-x^6 - x^2 + 1)/(x^3*y)) dx
[6nsage: -(C.x^(-3))*C.y.diffn() + 2*C.y*(C.x^(-4))*C.x.diffn()
((-1)/(x*y)) dx
[6nsage: sage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
omega8_lift.r() ((-1)/(x*y)) dx
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[6nsage: omega8_lift0 - omega8_lift
0
[6nsage: C.y.teichmuller().diffn()
[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[6nsage: C.y.teichmuller().diffn().r()
(1/y) dx
[6nsage: C.y.teichmuller().diffn().frobenius()
((x^3 - x)/y) dx
[6nsage: 2*C.y.teichmuller() * C.y.teichmuller().diffn() == (C.x^3 - C.x).teichmuller().diffn()
True
[6nsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
True
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])
 
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
 
0
 

[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[6nsagsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[6nssage: omega8_lift0
[2/x*y]
[6nsage: omega8_lift0.diffn()
[((x^2 + 1)/(x^4 + 2*x^2))*y] d[x] + V(((x^6 + 1)/(x^4*y - x^2*y)) dx) + dV([(2/(x^2 + 2))*y])
[6nsage: 2*sage: 2*((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() - 2*C.y.teichmuller()*(C.x.teichmuller())^(-2) * C.x.teichmuller().diffn()
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [34], in <cell line: 1>()
----> 1 Integer(2)*((C.x)**(-Integer(1))).teichmuller()*C.y.teichmuller().diffn() - Integer(2)*C.y.teichmuller()*(C.x.teichmuller())**(-Integer(2)) * C.x.teichmuller().diffn()
 
File /ext/sage/9.7/src/sage/rings/integer.pyx:2195, in sage.rings.integer.Integer.__pow__()
2193 return coercion_model.bin_op(left, right, operator.pow)
2194 # left is a non-Element: do the powering with a Python int
-> 2195 return left ** int(right)
2196
2197 cpdef _pow_(self, other):
 
TypeError: unsupported operand type(s) for ** or pow(): 'superelliptic_witt' and 'int'
[6nsage: 2*((sage: 2*((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() - 2*C.y.teichmuller()*((C.x^(-1)).teichmuller()) * C.x.teichmuller().diffn()
[((x^3 + 2*x + 2)/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 - x^4 - x^3 - x^2 - x - 1)/(x*y)) dx) + dV([(2/(x^2 + 2))*y])
[6nsage: 2*((C.x)^(-1)).teichmuller()sage: 2*((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() - 2*C.y.teichmuller()*((C.x^(-1)).teichmuller()) * C.x.teichmuller().diffn() == omega8_lift0.diffn()
False
[6nsage: (2*((C.x(^(-()).tesage: (2*((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() - 2*C.y.teichmuller()*((C.x^(-1)).teichmuller()) * C.x.teichmuller().diffn()).r()
((x^3 - x - 1)/(x*y)) dx
[6nsage: (2*(sage: omega8_lift0.diffn().r()
((x^2 + 1)/(x*y)) dx
[6nsage: omega8_lift0
[2/x*y]
[6nsage: (2*((C((((((((((C.x)sage: (((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*((C.x^(-1)).teichmuller()) * C.x.teichmuller().diffn()).r()
((x^3 - x + 1)/(x*y)) dx
[6nsage: sage: omega8_lift0.diffn().r() == (-C.y/C.x).diffn()
True
[6nsage: (((C.x)^(-1)).teichmuller()*sage: (((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*((C.x^(-1)).teichmuller()) * C.x.teichmuller().diffn()).r() == (-C.y/C.x).diffn()
False
[6nsagesage: (((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*((C.x^(-2)).teichmuller()) * C.x.teichmuller().diffn()).r() == (-C.y/C.x).diffn()
False
sage: -(((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*((C.x^(-2)).teichmuller()) * C.x.teichmuller().diffn()).r() == (-C.y/C.x).diffn()
False
sage: -(((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*((C.x^(-2)).teichmuller()) * C.x.teichmuller().diffn()).r()
((-x)/y) dx
[6nsage: (-C.y/C.x).diffn()
((x^2 + 1)/(x*y)) dx
[6nsage: (-C.y/C.x).diffn() == -(C.x)^(-1)*C.y.diffn() + C.y*(C.x)^(-2)*C.dx
True
[6nsage: a = -((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*((C.x)^(-2).teichmuller())*C.x.teichmuller().diffn()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [48], in <cell line: 1>()
----> 1 a = -((C.x)**(-Integer(1))).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*((C.x)**(-Integer(2)).teichmuller())*C.x.teichmuller().diffn()
 
File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
493 """
--> 494 return self.getattr_from_category(name)
495
496 cdef getattr_from_category(self, name):
 
File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
505 else:
506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
508
509 def __dir__(self):
 
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
359 dummy_error_message.cls = type(self)
360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
362 attribute = <object>attr
363 # Check for a descriptor (__get__ in Python)
 
AttributeError: 'sage.rings.integer.Integer' object has no attribute 'teichmuller'
[6nsage: a = -((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*(((C.x)^(-2)).teichmuller())*C.x.teichmuller().diffn()
[6nsagesage: a.r() == -(C.x)^(-1)*C.y.diffn() + C.y*(C.x)^(-2)*C.dx
True
[6nsag(: C.x)^(-1)x.teichmuleer()*(((C.xsage: omega8_lift0 - a
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [51], in <cell line: 1>()
----> 1 omega8_lift0 - a
 
File <string>:35, in __sub__(self, other)
 
File <string>:29, in __add__(self, other)
 
AttributeError: 'superelliptic_drw_form' object has no attribute 't'
[6nsage: sage: omega8_lift0
[2/x*y]
[6nsage: omega8_lift0.diffn() - a
0
[6nsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])
 
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
 
0
 

[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[6nsage: compare
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[6nsage: compare.r()
((-1)/(x*y)) dx
[6nsage: compare.frobenius()
((-x^2 + 1)/(x^6*y)) dx
[6nsage: compare.frobenius().expansion_at_infty()
2*t^8 + 2*t^16 + O(t^18)
[6nsage: omega0_lift0
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [59], in <cell line: 1>()
----> 1 omega0_lift0
 
NameError: name 'omega0_lift0' is not defined
[6nsage: omega8_lift0
([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[6nsage: omega8_lift0 - compare
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [61], in <cell line: 1>()
----> 1 omega8_lift0 - compare
 
File <string>:39, in __sub__(self, other)
 
AttributeError: 'superelliptic_drw_form' object has no attribute 'omega0'
[6nsage: omega8_lift0.omega8 - compare
dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
[6nsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [63], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:31, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:22, in <module>
 
File <string>:30, in de_rham_witt_lift(cech_class, prec)
 
File <string>:74, in __sub__(self, other)
 
File <string>:81, in __add__(self, other)
 
AttributeError: 'superelliptic_form' object has no attribute 'h1'
[6nsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
test: False
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])
 
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
 
0
 

[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[6nsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
test: False
test 2: dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[6nsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
test0: True
test: False
test 2: dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[6nsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
test: True
test 2: dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[6nsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
test: True
test 1: True
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[6nsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
test: True
test 1: True
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [69], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:31, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:22, in <module>
 
File <string>:33, in de_rham_witt_lift(cech_class, prec)
 
File <string>:29, in __add__(self, other)
 
AttributeError: 'superelliptic_drw_form' object has no attribute 't'
[6nsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
test: True
test 1: True
test 2: False
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[6nsage: load('init.sage')
 
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
test: True
test 1: True
test 2: True
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[6nsage:
[6nsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
test: True
test 1: True
test 2: True
test 3: False False True
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
[6nsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [73], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:31, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:22, in <module>
 
File <string>:28, in de_rham_witt_lift(cech_class, prec)
 
File <string>:29, in __add__(self, other)
 
AttributeError: 'superelliptic_drw_form' object has no attribute 't'
[6nsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
test: True
test 1: True
test 2: True
test 3: True True True
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
[22;0t[6nsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
test: True
test 1: True
test 2: True
test 3: True True True
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [1], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:31, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:24, in <module>
 
NameError: name 'aux' is not defined
[6n[6n[6nsasage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[6nsage: b = autom(eta2lift) - eta2lift
([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])) drw cech
[(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]) drw form
((x^4 + x^2 - 1)/(x^2*y - y)) dx form
(1/(x^2 + 2))*y function
(1/(x^2 + 2))*y function
[2/x*y] witt
2/x*y function
0 function
[6nsage: b
([(1/(x^3 + 2*x))*y] d[x] + V(((-x^4)/(x^3*y - x^2*y - x*y + y)) dx) + dV([((x^2 + 1)/(x^3 + 2*x^2 + 2*x + 1))*y]), [(1/(x^2 + x))*y] + V(((x + 2)/(x^2 + x))*y), [(1/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 - x^7 + x^2 - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((x^3 + 2*x^2 + 2*x + 2)/(x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 1))*y]))
[6nsage: b.r()
((1/y) dx, (1/(x^2 + x))*y, (1/(x^2*y + x*y)) dx)
[6nsagesage: b - eta1
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [6], in <cell line: 1>()
----> 1 b - eta1
 
NameError: name 'eta1' is not defined
sage: eta1 = de_rham_witt_lift(C.de_rham_basis[0])
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [7], in <cell line: 1>()
----> 1 eta1 = de_rham_witt_lift(C.de_rham_basis[Integer(0)])
 
TypeError: 'method' object is not subscriptable
[6nsage: eta1 = de_rham_witt_lift(C.de_rham_basis()[0])
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
[6nssage: b = autom(eta2lift) - eta2lift - eta1
([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])) drw cech
[(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]) drw form
((x^4 + x^2 - 1)/(x^2*y - y)) dx form
(1/(x^2 + 2))*y function
(1/(x^2 + 2))*y function
[2/x*y] witt
2/x*y function
0 function
[6nsage: b.omega0.frobenius()
(1/y) dx
[6nsage: b.omega8.frobenius()
((-x^3 + x^2 - 1)/(x^4*y - x^3*y + x^2*y)) dx
[6nsage: b.omega8.frobenius().expansion_at_infty()
2*t^2 + t^10 + O(t^12)
[6nsage: load('init.sage')
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[6nsage: autom(eta2lift).coordinates()
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [14], in <cell line: 1>()
----> 1 autom(eta2lift).coordinates()
 
File <string>:63, in coordinates(self, basis)
 
File <string>:81, in coordinates(self)
 
File <string>:87, in coordinates(self)
 
File <string>:87, in coordinates(self)
 
[... skipping similar frames: coordinates at line 87 (686 times)]
 
File <string>:87, in coordinates(self)
 
File <string>:52, in coordinates(self)
 
File <string>:102, in degrees_de_rham0(self)
 
File <string>:76, in basis_de_rham_degrees(self)
 
File <string>:60, in holomorphic_differentials_basis(self)
 
File <string>:52, in basis_holomorphic_differentials_degree(self)
 
File <string>:7, in __init__(self, C, g)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce)
704 x0, y0 = x, y
705 try:
--> 706 x, y = resolve_fractions(x0, y0)
707 except (AttributeError, TypeError):
708 raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
709 x0, y0, self))
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:688, in FractionField_generic._element_constructor_.<locals>.resolve_fractions(x, y)
686 yd = y.denominator()
687 try:
--> 688 return (xn * yd, yn * xd)
689 except (AttributeError, TypeError, ValueError):
690 pass
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
1514 return (<Element>left)._mul_(right)
1515 if BOTH_ARE_ELEMENT(cl):
-> 1516 return coercion_model.bin_op(left, right, mul)
1517
1518 cdef long value
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1200, in sage.structure.coerce.CoercionModel.bin_op()
1198 # Now coerce to a common parent and do the operation there
1199 try:
-> 1200 xy = self.canonical_coercion(x, y)
1201 except TypeError:
1202 self._record_exception()
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1315, in sage.structure.coerce.CoercionModel.canonical_coercion()
1313 x_elt = x
1314 if y_map is not None:
-> 1315 y_elt = (<Map>y_map)._call_(y)
1316 else:
1317 y_elt = y
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
285 raise TypeError("Cannot coerce {} to {}".format(x, C))
286 cdef Map m
--> 287 cdef Element e = method(C)
288 if e is None:
289 raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x)))
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:198, in sage.rings.polynomial.multi_polynomial.MPolynomial._polynomial_()
196 var = R.variable_name()
197 if var in self._parent.variable_names():
--> 198 return R(self.polynomial(self._parent(var)))
199 else:
200 return R([self])
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:426, in sage.rings.polynomial.multi_polynomial.MPolynomial.polynomial()
424 v.append(B(w))
425 z *= var
--> 426 return ring(v)
427
428 cpdef dict _mpoly_dict_recursive(self, tuple vars=None, base_ring=None):
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:416, in PolynomialRing_general._element_constructor_(self, x, check, is_gen, construct, **kwds)
414 C = self.element_class
415 if isinstance(x, (list, tuple)):
--> 416 return C(self, x, check=check, is_gen=False, construct=construct)
417 if isinstance(x, range):
418 return C(self, list(x), check=check, is_gen=False,
419 construct=construct)
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: autom(eta2lift)
([(1/(x^2 + 2*x))*y] d[x] + V(((x^4 - x^3 - x^2 + x + 1)/(x^2*y + x*y + y)) dx) + dV([(x/(x^2 + x + 1))*y]), [(2/(x + 1))*y], [(2/(x^4 + x^3 + 2*x^2 + 2*x))*y] d[x] + V(((-x^7 - x^6 + x^4 - x^3 - x^2 + 1)/(x^6*y - x^5*y - x^4*y - x^3*y - x^2*y - x*y + y)) dx) + dV([((2*x^4 + 2*x^3 + 2*x^2 + x)/(x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 1))*y]))
[6nsage: b = autom(eta2lift) - eta2lift - eta1
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [16], in <cell line: 1>()
----> 1 b = autom(eta2lift) - eta2lift - eta1
 
File <string>:23, in autom(self)
 
File <string>:20, in autom(self)
 
File <string>:99, in diffn(self, dy_w)
 
File <string>:99, in diffn(self, dy_w)
 
File <string>:73, in diffn(self, dy_w)
 
File <string>:177, in dy_w(C)
 
File /ext/sage/9.7/src/sage/rings/rational.pyx:2414, in sage.rings.rational.Rational.__mul__()
2412 return x
2413
-> 2414 return coercion_model.bin_op(left, right, operator.mul)
2415
2416 cpdef _mul_(self, right):
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:48, in __rmul__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
1526 if not err:
1527 return (<Element>right)._mul_long(value)
-> 1528 return coercion_model.bin_op(left, right, mul)
1529 except TypeError:
1530 return NotImplemented
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:43, in __rmul__(self, other)
 
File <string>:31, in __add__(self, other)
 
File /ext/sage/9.7/src/sage/rings/rational.pyx:2414, in sage.rings.rational.Rational.__mul__()
2412 return x
2413
-> 2414 return coercion_model.bin_op(left, right, operator.mul)
2415
2416 cpdef _mul_(self, right):
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:70, in __rmul__(self, constant)
 
File <string>:14, in __init__(self, C, g)
 
File <string>:223, in reduction(C, g)
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: b = autom(eta2lift)
[6nsage: b.coordinates()
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [18], in <cell line: 1>()
----> 1 b.coordinates()
 
File <string>:63, in coordinates(self, basis)
 
File <string>:81, in coordinates(self)
 
File <string>:87, in coordinates(self)
 
File <string>:87, in coordinates(self)
 
[... skipping similar frames: coordinates at line 87 (328 times)]
 
File <string>:87, in coordinates(self)
 
File <string>:86, in coordinates(self)
 
File <string>:52, in __sub__(self, other)
 
File <string>:14, in __init__(self, C, g)
 
File <string>:216, in reduction(C, g)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce)
704 x0, y0 = x, y
705 try:
--> 706 x, y = resolve_fractions(x0, y0)
707 except (AttributeError, TypeError):
708 raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
709 x0, y0, self))
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: b.r()
(((x + 1)/y) dx, (2/(x + 1))*y, ((-1)/(x*y + y)) dx)
[6nsage: b.r().coordinates()
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [20], in <cell line: 1>()
----> 1 b.r().coordinates()
 
File <string>:81, in coordinates(self)
 
File <string>:87, in coordinates(self)
 
File <string>:87, in coordinates(self)
 
[... skipping similar frames: coordinates at line 87 (295 times)]
 
File <string>:87, in coordinates(self)
 
File <string>:56, in coordinates(self)
 
File <string>:98, in de_rham_basis(self)
 
File <string>:76, in basis_de_rham_degrees(self)
 
File <string>:60, in holomorphic_differentials_basis(self)
 
File <string>:52, in basis_holomorphic_differentials_degree(self)
 
File <string>:7, in __init__(self, C, g)
 
File <string>:256, in reduction_form(C, g)
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: load('init.sage')
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [21], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:31, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:26, in <module>
 
TypeError: 'method' object is not subscriptable
[6nsage: load('init.sage')
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [22], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:31, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:26, in <module>
 
AttributeError: 'NoneType' object has no attribute 'coordinates'
[6nsage: C.de_rham_basis()[1]
((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
[6nsage: autom(C.de_rham_basis()[1])
[6nsage: load('init.sage')
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [25], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:31, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:26, in <module>
 
File <string>:16, in autom(self)
 
TypeError: superelliptic_cech.__init__() missing 1 required positional argument: 'fct'
[6nsage: load('init.sage')
self (((x + 1)/y) dx, (2/(x + 1))*y, ((-1)/(x*y + y)) dx)
self ((1/y) dx, (1/(x^2 + x))*y, (1/(x^2*y + x*y)) dx)
self ((1/y) dx, (2/(x^3 + x^2))*y, ((x^2 + x + 1)/(x^2*y + x*y)) dx)
self ((1/y) dx, (1/(x^4 + x^3))*y, ((x^4 + x^3 + x^2 - x - 1)/(x^4*y + x^3*y)) dx)
self ((1/y) dx, (2/(x^5 + x^4))*y, ((x^5 + x^4 + x^2 + x - 1)/(x^5*y + x^4*y)) dx)
self ((1/y) dx, (1/(x^6 + x^5))*y, ((x^5 + x^4 - 1)/(x^5*y + x^4*y)) dx)
self ((1/y) dx, (2/(x^7 + x^6))*y, ((x^7 + x^6 - x^2 + x + 1)/(x^7*y + x^6*y)) dx)
self ((1/y) dx, (1/(x^8 + x^7))*y, ((x^8 + x^7 - x^2 - x + 1)/(x^8*y + x^7*y)) dx)
self ((1/y) dx, (2/(x^9 + x^8))*y, ((x^8 + x^7 + 1)/(x^8*y + x^7*y)) dx)
self ((1/y) dx, (1/(x^10 + x^9))*y, ((x^10 + x^9 + x^2 - x - 1)/(x^10*y + x^9*y)) dx)
self ((1/y) dx, (2/(x^11 + x^10))*y, ((x^11 + x^10 + x^2 + x - 1)/(x^11*y + x^10*y)) dx)
self ((1/y) dx, (1/(x^12 + x^11))*y, ((x^11 + x^10 - 1)/(x^11*y + x^10*y)) dx)
self ((1/y) dx, (2/(x^13 + x^12))*y, ((x^13 + x^12 - x^2 + x + 1)/(x^13*y + x^12*y)) dx)
self ((1/y) dx, (1/(x^14 + x^13))*y, ((x^14 + x^13 - x^2 - x + 1)/(x^14*y + x^13*y)) dx)
self ((1/y) dx, (2/(x^15 + x^14))*y, ((x^14 + x^13 + 1)/(x^14*y + x^13*y)) dx)
self ((1/y) dx, (1/(x^16 + x^15))*y, ((x^16 + x^15 + x^2 - x - 1)/(x^16*y + x^15*y)) dx)
self ((1/y) dx, (2/(x^17 + x^16))*y, ((x^17 + x^16 + x^2 + x - 1)/(x^17*y + x^16*y)) dx)
self ((1/y) dx, (1/(x^18 + x^17))*y, ((x^17 + x^16 - 1)/(x^17*y + x^16*y)) dx)
self ((1/y) dx, (2/(x^19 + x^18))*y, ((x^19 + x^18 - x^2 + x + 1)/(x^19*y + x^18*y)) dx)
self ((1/y) dx, (1/(x^20 + x^19))*y, ((x^20 + x^19 - x^2 - x + 1)/(x^20*y + x^19*y)) dx)
self ((1/y) dx, (2/(x^21 + x^20))*y, ((x^20 + x^19 + 1)/(x^20*y + x^19*y)) dx)
self ((1/y) dx, (1/(x^22 + x^21))*y, ((x^22 + x^21 + x^2 - x - 1)/(x^22*y + x^21*y)) dx)
self ((1/y) dx, (2/(x^23 + x^22))*y, ((x^23 + x^22 + x^2 + x - 1)/(x^23*y + x^22*y)) dx)
self ((1/y) dx, (1/(x^24 + x^23))*y, ((x^23 + x^22 - 1)/(x^23*y + x^22*y)) dx)
self ((1/y) dx, (2/(x^25 + x^24))*y, ((x^25 + x^24 - x^2 + x + 1)/(x^25*y + x^24*y)) dx)
self ((1/y) dx, (1/(x^26 + x^25))*y, ((x^26 + x^25 - x^2 - x + 1)/(x^26*y + x^25*y)) dx)
self ((1/y) dx, (2/(x^27 + x^26))*y, ((x^26 + x^25 + 1)/(x^26*y + x^25*y)) dx)
self ((1/y) dx, (1/(x^28 + x^27))*y, ((x^28 + x^27 + x^2 - x - 1)/(x^28*y + x^27*y)) dx)
self ((1/y) dx, (2/(x^29 + x^28))*y, ((x^29 + x^28 + x^2 + x - 1)/(x^29*y + x^28*y)) dx)
self ((1/y) dx, (1/(x^30 + x^29))*y, ((x^29 + x^28 - 1)/(x^29*y + x^28*y)) dx)
self ((1/y) dx, (2/(x^31 + x^30))*y, ((x^31 + x^30 - x^2 + x + 1)/(x^31*y + x^30*y)) dx)
self ((1/y) dx, (1/(x^32 + x^31))*y, ((x^32 + x^31 - x^2 - x + 1)/(x^32*y + x^31*y)) dx)
self ((1/y) dx, (2/(x^33 + x^32))*y, ((x^32 + x^31 + 1)/(x^32*y + x^31*y)) dx)
self ((1/y) dx, (1/(x^34 + x^33))*y, ((x^34 + x^33 + x^2 - x - 1)/(x^34*y + x^33*y)) dx)
self ((1/y) dx, (2/(x^35 + x^34))*y, ((x^35 + x^34 + x^2 + x - 1)/(x^35*y + x^34*y)) dx)
self ((1/y) dx, (1/(x^36 + x^35))*y, ((x^35 + x^34 - 1)/(x^35*y + x^34*y)) dx)
self ((1/y) dx, (2/(x^37 + x^36))*y, ((x^37 + x^36 - x^2 + x + 1)/(x^37*y + x^36*y)) dx)
self ((1/y) dx, (1/(x^38 + x^37))*y, ((x^38 + x^37 - x^2 - x + 1)/(x^38*y + x^37*y)) dx)
self ((1/y) dx, (2/(x^39 + x^38))*y, ((x^38 + x^37 + 1)/(x^38*y + x^37*y)) dx)
self ((1/y) dx, (1/(x^40 + x^39))*y, ((x^40 + x^39 + x^2 - x - 1)/(x^40*y + x^39*y)) dx)
self ((1/y) dx, (2/(x^41 + x^40))*y, ((x^41 + x^40 + x^2 + x - 1)/(x^41*y + x^40*y)) dx)
self ((1/y) dx, (1/(x^42 + x^41))*y, ((x^41 + x^40 - 1)/(x^41*y + x^40*y)) dx)
self ((1/y) dx, (2/(x^43 + x^42))*y, ((x^43 + x^42 - x^2 + x + 1)/(x^43*y + x^42*y)) dx)
self ((1/y) dx, (1/(x^44 + x^43))*y, ((x^44 + x^43 - x^2 - x + 1)/(x^44*y + x^43*y)) dx)
self ((1/y) dx, (2/(x^45 + x^44))*y, ((x^44 + x^43 + 1)/(x^44*y + x^43*y)) dx)
self ((1/y) dx, (1/(x^46 + x^45))*y, ((x^46 + x^45 + x^2 - x - 1)/(x^46*y + x^45*y)) dx)
self ((1/y) dx, (2/(x^47 + x^46))*y, ((x^47 + x^46 + x^2 + x - 1)/(x^47*y + x^46*y)) dx)
self ((1/y) dx, (1/(x^48 + x^47))*y, ((x^47 + x^46 - 1)/(x^47*y + x^46*y)) dx)
self ((1/y) dx, (2/(x^49 + x^48))*y, ((x^49 + x^48 - x^2 + x + 1)/(x^49*y + x^48*y)) dx)
self ((1/y) dx, (1/(x^50 + x^49))*y, ((x^50 + x^49 - x^2 - x + 1)/(x^50*y + x^49*y)) dx)
self ((1/y) dx, (2/(x^51 + x^50))*y, ((x^50 + x^49 + 1)/(x^50*y + x^49*y)) dx)
self ((1/y) dx, (1/(x^52 + x^51))*y, ((x^52 + x^51 + x^2 - x - 1)/(x^52*y + x^51*y)) dx)
self ((1/y) dx, (2/(x^53 + x^52))*y, ((x^53 + x^52 + x^2 + x - 1)/(x^53*y + x^52*y)) dx)
self ((1/y) dx, (1/(x^54 + x^53))*y, ((x^53 + x^52 - 1)/(x^53*y + x^52*y)) dx)
self ((1/y) dx, (2/(x^55 + x^54))*y, ((x^55 + x^54 - x^2 + x + 1)/(x^55*y + x^54*y)) dx)
self ((1/y) dx, (1/(x^56 + x^55))*y, ((x^56 + x^55 - x^2 - x + 1)/(x^56*y + x^55*y)) dx)
self ((1/y) dx, (2/(x^57 + x^56))*y, ((x^56 + x^55 + 1)/(x^56*y + x^55*y)) dx)
self ((1/y) dx, (1/(x^58 + x^57))*y, ((x^58 + x^57 + x^2 - x - 1)/(x^58*y + x^57*y)) dx)
self ((1/y) dx, (2/(x^59 + x^58))*y, ((x^59 + x^58 + x^2 + x - 1)/(x^59*y + x^58*y)) dx)
self ((1/y) dx, (1/(x^60 + x^59))*y, ((x^59 + x^58 - 1)/(x^59*y + x^58*y)) dx)
self ((1/y) dx, (2/(x^61 + x^60))*y, ((x^61 + x^60 - x^2 + x + 1)/(x^61*y + x^60*y)) dx)
self ((1/y) dx, (1/(x^62 + x^61))*y, ((x^62 + x^61 - x^2 - x + 1)/(x^62*y + x^61*y)) dx)
self ((1/y) dx, (2/(x^63 + x^62))*y, ((x^62 + x^61 + 1)/(x^62*y + x^61*y)) dx)
self ((1/y) dx, (1/(x^64 + x^63))*y, ((x^64 + x^63 + x^2 - x - 1)/(x^64*y + x^63*y)) dx)
self ((1/y) dx, (2/(x^65 + x^64))*y, ((x^65 + x^64 + x^2 + x - 1)/(x^65*y + x^64*y)) dx)
self ((1/y) dx, (1/(x^66 + x^65))*y, ((x^65 + x^64 - 1)/(x^65*y + x^64*y)) dx)
self ((1/y) dx, (2/(x^67 + x^66))*y, ((x^67 + x^66 - x^2 + x + 1)/(x^67*y + x^66*y)) dx)
self ((1/y) dx, (1/(x^68 + x^67))*y, ((x^68 + x^67 - x^2 - x + 1)/(x^68*y + x^67*y)) dx)
self ((1/y) dx, (2/(x^69 + x^68))*y, ((x^68 + x^67 + 1)/(x^68*y + x^67*y)) dx)
self ((1/y) dx, (1/(x^70 + x^69))*y, ((x^70 + x^69 + x^2 - x - 1)/(x^70*y + x^69*y)) dx)
self ((1/y) dx, (2/(x^71 + x^70))*y, ((x^71 + x^70 + x^2 + x - 1)/(x^71*y + x^70*y)) dx)
self ((1/y) dx, (1/(x^72 + x^71))*y, ((x^71 + x^70 - 1)/(x^71*y + x^70*y)) dx)
self ((1/y) dx, (2/(x^73 + x^72))*y, ((x^73 + x^72 - x^2 + x + 1)/(x^73*y + x^72*y)) dx)
self ((1/y) dx, (1/(x^74 + x^73))*y, ((x^74 + x^73 - x^2 - x + 1)/(x^74*y + x^73*y)) dx)
self ((1/y) dx, (2/(x^75 + x^74))*y, ((x^74 + x^73 + 1)/(x^74*y + x^73*y)) dx)
self ((1/y) dx, (1/(x^76 + x^75))*y, ((x^76 + x^75 + x^2 - x - 1)/(x^76*y + x^75*y)) dx)
self ((1/y) dx, (2/(x^77 + x^76))*y, ((x^77 + x^76 + x^2 + x - 1)/(x^77*y + x^76*y)) dx)
self ((1/y) dx, (1/(x^78 + x^77))*y, ((x^77 + x^76 - 1)/(x^77*y + x^76*y)) dx)
self ((1/y) dx, (2/(x^79 + x^78))*y, ((x^79 + x^78 - x^2 + x + 1)/(x^79*y + x^78*y)) dx)
self ((1/y) dx, (1/(x^80 + x^79))*y, ((x^80 + x^79 - x^2 - x + 1)/(x^80*y + x^79*y)) dx)
self ((1/y) dx, (2/(x^81 + x^80))*y, ((x^80 + x^79 + 1)/(x^80*y + x^79*y)) dx)
self ((1/y) dx, (1/(x^82 + x^81))*y, ((x^82 + x^81 + x^2 - x - 1)/(x^82*y + x^81*y)) dx)
self ((1/y) dx, (2/(x^83 + x^82))*y, ((x^83 + x^82 + x^2 + x - 1)/(x^83*y + x^82*y)) dx)
self ((1/y) dx, (1/(x^84 + x^83))*y, ((x^83 + x^82 - 1)/(x^83*y + x^82*y)) dx)
self ((1/y) dx, (2/(x^85 + x^84))*y, ((x^85 + x^84 - x^2 + x + 1)/(x^85*y + x^84*y)) dx)
self ((1/y) dx, (1/(x^86 + x^85))*y, ((x^86 + x^85 - x^2 - x + 1)/(x^86*y + x^85*y)) dx)
self ((1/y) dx, (2/(x^87 + x^86))*y, ((x^86 + x^85 + 1)/(x^86*y + x^85*y)) dx)
self ((1/y) dx, (1/(x^88 + x^87))*y, ((x^88 + x^87 + x^2 - x - 1)/(x^88*y + x^87*y)) dx)
self ((1/y) dx, (2/(x^89 + x^88))*y, ((x^89 + x^88 + x^2 + x - 1)/(x^89*y + x^88*y)) dx)
self ((1/y) dx, (1/(x^90 + x^89))*y, ((x^89 + x^88 - 1)/(x^89*y + x^88*y)) dx)
self ((1/y) dx, (2/(x^91 + x^90))*y, ((x^91 + x^90 - x^2 + x + 1)/(x^91*y + x^90*y)) dx)
self ((1/y) dx, (1/(x^92 + x^91))*y, ((x^92 + x^91 - x^2 - x + 1)/(x^92*y + x^91*y)) dx)
self ((1/y) dx, (2/(x^93 + x^92))*y, ((x^92 + x^91 + 1)/(x^92*y + x^91*y)) dx)
self ((1/y) dx, (1/(x^94 + x^93))*y, ((x^94 + x^93 + x^2 - x - 1)/(x^94*y + x^93*y)) dx)
self ((1/y) dx, (2/(x^95 + x^94))*y, ((x^95 + x^94 + x^2 + x - 1)/(x^95*y + x^94*y)) dx)
self ((1/y) dx, (1/(x^96 + x^95))*y, ((x^95 + x^94 - 1)/(x^95*y + x^94*y)) dx)
self ((1/y) dx, (2/(x^97 + x^96))*y, ((x^97 + x^96 - x^2 + x + 1)/(x^97*y + x^96*y)) dx)
self ((1/y) dx, (1/(x^98 + x^97))*y, ((x^98 + x^97 - x^2 - x + 1)/(x^98*y + x^97*y)) dx)
self ((1/y) dx, (2/(x^99 + x^98))*y, ((x^98 + x^97 + 1)/(x^98*y + x^97*y)) dx)
self ((1/y) dx, (1/(x^100 + x^99))*y, ((x^100 + x^99 + x^2 - x - 1)/(x^100*y + x^99*y)) dx)
self ((1/y) dx, (2/(x^101 + x^100))*y, ((x^101 + x^100 + x^2 + x - 1)/(x^101*y + x^100*y)) dx)
self ((1/y) dx, (1/(x^102 + x^101))*y, ((x^101 + x^100 - 1)/(x^101*y + x^100*y)) dx)
self ((1/y) dx, (2/(x^103 + x^102))*y, ((x^103 + x^102 - x^2 + x + 1)/(x^103*y + x^102*y)) dx)
self ((1/y) dx, (1/(x^104 + x^103))*y, ((x^104 + x^103 - x^2 - x + 1)/(x^104*y + x^103*y)) dx)
self ((1/y) dx, (2/(x^105 + x^104))*y, ((x^104 + x^103 + 1)/(x^104*y + x^103*y)) dx)
self ((1/y) dx, (1/(x^106 + x^105))*y, ((x^106 + x^105 + x^2 - x - 1)/(x^106*y + x^105*y)) dx)
self ((1/y) dx, (2/(x^107 + x^106))*y, ((x^107 + x^106 + x^2 + x - 1)/(x^107*y + x^106*y)) dx)
self ((1/y) dx, (1/(x^108 + x^107))*y, ((x^107 + x^106 - 1)/(x^107*y + x^106*y)) dx)
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [26], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:31, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:26, in <module>
 
File <string>:82, in coordinates(self)
 
File <string>:88, in coordinates(self)
 
File <string>:88, in coordinates(self)
 
[... skipping similar frames: coordinates at line 88 (103 times)]
 
File <string>:88, in coordinates(self)
 
File <string>:53, in coordinates(self)
 
File <string>:102, in degrees_de_rham0(self)
 
File <string>:76, in basis_de_rham_degrees(self)
 
File <string>:60, in holomorphic_differentials_basis(self)
 
File <string>:52, in basis_holomorphic_differentials_degree(self)
 
File <string>:7, in __init__(self, C, g)
 
File <string>:259, in reduction_form(C, g)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:711, in FractionField_generic._element_constructor_(self, x, y, coerce)
708 raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
709 x0, y0, self))
710 try:
--> 711 return self._element_class(self, x, y, coerce=coerce)
712 except TypeError:
713 if parent(x) is parent(x0):
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:115, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
113 if coerce:
114 self.__numerator = parent.ring()(numerator)
--> 115 self.__denominator = parent.ring()(denominator)
116 else:
117 self.__numerator = numerator
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
1001
1002 try:
-> 1003 return self(str(element))
1004 except TypeError:
1005 pass
 
File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
192 except AttributeError:
193 return super().__repr__()
--> 194 result = reprfunc()
195 if isinstance(result, str):
196 return result
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_()
2688 NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3
2689 """
-> 2690 return self._repr()
2691
2692 def _latex_(self, name=None):
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2667, in sage.rings.polynomial.polynomial_element.Polynomial._repr()
2665 else:
2666 var = ""
-> 2667 s += "%s%s"%(x,var)
2668 s = s.replace(" + -", " - ")
2669 s = re.sub(r' 1(\.0+)?\*',' ', s)
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: quit()
[23;0t
~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
[22;0t[6nsage: load('init.sage')
self (((x + 1)/y) dx, (2/(x + 1))*y, ((-1)/(x*y + y)) dx)
self ((1/y) dx, (1/(x^2 + x))*y, (1/(x^2*y + x*y)) dx)
self ((1/y) dx, (2/(x^3 + x^2))*y, ((x^2 + x + 1)/(x^2*y + x*y)) dx)
self ((1/y) dx, (1/(x^4 + x^3))*y, ((x^4 + x^3 + x^2 - x - 1)/(x^4*y + x^3*y)) dx)
self ((1/y) dx, (2/(x^5 + x^4))*y, ((x^5 + x^4 + x^2 + x - 1)/(x^5*y + x^4*y)) dx)
self ((1/y) dx, (1/(x^6 + x^5))*y, ((x^5 + x^4 - 1)/(x^5*y + x^4*y)) dx)
self ((1/y) dx, (2/(x^7 + x^6))*y, ((x^7 + x^6 - x^2 + x + 1)/(x^7*y + x^6*y)) dx)
self ((1/y) dx, (1/(x^8 + x^7))*y, ((x^8 + x^7 - x^2 - x + 1)/(x^8*y + x^7*y)) dx)
self ((1/y) dx, (2/(x^9 + x^8))*y, ((x^8 + x^7 + 1)/(x^8*y + x^7*y)) dx)
self ((1/y) dx, (1/(x^10 + x^9))*y, ((x^10 + x^9 + x^2 - x - 1)/(x^10*y + x^9*y)) dx)
self ((1/y) dx, (2/(x^11 + x^10))*y, ((x^11 + x^10 + x^2 + x - 1)/(x^11*y + x^10*y)) dx)
self ((1/y) dx, (1/(x^12 + x^11))*y, ((x^11 + x^10 - 1)/(x^11*y + x^10*y)) dx)
self ((1/y) dx, (2/(x^13 + x^12))*y, ((x^13 + x^12 - x^2 + x + 1)/(x^13*y + x^12*y)) dx)
self ((1/y) dx, (1/(x^14 + x^13))*y, ((x^14 + x^13 - x^2 - x + 1)/(x^14*y + x^13*y)) dx)
self ((1/y) dx, (2/(x^15 + x^14))*y, ((x^14 + x^13 + 1)/(x^14*y + x^13*y)) dx)
self ((1/y) dx, (1/(x^16 + x^15))*y, ((x^16 + x^15 + x^2 - x - 1)/(x^16*y + x^15*y)) dx)
self ((1/y) dx, (2/(x^17 + x^16))*y, ((x^17 + x^16 + x^2 + x - 1)/(x^17*y + x^16*y)) dx)
self ((1/y) dx, (1/(x^18 + x^17))*y, ((x^17 + x^16 - 1)/(x^17*y + x^16*y)) dx)
self ((1/y) dx, (2/(x^19 + x^18))*y, ((x^19 + x^18 - x^2 + x + 1)/(x^19*y + x^18*y)) dx)
self ((1/y) dx, (1/(x^20 + x^19))*y, ((x^20 + x^19 - x^2 - x + 1)/(x^20*y + x^19*y)) dx)
self ((1/y) dx, (2/(x^21 + x^20))*y, ((x^20 + x^19 + 1)/(x^20*y + x^19*y)) dx)
self ((1/y) dx, (1/(x^22 + x^21))*y, ((x^22 + x^21 + x^2 - x - 1)/(x^22*y + x^21*y)) dx)
self ((1/y) dx, (2/(x^23 + x^22))*y, ((x^23 + x^22 + x^2 + x - 1)/(x^23*y + x^22*y)) dx)
self ((1/y) dx, (1/(x^24 + x^23))*y, ((x^23 + x^22 - 1)/(x^23*y + x^22*y)) dx)
self ((1/y) dx, (2/(x^25 + x^24))*y, ((x^25 + x^24 - x^2 + x + 1)/(x^25*y + x^24*y)) dx)
self ((1/y) dx, (1/(x^26 + x^25))*y, ((x^26 + x^25 - x^2 - x + 1)/(x^26*y + x^25*y)) dx)
self ((1/y) dx, (2/(x^27 + x^26))*y, ((x^26 + x^25 + 1)/(x^26*y + x^25*y)) dx)
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [1], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:31, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:26, in <module>
 
File <string>:82, in coordinates(self)
 
File <string>:88, in coordinates(self)
 
File <string>:88, in coordinates(self)
 
[... skipping similar frames: coordinates at line 88 (22 times)]
 
File <string>:88, in coordinates(self)
 
File <string>:57, in coordinates(self)
 
File <string>:98, in de_rham_basis(self)
 
File <string>:91, in basis_de_rham_degrees(self)
 
File <string>:5, in __init__(self, C, omega, fct)
 
File <string>:93, in diffn(self)
 
File /ext/sage/9.7/src/sage/categories/quotient_fields.py:610, in QuotientFields.ElementMethods.derivative(self, *args)
580 r"""
581 The derivative of this rational function, with respect to variables
582 supplied in args.
(...)
607 2/(x^3 + 3*x^2*y + 3*x*y^2 + y^3)
608 """
609 from sage.misc.derivative import multi_derivative
--> 610 return multi_derivative(self, args)
 
File /ext/sage/9.7/src/sage/misc/derivative.pyx:222, in sage.misc.derivative.multi_derivative()
220
221 for arg in derivative_parse(args):
--> 222 F = F._derivative(arg)
223 return F
224
 
File /ext/sage/9.7/src/sage/categories/quotient_fields.py:612, in QuotientFields.ElementMethods._derivative(self, var)
609 from sage.misc.derivative import multi_derivative
610 return multi_derivative(self, args)
--> 612 def _derivative(self, var=None):
613 r"""
614 Returns the derivative of this rational function with respect to the
615 variable ``var``.
(...)
668 (-t + 1)/(t^3 + 3*t^2 + 3*t + 1)
669 """
670 R = self.parent()
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: load('init.sage')
sage: C.cohomology_of_structure_sheaf_basis()
[2/x*y]
sage: autom(C.cohomology_of_structure_sheaf_basis()[0]).coordinates()
[1]
sage: C = superelliptic(x^7 + 1, 2)
[6nsage: C.de_rham_basis()
[((1/y) dx, 0, (1/y) dx),
((x/y) dx, 0, (x/y) dx),
((x^2/y) dx, 0, (x^2/y) dx),
(((-x^5)/y) dx, 2/x*y, ((-1)/(x^2*y)) dx),
(0 dx, 2/x^2*y, (1/(x^3*y)) dx),
((x^3/y) dx, 2/x^3*y, 0 dx)]
[6nsage: C.cohomology_of_structure_sheaf_basis()
[2/x*y, 2/x^2*y, 2/x^3*y]
[6nsage: C = superelliptic(x^7 + 1, 5)
[6nsage: C.cohomology_of_structure_sheaf_basis()
[2/x*y,
2/x*y^2,
2/x^2*y^2,
2/x*y^3,
2/x^2*y^3,
2/x^3*y^3,
2/x^4*y^3,
2/x*y^4,
2/x^2*y^4,
2/x^3*y^4,
2/x^4*y^4,
2/x^5*y^4]
[6nsage: C = superelliptic(x^7 + 1, 5)
[6nsage: C.de_rham_basis()
[((1/y) dx, 0, (1/y) dx),
((1/y^2) dx, 0, (1/y^2) dx),
((x/y^2) dx, 0, (x/y^2) dx),
((1/y^3) dx, 0, (1/y^3) dx),
((x/y^3) dx, 0, (x/y^3) dx),
((x^2/y^3) dx, 0, (x^2/y^3) dx),
((x^3/y^3) dx, 0, (x^3/y^3) dx),
((1/y^4) dx, 0, (1/y^4) dx),
((x/y^4) dx, 0, (x/y^4) dx),
((x^2/y^4) dx, 0, (x^2/y^4) dx),
((x^3/y^4) dx, 0, (x^3/y^4) dx),
((x^4/y^4) dx, 0, (x^4/y^4) dx),
(((-x^5)/y) dx, 2/x*y^4, ((-1)/(x^2*y)) dx),
(0 dx, 2/x^2*y^4, (1/(x^3*y)) dx),
((x^3/y) dx, 2/x^3*y^4, 0 dx),
(((-x^2)/y) dx, 2/x^4*y^4, ((-1)/(x^5*y)) dx),
(0 dx, 2/x^5*y^4, (1/(x^6*y)) dx),
((x^5/y^2) dx, 2/x*y^3, ((-1)/(x^2*y^2)) dx),
(((-x^4)/y^2) dx, 2/x^2*y^3, (1/(x^3*y^2)) dx),
(0 dx, 2/x^3*y^3, 0 dx),
((x^2/y^2) dx, 2/x^4*y^3, ((-1)/(x^5*y^2)) dx),
(0 dx, 2/x*y^2, ((-1)/(x^2*y^3)) dx),
((x^4/y^3) dx, 2/x^2*y^2, (1/(x^3*y^3)) dx),
(((-x^5)/y^4) dx, 2/x*y, ((-1)/(x^2*y^4)) dx)]
[6nsage: load('init.sage')
[6nsage: C = superelliptic(x^7 + 1, 5)
[6nsage: C.de_rham_basis()
[((1/y) dx, 0, (1/y) dx),
((1/y^2) dx, 0, (1/y^2) dx),
((x/y^2) dx, 0, (x/y^2) dx),
((1/y^3) dx, 0, (1/y^3) dx),
((x/y^3) dx, 0, (x/y^3) dx),
((x^2/y^3) dx, 0, (x^2/y^3) dx),
((x^3/y^3) dx, 0, (x^3/y^3) dx),
((1/y^4) dx, 0, (1/y^4) dx),
((x/y^4) dx, 0, (x/y^4) dx),
((x^2/y^4) dx, 0, (x^2/y^4) dx),
((x^3/y^4) dx, 0, (x^3/y^4) dx),
((x^4/y^4) dx, 0, (x^4/y^4) dx),
(((-x^5)/y) dx, 2/x*y^4, ((-1)/(x^2*y)) dx),
(0 dx, 2/x^2*y^4, (1/(x^3*y)) dx),
((x^3/y) dx, 2/x^3*y^4, 0 dx),
(((-x^2)/y) dx, 2/x^4*y^4, ((-1)/(x^5*y)) dx),
(0 dx, 2/x^5*y^4, (1/(x^6*y)) dx),
((x^5/y^2) dx, 2/x*y^3, ((-1)/(x^2*y^2)) dx),
(((-x^4)/y^2) dx, 2/x^2*y^3, (1/(x^3*y^2)) dx),
(0 dx, 2/x^3*y^3, 0 dx),
((x^2/y^2) dx, 2/x^4*y^3, ((-1)/(x^5*y^2)) dx),
(0 dx, 2/x*y^2, ((-1)/(x^2*y^3)) dx),
((x^4/y^3) dx, 2/x^2*y^2, (1/(x^3*y^3)) dx),
(((-x^5)/y^4) dx, 2/x*y, ((-1)/(x^2*y^4)) dx)]
[6nsage: C.cohomology_of_structure_sheaf_basis()
[2/x*y^4,
2/x^2*y^4,
2/x^3*y^4,
2/x^4*y^4,
2/x^5*y^4,
2/x*y^3,
2/x^2*y^3,
2/x^3*y^3,
2/x^4*y^3,
2/x*y^2,
2/x^2*y^2,
2/x*y]
[6nsage: load('init.sage')
[6nsage: autom(C.de_rham_basis[0]).coordinates()
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [17], in <cell line: 1>()
----> 1 autom(C.de_rham_basis[Integer(0)]).coordinates()
 
TypeError: 'method' object is not subscriptable
[6nsage: autom(C.de_rham_basis()[0]).coordinates()
self ((1/y) dx, 0, (1/y) dx)
[1, 0]
[6nsage: autom(C.de_rham_basis()[1]).coordinates()
self (((x + 1)/y) dx, (2/(x + 1))*y, ((-1)/(x*y + y)) dx)
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [19], in <cell line: 1>()
----> 1 autom(C.de_rham_basis()[Integer(1)]).coordinates()
 
File <string>:71, in coordinates(self)
 
AttributeError: 'superelliptic_cech' object has no attribute 'coorinates'
[6nsage: load('init.sage')
[6nsage: autom(C.de_rham_basis()[1]).coordinates()
self (((x + 1)/y) dx, (2/(x + 1))*y, ((-1)/(x*y + y)) dx)
self ((1/y) dx, 0, (1/y) dx)
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [21], in <cell line: 1>()
----> 1 autom(C.de_rham_basis()[Integer(1)]).coordinates()
 
File <string>:71, in coordinates(self)
 
File <string>:56, in coordinates(self)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
493 """
--> 494 return self.getattr_from_category(name)
495
496 cdef getattr_from_category(self, name):
 
File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
505 else:
506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
508
509 def __dir__(self):
 
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
359 dummy_error_message.cls = type(self)
360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
362 attribute = <object>attr
363 # Check for a descriptor (__get__ in Python)
 
AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function'
[6nsage: load('init.sage')
[6nsage: autom(C.de_rham_basis()[1]).coordinates()
self (((x + 1)/y) dx, (2/(x + 1))*y, ((-1)/(x*y + y)) dx)
self ((1/y) dx, 0, (1/y) dx)
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [23], in <cell line: 1>()
----> 1 autom(C.de_rham_basis()[Integer(1)]).coordinates()
 
File <string>:71, in coordinates(self)
 
TypeError: unsupported operand type(s) for +: 'sage.modules.vector_modn_dense.Vector_modn_dense' and 'list'
[6nsage: load('init.sage')
[6nsage: autom(C.de_rham_basis()[1]).coordinates()
self (((x + 1)/y) dx, (2/(x + 1))*y, ((-1)/(x*y + y)) dx)
self ((1/y) dx, 0, (1/y) dx)
(1, 1)
[6nsage: load('init.sage')
[6nsage: autom(C.de_rham_basis()[1]).coordinates()
(1, 1)
~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
[22;0t[6nsage: load('init.sage')
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
(1, 1)
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
aux before reduce (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(1/(x^2 + x + 1))*y]), [(1/(x^2 + x))*y] + V((1/(x^2 + x))*y), [((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*y]))
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [1], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:31, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:26, in <module>
 
File <string>:74, in coordinates(self, basis)
 
TypeError: unsupported operand type(s) for /: 'superelliptic_form' and 'superelliptic_function'
[6nsage: load('init.sage')
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
(1, 1)
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
aux before reduce (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(1/(x^2 + x + 1))*y]), [(1/(x^2 + x))*y] + V((1/(x^2 + x))*y), [((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*y]))
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [2], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:31, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:26, in <module>
 
File <string>:75, in coordinates(self, basis)
 
File <string>:168, in pth_root(self)
 
ValueError: Function is not a p-th power.
[6nsage: load('init.sage')
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
(1, 1)
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
aux before reduce (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(1/(x^2 + x + 1))*y]), [(1/(x^2 + x))*y] + V((1/(x^2 + x))*y), [((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*y]))
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [3], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:31, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:26, in <module>
 
File <string>:79, in coordinates(self, basis)
 
File <string>:168, in pth_root(self)
 
ValueError: Function is not a p-th power.
[6nsage: C.y/(C.x^2+C.x)
(1/(x^2 + x))*y
[6nsage: (C.y/(C.x^2+C.x)).expansion_at_infty()
t + 2*t^3 + t^5 + 2*t^9 + 2*t^13 + t^17 + O(t^21)
[6nsage: C.x.teichmuller().f
0
[6nsage: C.x.teichmuller().t
x
[6nsage: load('init.sage')
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
(1, 1)
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
aux_f_t_0 0
aux (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(1/(x^2 + x + 1))*y]), V((1/(x^2 + x))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(2/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [8], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:31, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:26, in <module>
 
File <string>:82, in coordinates(self, basis)
 
File <string>:168, in pth_root(self)
 
ValueError: Function is not a p-th power.
[6nsagsage: load('init.sage')
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
(1, 1)
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
aux_f_t_0 0
aux (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), V((1/(x^4 + 2*x^3 + 2*x^2 + x))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(2/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [9], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:31, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:26, in <module>
 
File <string>:82, in coordinates(self, basis)
 
File <string>:168, in pth_root(self)
 
ValueError: Function is not a p-th power.
[6nsage: load('init.sage')
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
(1, 1)
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
aux (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), [0], V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [10], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:31, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:26, in <module>
 
File <string>:84, in coordinates(self, basis)
 
File <string>:168, in pth_root(self)
 
ValueError: Function is not a p-th power.
~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
[22;0t[6nsage: load('init.sage')
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
(1, 1)
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
aux (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), [0], V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [1], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:31, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:26, in <module>
 
File <string>:84, in coordinates(self, basis)
 
File <string>:168, in pth_root(self)
 
ValueError: Function is not a p-th power.
[6nsage: (0*C.x).pth_root()
0
sage: ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx
....:
....: )
((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx
sage: a = (-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx
sage: a.expansion_at_infty()
2*t^-2 + 2 + 2*t^4 + t^6 + O(t^8)
sage: a.is_regular_on_U0
<bound method superelliptic_form.is_regular_on_U0 of ((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx>
[sage: a.is_regular_on_U0()
False
sage: a = C.de_rham_basis()[0]
[6nsage: b = C.de_rham_basis()[1]
[6nsage: A = C.crystalline_cohomology_basis()[0]
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[6nsage: B = C.crystalline_cohomology_basis()[1]
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[6nsage: autom(b)
(((x + 1)/y) dx, (2/(x + 1))*y, ((-1)/(x*y + y)) dx)
[6nsage: autom(b).coordinates()
(1, 1)
[6nssage: autom(B) - B - A
(V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(1/(x^2 + x + 1))*y]), [(1/(x^2 + x))*y] + V((1/(x^2 + x))*y), [((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*y]))
[6nsage: (C.y/(C.x^2+C.x)).expansion_at_infty()
t + 2*t^3 + t^5 + 2*t^9 + 2*t^13 + t^17 + O(t^21)
[6nsage: D = autom(B) - B - A
[6nsage: D.r()
(0 dx, (1/(x^2 + x))*y, ((-x^2 - x + 1)/(x^2*y + x*y)) dx)
[6nsage: D.r().omega8 == -D.r().f.diffn()
True
[6nsage: sage: D.f -= (C.y/(C.x^2+C.x)).teichmuller()
[6nsage: D.omega8 = D.omega0 - D.f.diffn()
[6nsage: D
(V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(1/(x^2 + x + 1))*y]), V((1/(x^2 + x))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(2/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
[6nsage:sage: D.omega0.h2 = 0*C.x
[6nsage: D.f -= (C.y/(C.x^2 + C.x + C.one)).verschiebung()
[6nsage: D.omega8 = D.omega0 - D.f.diffn()
[6nsage: D
(V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), V((1/(x^4 + 2*x^3 + 2*x^2 + x))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(2/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
[6nsagesage: D.omega8.h2 = 0*C.x
[6nsage: D.f += ((2*C.one/(C.x^4 + 2*C.x^3 + 2*C.x^2 + C.x))*C.y).verschiebung()
[6nsage: D.omega0 - D.f.diffn() == D.omega8
True
[6nsage: D
(V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), [0], V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
[6nsage: aa = (-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))* C.dx
Input In [30]
aa = (-C.x**Integer(3) + C.x**Integer(2) + C.x)/(C.x**Integer(2)*C.y + C.x*C.y + C.y))* C.dx
^
SyntaxError: unmatched ')'
 
[6nsage: aa = (-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)* C.dx
sage: aa.is_regular_on_Uinfty()
False
sage: aa.is_regular_on_U0()
False
sage: B
([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[6nsage: B.r()
((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
[6nsage: B0 = B.omega0
[6nsage: B0
[(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y])
[6nsage: B0.r()
(x/y) dx
[6nsage: B0 - C.x.teichmuller()*C.y.teichmuller().diffn()
V(((x^8 - x^6 + 1)/y) dx) + dV([(2*x^4 + 2*x^2 + 2)*y])
[6nsage: B0 -= C.x.teichmuller()*C.y.teichmuller().diffn()
[6nsage: B0
V(((x^8 - x^6 + 1)/y) dx) + dV([(2*x^4 + 2*x^2 + 2)*y])
[6nsage: C.x*C.y.diffn() == B.r()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [42], in <cell line: 1>()
----> 1 C.x*C.y.diffn() == B.r()
 
File <string>:12, in __eq__(self, other)
 
AttributeError: 'superelliptic_cech' object has no attribute 'reduce'
[6nsage: C.x*C.y.diffn() == B.omega0.r()
True
[6nsage: B
([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[6nsage: load('init.sage')
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
(1, 1)
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
aux (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), [0], V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [45], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:31, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:26, in <module>
 
File <string>:84, in coordinates(self, basis)
 
File <string>:168, in pth_root(self)
 
ValueError: Function is not a p-th power.
[6nsage: B = C.crystalline_cohomology_basis()[1]
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[6nsage: B
([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[6nsage: B0 = B.omega0
[6nsage: B0 -= C.x.teichmuller()*C.y.teichmuller().diffn()
[6nsage: B0
V(((x^8 - x^6 + 1)/y) dx)
[6nsage: B8 = B.omega8
[6nsage: B.r()
((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
[6nsage: B.r().omega8
((-1)/(x*y)) dx
[6nsage: second_patch(B.r().omega8)
(x/y) dx
[6nsage: u = C.one
[6nsage: u = C.one/C.x
[6nsage: v = C.y/(C.x)^2
[6nsage: B8 -= u.teichmuller()*v.teichmuller().diffn()
[6nsage: B8
[(1/(x^4 + 2*x^2))*y] d[x] + V(((x^8 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([((2*x^6 + 2)/(x^8 + 2*x^6))*y])
[6nsage: B8 += u.teichmuller()*v.teichmuller().diffn()
[6nsage: B8 += u.teichmuller()*v.teichmuller().diffn()
[6nsage: B8
V(((x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
[6nsage: B.r()
((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
[6nsage: ((C.x^8 - C.x^4 - C.x^2 - C.one)/(C.x^10*C.y - C.x^8*C.y))* C.dx
((x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx
[6nsage: a = ((C.x^8 - C.x^4 - C.x^2 - C.one)/(C.x^10*C.y - C.x^8*C.y))* C.dx
[6nsage: a.is_regular_on_Uinfty()
True
[6nsage: sage: b = ((2*C.x^6 + 2*C.one)/(C.x^8 + 2*C.x^6))*C.y
sage: b.expansion_at_infty()
2*t + 2*t^5 + t^9 + t^17 + O(t^21)
sage: B
([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[6nsage: B.r()
((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
[6nsage: C.de_rham_basis()[1]
((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
[6nsage: sage: B = C.crystalline_cohomology_basis()[0]
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
[6nsage: B0 = B.omega0
[6nsage: B0 - C.y.teichmuller().diffn()
V(((x^5 + x^3)/y) dx)
[6nsage: aaB8 - C.y.teichmuller().diffn()
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [75], in <cell line: 1>()
----> 1 aaB8 - C.y.teichmuller().diffn()
 
NameError: name 'aaB8' is not defined
[6nsage: v = C.y/(C.x)^2
[6nssage: B8 + C.v.teichmuller().diffn()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [77], in <cell line: 1>()
----> 1 B8 + C.v.teichmuller().diffn()
 
AttributeError: 'superelliptic' object has no attribute 'v'
[6nsage: B8 + v.teichmuller().diffn()
[(1/(x^3 + 2*x))*y] d[x] + V(((x^8 + x^6 - x^5 + x^4 + x^3 + x^2 + x - 1)/(x^9*y - x^8*y)) dx) + dV([((2*x^6 + x^3 + 1)/(x^8 + 2*x^6))*y])
[6nsage: B8 - v.teichmuller().diffn()
[(2/(x^3 + 2*x))*y] d[x] + V(((-x^8 - x^6 - x^5 - x^4 + x^3 - x^2 + x + 1)/(x^9*y + x^8*y)) dx) + dV([((2*x^6 + 2*x^3 + 1)/(x^8 + 2*x^6))*y])
[6nsage: B.r()
((1/y) dx, 0, (1/y) dx)
[6nsage: second_patch(B.r().omega8)
((-1)/y) dx
[6nsagsage:
[6nsage: C.genus()
1
[6nsage: lo
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [83], in <cell line: 1>()
----> 1 lo
 
NameError: name 'lo' is not defined
[6nsage: load('init.sage')
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
omega8_lift [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
(1, 1)
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
omega8_lift [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
aux (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), [0], V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [84], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:31, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:26, in <module>
 
File <string>:84, in coordinates(self, basis)
 
File <string>:168, in pth_root(self)
 
ValueError: Function is not a p-th power.
[6nsage: load('init.sage')
[6nsage: C.crystalline_cohomology_basis()
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
omega8_lift - 0
omega8_lift + [(2/(x^3 + 2*x))*y] d[x] + V(((-x^2 - 1)/(x^5*y)) dx) + dV([(2/(x^5 + 2*x^3))*y])
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
omega8_lift [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
omega8_lift - [(2/(x^3 + 2*x^2))*y] d[x] + V(((-x^7 + x^6 - x^5 - x^3 + x^2 - 1)/(x^8*y)) dx) + dV([((2*x^2 + x + 2)/(x^7 + 2*x^6))*y])
omega8_lift + [(1/(x^3 + x^2))*y] d[x] + V(((x^7 + x^6 + x^5 + x^3 + x^2 - 1)/(x^8*y)) dx) + dV([((x^2 + x + 1)/(x^7 + x^6))*y])
[([(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), V(((x^2 + 1)/x)*y), [(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y])),
([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))]
[6nsage: a = C.crystalline_cohomology_basis()[0]
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
omega8_lift - 0
omega8_lift + [(2/(x^3 + 2*x))*y] d[x] + V(((-x^2 - 1)/(x^5*y)) dx) + dV([(2/(x^5 + 2*x^3))*y])
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
omega8_lift [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
omega8_lift - [(2/(x^3 + 2*x^2))*y] d[x] + V(((-x^7 + x^6 - x^5 - x^3 + x^2 - 1)/(x^8*y)) dx) + dV([((2*x^2 + x + 2)/(x^7 + 2*x^6))*y])
omega8_lift + [(1/(x^3 + x^2))*y] d[x] + V(((x^7 + x^6 + x^5 + x^3 + x^2 - 1)/(x^8*y)) dx) + dV([((x^2 + x + 1)/(x^7 + x^6))*y])
~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
[22;0t[6nsage: load('init.sage')
[6nsage: a = C.crystalline_cohomology_basis()[0]
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
omega8_lift - 0
omega8_lift + [(2/(x^3 + 2*x))*y] d[x] + V(((-x^2 - 1)/(x^5*y)) dx) + dV([(2/(x^5 + 2*x^3))*y])
omega0_regular (0, x)
omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
omega8_regular 1 (0, 2*x)
omega8_regular 2 (0, 2/x)
omega8_lift [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
omega8_lift - [(2/(x^3 + 2*x^2))*y] d[x] + V(((-x^7 + x^6 - x^5 - x^3 + x^2 - 1)/(x^8*y)) dx) + dV([((2*x^2 + x + 2)/(x^7 + 2*x^6))*y])
omega8_lift + [(1/(x^3 + x^2))*y] d[x] + V(((x^7 + x^6 + x^5 + x^3 + x^2 - 1)/(x^8*y)) dx) + dV([((x^2 + x + 1)/(x^7 + x^6))*y])
[6nsage: a.omega8
[(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y])
[6nsage: sage: v = C.y/(C.x)^2
[6nssage: u = C.one/C.x
[6nsasage: v^2 - u - u^3
1/x^3
[6nsage: v^2 - u + u^3
0
[6nsage: a.omega8
[(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y])
[6nsage: a.omega8 + v.diffn()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [9], in <cell line: 1>()
----> 1 a.omega8 + v.diffn()
 
File <string>:81, in __add__(self, other)
 
AttributeError: 'superelliptic_form' object has no attribute 'h1'
[6nsage: a.omega8 + v.teichmuller().diffn()
[(2/(x^3 + 2*x))*y] d[x] + V(((x^2 + 1)/(x^5*y)) dx) + dV([((x^2 + 1)/(x^5 + 2*x^3))*y])
[6nsage: a.omega8 - v.teichmuller().diffn()
V(((-x^2 - 1)/(x^5*y)) dx) + dV([1/x^3*y])
[6nsage: a
([(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), V(((x^2 + 1)/x)*y), [(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[6nsage: a.r()
((1/y) dx, 0, (1/y) dx)
[6nsage: v.diffn()
(1/y) dx
[6nsage: a.omega8 - v.teichmuller().diffn()
V(((-x^2 - 1)/(x^5*y)) dx) + dV([1/x^3*y])
[6nsage: (a.omega8 - v.teichmuller().diffn()).omega.is_regular_on_U0()
False
[6nsage: (a.omega8 - v.teichmuller().diffn()).omega.is_regular_on_Uinfty()
True
[6nsage: (a.omega8 - v.teichmuller().diffn()).h2.is_regular_on_Uinfty()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [18], in <cell line: 1>()
----> 1 (a.omega8 - v.teichmuller().diffn()).h2.is_regular_on_Uinfty()
 
AttributeError: 'superelliptic_function' object has no attribute 'is_regular_on_Uinfty'
[6nsage: (a.omega8 - v.teichmuller().diffn()).h2.expansion()
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [19], in <cell line: 1>()
----> 1 (a.omega8 - v.teichmuller().diffn()).h2.expansion()
 
TypeError: superelliptic_function.expansion() missing 1 required positional argument: 'pt'
[6nsage: (a.omega8 - v.teichmuller().diffn()).h2.expansion_at_infty()
t^3 + 2*t^7 + 2*t^11 + t^15 + 2*t^19 + O(t^23)
[6nsage: a
([(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), V(((x^2 + 1)/x)*y), [(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
[22;0t[6nsage: load('init.sage')
sage: regular_form(C.dx)
sage: regular_form(C.dx)
sage: de_rham_witt_lift(C.de_rham_basis()[0])
omega0_regular (0, 1)
omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
omega8_regular 1 (0, 1)
omega8_regular 2 (0, 1)
omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
omega8_lift - 0
omega8_lift + [(2/(x^3 + 2*x))*y] d[x] + V(((-x^2 - 1)/(x^5*y)) dx) + dV([(2/(x^5 + 2*x^3))*y])
([(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), V(((x^2 + 1)/x)*y), [(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[6nsage: load('init.sage')
[6nsage: C.dx.regular_form()
[6nsage: load('init.sage')
[6nsage: C.dx.regular_form()
<repr(<__main__.superelliptic_regular_form at 0x7f293c63c4f0>) failed: NameError: name 'A' is not defined>
[6nsage: load('init.sage')
[6nsage: C.dx.regular_form()
1 dx + 0 dy
[6nsage: load('init.sage')
Traceback (most recent call last):
 
File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
exec(code_obj, self.user_global_ns, self.user_ns)
 
Input In [11] in <cell line: 1>
load('init.sage')
 
File sage/misc/persist.pyx:175 in sage.misc.persist.load
sage.repl.load.load(filename, globals())
 
File /ext/sage/9.7/src/sage/repl/load.py:272 in load
exec(preparse_file(f.read()) + "\n", globals)
 
File <string>:18 in <module>
 
File sage/misc/persist.pyx:175 in sage.misc.persist.load
sage.repl.load.load(filename, globals())
 
File /ext/sage/9.7/src/sage/repl/load.py:272 in load
exec(preparse_file(f.read()) + "\n", globals)
 
File <string>:8
if self.dx.form = _sage_const_0 :
^
SyntaxError: cannot assign to attribute here. Maybe you meant '==' instead of '='?
 
[6nssage: load('init.sage')
[6nsage: C.dx.regular_form()
<repr(<__main__.superelliptic_regular_form at 0x7f293c5f6ec0>) failed: AttributeError: 'superelliptic_function' object has no attribute 'form'>
[6nsage: load('init.sage')
[6nsage: C.dx.regular_form()
1 dx
[6nsage: ((C.y)^(-1)*C.dx).regular_form()
1 dy
[6nsage: load('init.sage')
[6nsage: A = ((C.y)^(-1)*C.dx).regular_form()
[6nsage: A
1 dy
[6nsage: A.form
<bound method superelliptic_regular_form.form of 1 dy>
[6nsage: A.form()
(1/y) dx
[6nsage: load('init.sage')
[6nsasage: C.crystalline_cohomology_basis()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [23], in <cell line: 1>()
----> 1 C.crystalline_cohomology_basis()
 
File <string>:39, in crystalline_cohomology_basis(self, prec)
 
File <string>:15, in de_rham_witt_lift(cech_class, prec)
 
AttributeError: 'tuple' object has no attribute 'dx'
[6nsage: load('init.sage')
[6nsage: load('init.sage')
[6nsage: C.crystalline_cohomology_basis()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [26], in <cell line: 1>()
----> 1 C.crystalline_cohomology_basis()
 
File <string>:39, in crystalline_cohomology_basis(self, prec)
 
File <string>:15, in de_rham_witt_lift(cech_class, prec)
 
AttributeError: 'tuple' object has no attribute 'dx'
[6nsage: regular_form(C.dx)
1 dx
[6nsage: load('init.sage')
[6nsage: C.crystalline_cohomology_basis()
[([(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), V(((x^2 + 1)/x)*y), [(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y])),
([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))]
[6nsage: B = C.crystalline_cohomology_basis()
[6nsage: B[0].omega0.regular_form()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [31], in <cell line: 1>()
----> 1 B[Integer(0)].omega0.regular_form()
 
AttributeError: 'superelliptic_drw_form' object has no attribute 'regular_form'
sage: B01 = B[0].omega0
[6sage: load('superelliptic_drw/regular_form.sage')
sage: B = C.crystalline_cohomology_basis()
sage: B01 = B[0].omega0
sage: B01.regular_form()
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [36], in <cell line: 1>()
----> 1 B01.regular_form()
 
File <string>:37, in regular_drw_form(omega)
 
TypeError: 'superelliptic' object is not callable
sage: load('superelliptic_drw/regular_form.sage')
sage: load('init.sage')
sage: load('superelliptic_drw/regular_form.sage')
sage: B = C.crystalline_cohomology_basis()
sage: B01 = B[0].omega0
sage: B01.regular_form()
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [42], in <cell line: 1>()
----> 1 B01.regular_form()
 
File <string>:41, in regular_drw_form(omega)
 
TypeError: superelliptic_drw_form.__init__() takes 4 positional arguments but 5 were given
[6nsage: load('superelliptic_drw/regular_form.sage')
[6nsage: load('init.sage')
[6nsage: B = C.crystalline_cohomology_basis()
[6nsage: B01 = B[0].omega0
[6nsage: B01.regular_form()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [47], in <cell line: 1>()
----> 1 B01.regular_form()
 
AttributeError: 'superelliptic_drw_form' object has no attribute 'regular_form'
[6nsage: load('superelliptic_drw/regular_form.sage')
[6nsage: B = C.crystalline_cohomology_basis()
[6nsage: B01.regular_form()
[0] d[x] + [1] d[y] + V(((x^5 + x^3)/y) dx) + dV(0)
[6nsage: B01 = B[0].omega8
[6nsage: sage: B01 = second_patch(B01)
[6nsage: B01.regular_form()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [53], in <cell line: 1>()
----> 1 B01.regular_form()
 
AttributeError: 'NoneType' object has no attribute 'regular_form'
[6nsage: B01
~/Research/2021 De Rham/DeRhamComputation/sage$ sage -i parsivelib galois Representations
make build/make/Makefile --stop
make[1]: Entering directory '/ext/sage/9.7'
make[1]: 'build/make/Makefile' is up to date.
make[1]: Leaving directory '/ext/sage/9.7'
build/bin/sage-logger \
"cd build/make && ./install 'all-toolchain'" logs/install.log
tee: logs/install.log: Read-only file system
make[1]: Entering directory '/ext/sage/9.7/build/make'
make[1]: Leaving directory '/ext/sage/9.7/build/make'
*** ALL ENVIRONMENT VARIABLES BEFORE BUILD: ***
ANACONDA2019=/ext/anaconda-2019.03
ANACONDA2020=/ext/anaconda2020.02
ANACONDA2021=/ext/anaconda2021.11
ANACONDA2022=/ext/anaconda2022.05
ANACONDA3=/ext/anaconda3
ANACONDA5=/ext/anaconda5
BROWSER_PORT=6001
COCALC_CODE_PORT=6004
COCALC_EXTRA_ENV=e30=
COCALC_JUPYTERLAB_PORT=6002
COCALC_JUPYTER_PORT=6003
COCALC_NODE=kucalc-prod3-node-pbpa
COCALC_PLUTO_PORT=6005
COCALC_PROJECT_CONFIG=eyJxdW90YSI6eyJuZXR3b3JrIjp0cnVlLCJtZW1iZXJfaG9zdCI6dHJ1ZSwicHJpdmlsZWdlZCI6ZmFsc2UsIm1lbW9yeV9yZXF1ZXN0IjozMDAsImNwdV9yZXF1ZXN0IjowLjA1LCJkaXNrX3F1b3RhIjo4MDAwLCJtZW1vcnlfbGltaXQiOjEyMDAwLCJjcHVfbGltaXQiOjIsImlkbGVfdGltZW91dCI6MTgwMCwiYWx3YXlzX3J1bm5pbmciOmZhbHNlLCJkZWRpY2F0ZWRfdm0iOmZhbHNlLCJkZWRpY2F0ZWRfZGlza3MiOltdfX0=
COCALC_PROJECT_DATASTORE=false
COCALC_PROJECT_ID=6b7177d7-4a24-4810-937c-d1fa861bd29e
COCALC_PROJECT_IMAGE_NAME=ubuntu2004
COCALC_SECRET_TOKEN=/secrets/secret-token/token
COCALC_SSH_PORT=2222
COCALC_TERMINAL_FILENAME=.run.term-0.term
COCALC_ULIMIT_OPEN_FILES=10000
COCALC_USERNAME=user
DEBUG=project:*,cocalc:*
DEBUG_HIDE_DATE=yes
ELAN_HOME=/ext/lean
EXT=/ext
HISTCONTROL=ignoredups
HOME=/home/user
HOSTNAME=project-6b7177d7-4a24-4810-937c-d1fa861bd29e
HUB_PORT=6000
ISOCHRONES=/ext/data/isochrones
JULIA_DEPOT_PATH=/home/user/.julia:/ext/julia/depot/
JUPYTER_PATH=/ext/jupyter
LANG=en_US.UTF-8
LANGUAGE=en_US:en
LC_ALL=C.UTF-8
LESSCLOSE=/usr/bin/lesspipe %s %s
LESSOPEN=| /usr/bin/lesspipe %s
LESS_TERMCAP_se=
LESS_TERMCAP_so=
LS_COLORS=rs=0:di=01;34:ln=01;36:mh=00:pi=40;33:so=01;35:do=01;35:bd=40;33;01:cd=40;33;01:or=40;31;01:mi=00:su=37;41:sg=30;43:ca=30;41:tw=30;42:ow=34;42:st=37;44:ex=01;32:*.tar=01;31:*.tgz=01;31:*.arc=01;31:*.arj=01;31:*.taz=01;31:*.lha=01;31:*.lz4=01;31:*.lzh=01;31:*.lzma=01;31:*.tlz=01;31:*.txz=01;31:*.tzo=01;31:*.t7z=01;31:*.zip=01;31:*.z=01;31:*.dz=01;31:*.gz=01;31:*.lrz=01;31:*.lz=01;31:*.lzo=01;31:*.xz=01;31:*.zst=01;31:*.tzst=01;31:*.bz2=01;31:*.bz=01;31:*.tbz=01;31:*.tbz2=01;31:*.tz=01;31:*.deb=01;31:*.rpm=01;31:*.jar=01;31:*.war=01;31:*.ear=01;31:*.sar=01;31:*.rar=01;31:*.alz=01;31:*.ace=01;31:*.zoo=01;31:*.cpio=01;31:*.7z=01;31:*.rz=01;31:*.cab=01;31:*.wim=01;31:*.swm=01;31:*.dwm=01;31:*.esd=01;31:*.jpg=01;35:*.jpeg=01;35:*.mjpg=01;35:*.mjpeg=01;35:*.gif=01;35:*.bmp=01;35:*.pbm=01;35:*.pgm=01;35:*.ppm=01;35:*.tga=01;35:*.xbm=01;35:*.xpm=01;35:*.tif=01;35:*.tiff=01;35:*.png=01;35:*.svg=01;35:*.svgz=01;35:*.mng=01;35:*.pcx=01;35:*.mov=01;35:*.mpg=01;35:*.mpeg=01;35:*.m2v=01;35:*.mkv=01;35:*.webm=01;35:*.ogm=01;35:*.mp4=01;35:*.m4v=01;35:*.mp4v=01;35:*.vob=01;35:*.qt=01;35:*.nuv=01;35:*.wmv=01;35:*.asf=01;35:*.rm=01;35:*.rmvb=01;35:*.flc=01;35:*.avi=01;35:*.fli=01;35:*.flv=01;35:*.gl=01;35:*.dl=01;35:*.xcf=01;35:*.xwd=01;35:*.yuv=01;35:*.cgm=01;35:*.emf=01;35:*.ogv=01;35:*.ogx=01;35:*.aac=00;36:*.au=00;36:*.flac=00;36:*.m4a=00;36:*.mid=00;36:*.midi=00;36:*.mka=00;36:*.mp3=00;36:*.mpc=00;36:*.ogg=00;36:*.ra=00;36:*.wav=00;36:*.oga=00;36:*.opus=00;36:*.spx=00;36:*.xspf=00;36:
MAKE=make
MAKEFLAGS= V=1
MAKELEVEL=1
MAKE_TERMERR=/dev/pts/0
MAKE_TERMOUT=/dev/pts/0
MFLAGS=
MKL_THREADING_LAYER=GNU
MPLBACKEND=Agg
NLTK_DATA=/ext/data/nltk_data
NVM_INC=/cocalc/nvm/versions/node/v16.19.1/include/node
OLDPWD=/ext/sage/9.7
PATH=/ext/sage/9.7/build/bin:/ext/sage/9.7/src/bin:/ext/sage/9.7/local/bin:/cocalc/bin:/cocalc/src/smc-project/bin:/home/user/bin:/home/user/.local/bin:/ext/bin:/usr/lib/xpra:/opt/ghc/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/ext/data/homer/bin:/ext/data/weblogo:/usr/lib/postgresql/10/bin
PGHOST=localhost
PROMPT_COMMAND=history -a
PWD=/ext/sage/9.7/build/make
PYTHONPATH=/ext/sage/9.7/local
PYTHONUSERBASE=/home/user/.local
QT_QPA_PLATFORM=xcb
SAGE_ATLAS_LIB=/usr/lib/
SAGE_ENV_CONFIG_SOURCED=1
SAGE_LOCAL=/ext/sage/9.7/local
SAGE_LOGFILE=logs/install.log
SAGE_LOGS=/ext/sage/9.7/logs/pkgs
SAGE_NUM_THREADS=1
SAGE_NUM_THREADS_PARALLEL=4
SAGE_ORIG_PATH=/cocalc/bin:/cocalc/src/smc-project/bin:/home/user/bin:/home/user/.local/bin:/ext/bin:/usr/lib/xpra:/opt/ghc/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/ext/data/homer/bin:/ext/data/weblogo:/usr/lib/postgresql/10/bin
SAGE_ORIG_PATH_SET=True
SAGE_PKGCONFIG=/ext/sage/9.7/local/lib/pkgconfig
SAGE_ROOT=/ext/sage/9.7
SAGE_SHARE=/ext/sage/9.7/local/share
SAGE_SRC=/ext/sage/9.7/src
SAGE_VENV=/ext/sage/9.7/local/var/lib/sage/venv-python3.10.5
SCREENDIR=/tmp/screen
SHELL=/bin/bash
SHLVL=3
SMC=/tmp/.cocalc
TERM=xterm-256color
TZ=Etc/UTC
USER=user
XDG_RUNTIME_DIR=/tmp/xdg-runtime-user
_=/usr/bin/env
_JAVA_OPTIONS=-Xms64m
***********************************************
make[1]: Entering directory '/ext/sage/9.7/build/make'
make --no-print-directory toolchain
make[2]: Nothing to be done for 'toolchain'.
make --no-print-directory toolchain-deps
make --no-print-directory /ext/sage/9.7/local/var/lib/sage/installed/.dummy
make[3]: '/ext/sage/9.7/local/var/lib/sage/installed/.dummy' is up to date.
make --no-print-directory /ext/sage/9.7/local/var/lib/sage/installed/.dummy
make[3]: '/ext/sage/9.7/local/var/lib/sage/installed/.dummy' is up to date.
make --no-print-directory /ext/sage/9.7/local/var/lib/sage/installed/.dummy
make[3]: '/ext/sage/9.7/local/var/lib/sage/installed/.dummy' is up to date.
make --no-print-directory /ext/sage/9.7/local/var/lib/sage/installed/.dummy
make[3]: '/ext/sage/9.7/local/var/lib/sage/installed/.dummy' is up to date.
make[1]: Leaving directory '/ext/sage/9.7/build/make'
 
real 0m0.278s
user 0m0.238s
sys 0m0.020s
Sage build/upgrade complete!
 
Error: package 'parsivelib' not found
Note: if it is an old-style package, installing these is no longer supported
~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
[22;0t[6nsage: load('init.sage')
[6nsage: B = C.crystalline_cohomology_basis()
[6nsage: B0 = B[0]
[6nsage: sage: om = B[0].omega8
[6nsage: om
[(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y])
[6nsage: second_patch(om)
[(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(2*x/(x^2 + 2))*y])
[6nsage: second_patch(om).r()
((-1)/y) dx
[6nsage: second_patch(om.r())
((-1)/y) dx
[6nssage: om = second_patch(om)
[6nsage: om.regular_form()
[0] d[x] + [1] d[y] + V(((x^5 + x^3)/y) dx) + dV(x*y)
[6nsage: om = B[1].omega8
[6nsage: om = second_patch(om)
[6nsage: om.regular_form()
[0] d[x] + [2*x] d[y] + V(((-x^10 - x^8 - x^6 + x^2)/(x^2*y - y)) dx) + dV((2*x^4 + 2*x^2 + 2)*y)
[6nsage: Rx
Univariate Polynomial Ring in x over Finite Field of size 3
[6nsage: (-x^10 - x^8 - x^6 + x^2).quo_rem(x^2 - 1)
(2*x^8 + x^6 + 1, 1)
~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
[22;0t[6nsage: load('init.sage')
[6nsage: load('init.sage')
[6nsage: eta2
([(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^10 + x^8 - x^2 + 1)/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[6nsage: eta2.r()
((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
[6nsage: eta2.omega0.regular_form()
[0] d[x] + [x] d[y] + V(0 dx) + dV((2*x^4 + 2*x^2 + 2)*y)
[6nsage: second_patch(eta2.omega8).regular_form()
[0] d[x] + [2*x] d[y] + V(((-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV((2*x^4 + 2*x^2 + 2)*y)
[6nsage: (-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1).quo_rem(x^10 - x^8)
(2*x^8 + x^6 + 2, x^8 + 2*x^4 + 2*x^2 + 2)
[6nsage: C.crystalline_cohomology_basis()[1]
([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[6nssage: ETA2 = C.crystalline_cohomology_basis()[1]
[6nsage: ETA2 - eta2
(V(((x^8 - x^6 + 1)/y) dx) + dV([(x^4 + x^2 + 1)*y]), V((x^4 + x^2 + 1)*y), V(((x^8 - x^6 + 1)/y) dx))
[6nsage: (C.x^8 - C.x^6 + C.one)/C.y)*C.dx
Input In [11]
(C.x**Integer(8) - C.x**Integer(6) + C.one)/C.y)*C.dx
^
SyntaxError: unmatched ')'
 
[6nsage: (C.x^8 - C.x^6 + C.one)/C.y*C.dx
((x^8 - x^6 + 1)/y) dx
[6nsage: ((C.x^8 - C.x^6 + C.one)/C.y*C.dx).expansion_at_infty()
t^-16 + t^-8 + O(t^-6)
[6nsage: om = eta.omega8
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [14], in <cell line: 1>()
----> 1 om = eta.omega8
 
AttributeError: 'function' object has no attribute 'omega8'
[6nsage: om = eta2.omega8
[6nsage: om.r()
((-1)/(x*y)) dx
[6nsage: second_patch(om.r())
(x/y) dx
[6nsage: u = C.one/C.x
[6nsage: v = C.y/(C.x)^2
[6nsasage: om - u.teichmuller()*v.teichmuller().diffn()
[(1/(x^4 + 2*x^2))*y] d[x] + V(((-x^18 - x^16 - x^14 - x^10 - x^8 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([((2*x^6 + 2)/(x^8 + 2*x^6))*y])
[6nsage: om + u.teichmuller()*v.teichmuller().diffn()
V(((-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
[6nsage: sage: om1 = om + u.teichmuller()*v.teichmuller().diffn()
sage: om1.omega.expansion_at_infty()
2*t^-16 + 2*t^-8 + O(t^-6)
sage: om1.frobenius()
((-x^6 + x^4 + x^2 - 1)/(x^6*y)) dx
sage: om1.frobenius().expansion_at_infty()
2 + 2*t^4 + t^8 + O(t^10)
sage: om1.h2.expansion_at_infty()
2*t + 2*t^5 + t^9 + 2*t^13 + O(t^21)
sage: load('init.sage')
sage: C.crystalline_cohomology_basis()[1]
result.omega8 == compare False
result.omega8 == compare False
([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[6nsage: load('init.sage')
[6nsage: C.crystalline_cohomology_basis()[1]
result.omega8 == compare False
result.omega8 - compare dV([((x^2 + 1)/x^3)*y])
result.omega8 == compare False
result.omega8 - compare dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[6nsage:
sage: ETA2 = C.crystalline_cohomology_basis()[1]
result.omega8 == compare False
result.omega8 - compare dV([((x^2 + 1)/x^3)*y])
result.omega8 == compare False
result.omega8 - compare dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
sage: load('init.sage')
sage: ETA2 = C.crystalline_cohomology_basis()[1]
result.omega8 == compare False
result.omega8 - compare dV([((2*x^2 + 1)/x^3)*y])
result.omega8 == compare False
result.omega8 - compare dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
sage: load('init.sage')
sage: ETA2 = C.crystalline_cohomology_basis()[1]
result.omega8 == compare False
result.omega8 - compare dV([1/x^3*y])
result.omega8 == compare False
result.omega8 - compare dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
[6nsage: load('init.sage')
[6nsage: ETA2 = C.crystalline_cohomology_basis()[1]
result.omega8 == compare True
result.omega8 - compare 0
result.omega8 == compare True
result.omega8 - compare 0
[6nsage: om = ETA2.omega8
[6nsage: second_patch(om)
[(2/(x^2 + 2))*y] d[x] + V(((-x^2)/y) dx) + dV([(1/(x^2 + 2))*y])
[6nsage: u = C.one/C.x
[6nsage:
[6nsage: v = C.y/(C.x)^2
[6nsage: om - u.teichmuller()*v.teichmuller().diffn()
[(1/(x^4 + 2*x^2))*y] d[x] + V(((x^8 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([((2*x^6 + 2)/(x^8 + 2*x^6))*y])
[6nsage: om + u.teichmuller()*v.teichmuller().diffn()
V(((x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
[6nsage: A = om + u.teichmuller()*v.teichmuller().diffn()
sage: A.omega.expansion_at_infty()
t^4 + t^8 + 2*t^12 + O(t^14)
sage: A.h2.expansion_at_infty()
2*t + 2*t^5 + t^9 + 2*t^13 + O(t^21)
sage: autom(ETA2).coordinates()
(1, 1)
result.omega8 == compare True
result.omega8 - compare 0
result.omega8 == compare True
result.omega8 - compare 0
aux (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), [0], V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [47], in <cell line: 1>()
----> 1 autom(ETA2).coordinates()
 
File <string>:84, in coordinates(self, basis)
 
File <string>:168, in pth_root(self)
 
ValueError: Function is not a p-th power.
[6nsasage: ETA1 = C.crystalline_cohomology_basis()[0]
result.omega8 == compare True
result.omega8 - compare 0
result.omega8 == compare True
result.omega8 - compare 0
[6nsage: aux = autom(ETA2) - ETA1 - ETA2
[6nsage: aux
(V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y]), [(1/(x^2 + x))*y] + V(((x^5 + x^4 + 2*x^3 + x^2 + 2*x + 1)/(x^2 + x))*y), [((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*y]))
[6nsage: aux1 = C.x.teisage: aux1 = aux
[6nsage: sage: C.y/(C.x^2+C.x)
(1/(x^2 + x))*y
[6nsage: C.y/(C.x^2+C.x).expansion_at_infty()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [53], in <cell line: 1>()
----> 1 C.y/(C.x**Integer(2)+C.x).expansion_at_infty()
 
File <string>:75, in __truediv__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
493 """
--> 494 return self.getattr_from_category(name)
495
496 cdef getattr_from_category(self, name):
 
File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
505 else:
506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
508
509 def __dir__(self):
 
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
359 dummy_error_message.cls = type(self)
360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
362 attribute = <object>attr
363 # Check for a descriptor (__get__ in Python)
 
AttributeError: 'sage.rings.laurent_series_ring_element.LaurentSeries' object has no attribute 'function'
[6nsage: (C.y/(C.x^2+C.x)).expansion_at_infty()
t + 2*t^3 + t^5 + 2*t^9 + 2*t^13 + t^17 + O(t^21)
[6nsage: aux1
(V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y]), [(1/(x^2 + x))*y] + V(((x^5 + x^4 + 2*x^3 + x^2 + 2*x + 1)/(x^2 + x))*y), [((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*y]))
[6nsage: aux1.f.t = 0*C.x
[6nsage: aux1.omega0.h2 = 0*Cx
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [57], in <cell line: 1>()
----> 1 aux1.omega0.h2 = Integer(0)*Cx
 
NameError: name 'Cx' is not defined
[6nsage: aux1.omega0.h2 = 0*C.x
[6nsage: aux1.f -= aux.omega0.h2.verschiebung()
[6nsage: aux1
(V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), V(((x^5 + x^4 + 2*x^3 + x^2 + 2*x + 1)/(x^2 + x))*y), [((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*y]))
[6nsage: aux1.omega8 = aux1.omega0 - aux1.f.diffn()
[6nsage: aux1
(V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), V(((x^5 + x^4 + 2*x^3 + x^2 + 2*x + 1)/(x^2 + x))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((2*x^5 + 2*x^4 + x^3 + 2*x^2 + x + 2)/(x^2 + x))*y]))
[6nsasage: test = (C.x)^(-p+1)*aux1.omega0.omega
[6nsage: test
((-x^2 + x + 1)/(x^3*y + x^2*y + x*y)) dx
[6nsage: fct = superellliptic_function(C, test.form)
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [65], in <cell line: 1>()
----> 1 fct = superellliptic_function(C, test.form)
 
NameError: name 'superellliptic_function' is not defined
[6nsage: fct = superelliptic_function(C, test.form)
[6nsage: fct.pth_root()
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [67], in <cell line: 1>()
----> 1 fct.pth_root()
 
File <string>:168, in pth_root(self)
 
ValueError: Function is not a p-th power.
[6nsage: (3*C.x.teichmuller()).diffn()
dV([x^3])
[6nsage: (2*C.x.teichmuller()).diffn()
[2] d[x]dV([x^3])
[6nsage: ETA1
([(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), V(((x^2 + 1)/x)*y), [(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[6nsage: (2*C.x.teichmuller()).diffn()
[2] d[x]dV([x^3])
[6nsage: load('init.sage')
[6nsage: (2*C.x.teichmuller()).diffn()
[2] d[x] + dV([x^3])
[6nsage: 2*((C.x.teichmuller()).diffn())
[2] d[x] + V((x^2) dx)
[6nsage: (2*C.x.teichmuller()).diffn() == 2*((C.x.teichmuller()).diffn())
False
[6nsage: sage: load('init.sage')
[6n[6n[6nsage: (2*C.x.teichmuller()).diffn(), 2*((C.x.teichmuller()).diffn())
([2] d[x] + dV([x^3]), [2] d[x] + V((x^2) dx))
[6nsage: (2*(C.x.teichmuller())).diffn(), 2*((C.x.teichmuller()).diffn())
([2] d[x] + dV([x^3]), [2] d[x] + V((x^2) dx))
[6nsage: (2*(C.x.teichmuller())).diffn(), (C.x.teichmuller()+C.x.teichmuller()).diffn()
([2] d[x] + dV([x^3]), [2] d[x] + dV([x^3]))
~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
[22;0t[6nsage: load('init.sage')
[6nsasage: (2*(C.x.teichmuller())).diffn(), (C.x.teichmuller()+C.x.teichmuller()).diffn()
([2] d[x] + dV([x^3]), [2] d[x] + dV([x^3]))
[6nsage: sage: (2*C.x.teichmuller()).diffn(), 2*((C.x.teichmuller()).diffn())
([2] d[x] + dV([x^3]), [2] d[x] + V((x^2) dx))
[6nsage: (2*(C.x.teichmuller())).diffn(), 2*((C.x.teichmuller()).diffn())
([2] d[x] + dV([x^3]), [2] d[x] + V((x^2) dx))
[6nsage: 3*(C.x.teichmuller().diffn())
+ V((x^2) dx)
[6nsage: 3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()
False
[6nsage: load('init.sage')
[6nsage: 3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()
True False
False
[6nsage: load('init.sage')
[6nsage: 3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()
(self.omega - other.omega).cartier() - H.diffn() (-1) dx
False
[6nsage: load('init.sage')
[6nsage: 3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()
H 2*x
(self.omega - other.omega).cartier() - H.diffn() (-1) dx
False
[6nsage: load('init.sage')
[6nsage: 3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()
H 2*x
(self.omega - other.omega).cartier() 1 dx
False
[6nsage: load('init.sage')
[6nsage: 3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()
True
sage: for a in range(0, 9):
....: print(a*(C.x.teichmuller().diffn()) == a*(C.x.teichmuller()).diffn())
....:
True
True
True
True
True
True
True
True
True
[6nsage: C.y.teichmuller().diffn()
[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[6nssage: ETA2 = C.crystalline_cohomology_basis()[1]
result.omega8 == compare True
result.omega8 - compare 0
result.omega8 == compare True
result.omega8 - compare 0
[6nsage: ETA1 = C.crystalline_cohomology_basis()[0]
result.omega8 == compare True
result.omega8 - compare 0
result.omega8 == compare True
result.omega8 - compare 0
[6nsage: ETA2
([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[6nsage: load('init.sage')
[6nsage: ETA2 = C.crystalline_cohomology_basis()[1]
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
[6nsage: C.de_rham_basis()[1]
((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
[6nssage: (3/2)%9
6
[6nsage: C.y.teichmuller().diffn()
[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[6nsage: (-1/2)%9
4
[6nsage: 3*C.x.teichmuller()
V(x^3)
[6nsage: 3*C.x.teichmuller().diffn()
V((x^2) dx)
[6nsage: C.y.diffn()
(1/y) dx
[6nsage: ((-C.x^7 + C.x^3 + C.x)/(C.x^2*C.y - C.y)) == (C.y)^(-3)*C.x^2*C.dx+ 2*C.x^8*(C.y)^(-3)+(C.x^5 - C.x^7)/(2*C.y^5)
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [31], in <cell line: 1>()
----> 1 ((-C.x**Integer(7) + C.x**Integer(3) + C.x)/(C.x**Integer(2)*C.y - C.y)) == (C.y)**(-Integer(3))*C.x**Integer(2)*C.dx+ Integer(2)*C.x**Integer(8)*(C.y)**(-Integer(3))+(C.x**Integer(5) - C.x**Integer(7))/(Integer(2)*C.y**Integer(5))
 
File <string>:19, in __add__(self, other)
 
AttributeError: 'superelliptic_function' object has no attribute 'form'
[6nsage: ((-C.x^7 + C.x^3 + C.x)/(C.x^2*C.y - C.y)) == (C.y)^(-3)*C.x^2+ 2*C.x^8*(C.y)^(-3)+(C.x^5 - C.x^7)/(2*C.y^5)
True
[6nsage: C.de_rham_basis()[1]
((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
[6nsage: om = C.de_rham_basis()[1].omega8
[6nsage: second_patch(om)
(x/y) dx
[6nsage: second_patch(om).regular_form()
2*x dy
[6nsage: load('init.sage')
[6nsage: C.crystalline_cohomology_basis()[1]
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [38], in <cell line: 1>()
----> 1 C.crystalline_cohomology_basis()[Integer(1)]
 
File <string>:52, in crystalline_cohomology_basis(self, prec)
 
File <string>:23, in de_rham_witt_lift(cech_class, prec)
 
NameError: name 'omega' is not defined
[6nsage: load('init.sage')
[6nsage: C.crystalline_cohomology_basis()[1]
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [40], in <cell line: 1>()
----> 1 C.crystalline_cohomology_basis()[Integer(1)]
 
File <string>:52, in crystalline_cohomology_basis(self, prec)
 
File <string>:24, in de_rham_witt_lift(cech_class, prec)
 
File <string>:13, in de_rham_witt_lift_form8(omega)
 
NameError: name 'g' is not defined
[6nsage: load('init.sage')
[6nsage: C.crystalline_cohomology_basis()[1]
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[6nsage: C.x.teichmuller()*C.y.teichmuller().diffn()
[(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y])
[6nsage: A = C.x.teichmuller()*C.y.teichmuller().diffn()
[6nsage: B = de_rham_witt_lift_form0(C.x/C.y*C.dx)
[6nsage: A == B
True
sage: eta1 = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).verschiebung())
sage: ETA1 = C.crystalline_cohomology_basis()[0]
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
sage: eta1 - ETA1
( + V(((-x^3)/y) dx) + dV([2*x*y]), V(2*x*y), V(((-x^3)/y) dx))
sage: (eta1 - ETA1).reduce()
(V(((-x^3)/y) dx), [0], V(((-x^3)/y) dx))
sage: eta1
([(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^3 + x)/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^3 + x)/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[6nsage: eta1.omega0
[(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^3 + x)/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y])
[6nsage: eta1.omega0.regular_form()
[0] d[x] + [1] d[y] + V((x^5/y) dx) + dV(2*x*y)
[6nsage: second_patch(eta1.omega8).regular_form()
[0] d[x] + [1] d[y] + V(((x^8 + x^6 + 1)/(x^3*y)) dx) + dV(x*y)
[6nsage: second_patch(ETA1.omega8).regular_form()
[0] d[x] + [1] d[y] + V(((x^5 + x^3)/y) dx) + dV(x*y)
[6nsage: v = C.y/(C.x)^2
[6nsage: C.y - C.v - (C.y/C.x)^3
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [57], in <cell line: 1>()
----> 1 C.y - C.v - (C.y/C.x)**Integer(3)
 
AttributeError: 'superelliptic' object has no attribute 'v'
[6nsage: C.y - v - (C.y/C.x)^3
0
;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R;1R
bash: syntax error near unexpected token `;'
~/Research/2021 De Rham/DeRhamComputation/sage$
~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
[22;0t[6nsage: load('init.sage')
[6nsage: v = C.y/(C.x)^2
sage: C.y.teichmuller() - v.teichmuller()+ (C.y*v^2 - C.y^2*v).verschiebung() ==
....: ( (C.y/C.x)^3).teichmuller()
True
sage: C.y.teichmuller().diffn() - v.teichmuller().diffn()+ (C.y*v^2 - C.y^2*v).v
....: erschiebung().diffn() =( (C.y/C.x)^3).teichmuller().diffn()
Input In [4]
C.y.teichmuller().diffn() - v.teichmuller().diffn()+ (C.y*v**Integer(2) - C.y**Integer(2)*v).verschiebung().diffn() =( (C.y/C.x)**Integer(3)).teichmuller().diffn()
^
SyntaxError: cannot assign to expression here. Maybe you meant '==' instead of '='?
 
sage: C.y.teichmuller().diffn() - v.teichmuller().diffn()+ (C.y*v^2 - C.y^2*v).v
....: erschiebung().diffn()==( (C.y/C.x)^3).teichmuller().diffn()
 
True
[6nsage:
[6nsasage: (C.y/C.x)^2*(C.y/C.x).diffn()
((-x^4 + 1)/(x^2*y)) dx
sage: eta1 = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).vers
....: chiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).verschi
....: ebung())
[6nsage: ETA1 = C.crystalline_cohomology_basis()[0]
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
[6nsage: v
1/x^2*y
sage: (C.y/C.x)^2*(C.y/C.x).diffn()
((-x^4 + 1)/(x^2*y)) dx
[6nsage: (C.y*v^2 - C.y^2*v)
((2*x^4 + 2*x^2 + 2)/x^3)*y
[6nsage: (C.y*v^2 - C.y^2*v).coordinates()
[1]
sage: eta1
([(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^3 + x)/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^3 + x)/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
sage: om1 = v.teichmuller().diffn() + ((C.x)^(-2)*(C.y)^(-1)*C.dx).mult_by_p() +
....: (C.y/C.x^3).verschiebung().diffn()
 
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [14], in <cell line: 1>()
----> 1 om1 = v.teichmuller().diffn() + ((C.x)**(-Integer(2))*(C.y)**(-Integer(1))*C.dx).mult_by_p() +(C.y/C.x**Integer(3)).verschiebung().diffn()
 
AttributeError: 'superelliptic_form' object has no attribute 'mult_by_p'
[6nsage:
[6nsage: A = C.dx
[6nsagsage: mult_by_p(A)
V((x^2) dx)
sage: om1 = v.teichmuller().diffn() + mult_by_p((C.x)^(-2)*(C.y)^(-1)*C.dx) +(C.
....: y/C.x^3).verschiebung().diffn()
[6nsage: eta1.omega8 == om1
True
sage: eta1 - ETA1
( + V(((-x^3)/y) dx) + dV([2*x*y]), V(2*x*y), V(((-x^3)/y) dx))
[6nsage: (eta1 - ETA1).reduce()
(V(((-x^3)/y) dx), [0], V(((-x^3)/y) dx))
[6nsage: second_patch(C.x^3*C.y.diffn())
((-1)/(x^3*y)) dx
[6nsage: sage: (C.x^3*C.y.diffn()).expansion_at_infty()
t^-6 + 2*t^-2 + O(t^4)
[6nsage: (C.x^3*C.y.diffn()).expansion_at_infty(prec = 30)
t^-6 + 2*t^-2 + t^10 + t^18 + O(t^24)
[6nsage: [6n[6nsage: ETA2 = C.crystalline_cohomology_basis()[1]
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
[6nsage: ETA2 - eta2
( + V(((x^8 - x^6 + 1)/y) dx) + dV([(x^4 + x^2 + 1)*y]), V((x^4 + x^2 + 1)*y), V(((x^8 - x^6 + 1)/y) dx))
[6nsage: (ETA2 - eta2).reduce()
(V(((x^8 - x^6 + 1)/y) dx), [0], V(((x^8 - x^6 + 1)/y) dx))
[6nsage: A = (ETA2 - eta2).reduce()
[6nsage: A = A.omega8.omega
sage: A.expansion_at_infty()
t^-16 + t^-8 + O(t^-6)
sage: A.expansion_at_infty(prec = 30)
t^-16 + t^-8 + t^-4 + 1 + 2*t^4 + 2*t^12 + O(t^14)
sage: A.cartier().expansion_at_infty()
t^-6 + 2*t^-2 + O(t^4)
[6nsage:sage: C.de_rham_basis()[1]
((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
[6nsage: second_patch(C.de_rham_basis()[1].omega8)
(x/y) dx
[6nsage: u
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [34], in <cell line: 1>()
----> 1 u
 
NameError: name 'u' is not defined
[6nsage: u = C.one/C.x
[6nsage: sage: -u*v.diffn()
((-1)/(x*y)) dx
[6nsage: autom(ETA2).coordinates()
(1, 1)
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
aux (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), [0], V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [37], in <cell line: 1>()
----> 1 autom(ETA2).coordinates()
 
File <string>:84, in coordinates(self, basis)
 
File <string>:168, in pth_root(self)
 
ValueError: Function is not a p-th power.
[6nsage: A = ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))* C.dx
[6nsage: A.cartier().expansion_at_infty()
1 + 2*t^2 + t^4 + t^6 + 2*t^8 + O(t^10)
[6nsage: A.expansion_at_infty(prec = 30)
2*t^-2 + 2 + 2*t^4 + t^6 + t^12 + t^16 + t^18 + 2*t^22 + O(t^28)
[6nsage: load('init.sage')
[6nssage: Bcrys = C.crystalline_cohomology_basis()
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
[6nsasage: autom(Bcrys[1]).coordinates(basis = Bcrys)
(1, 1)
aux (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), [0], V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [43], in <cell line: 1>()
----> 1 autom(Bcrys[Integer(1)]).coordinates(basis = Bcrys)
 
File <string>:85, in coordinates(self, basis)
 
File <string>:56, in coordinates(self)
 
File <string>:93, in coordinates(self, basis)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
786 return self._call_with_args(x, args, kwds)
787
--> 788 cpdef Element _call_(self, x):
789 """
790 Call method with a single argument, not implemented in the base class.
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
1249 return num
1250 if check and not den.is_unit():
1251 # This should probably be a ValueError.
1252 # However, too much existing code is expecting this to throw a
1253 # TypeError, so we decided to keep it for the time being.
-> 1254 raise TypeError("fraction must have unit denominator")
1255 return num * den.inverse_of_unit()
 
TypeError: fraction must have unit denominator
[6nsage: load('init.sage')
[6nsasage: load('init.sage')
[6nsage: Bcrys = C.crystalline_cohomology_basis()
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
[6nsage: autom(Bcrys[1]).coordinates(basis = Bcrys)
coordinates of form self (1/y) dx
(1, 1)
aux (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), [0], V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
aux_divided_by_p (((x + 1)/(x*y - y)) dx, 0, ((x + 1)/(x*y - y)) dx)
aux_divided_by_p.omega8 == aux.omega8.omega.cartier() True
coordinates of form self ((x + 1)/(x*y - y)) dx
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [47], in <cell line: 1>()
----> 1 autom(Bcrys[Integer(1)]).coordinates(basis = Bcrys)
 
File <string>:87, in coordinates(self, basis)
 
File <string>:56, in coordinates(self)
 
File <string>:94, in coordinates(self, basis)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
786 return self._call_with_args(x, args, kwds)
787
--> 788 cpdef Element _call_(self, x):
789 """
790 Call method with a single argument, not implemented in the base class.
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
1249 return num
1250 if check and not den.is_unit():
1251 # This should probably be a ValueError.
1252 # However, too much existing code is expecting this to throw a
1253 # TypeError, so we decided to keep it for the time being.
-> 1254 raise TypeError("fraction must have unit denominator")
1255 return num * den.inverse_of_unit()
 
TypeError: fraction must have unit denominator
[6nsage: load('init.sage')
[6nsage: Bcrys = C.crystalline_cohomology_basis()
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
[6nsage: AA = autom(Bcrys[1]).coordinates(basis = Bcrys)
coordinates of form self (1/y) dx
(1, 1)
[6nsage: AA
( + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y]), [(1/(x^2 + x))*y] + V(((x^5 + x^4 + 2*x^3 + x^2 + 2*x + 1)/(x^2 + x))*y), [((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*y]))
[6nsage: AA.reduce()
( + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(1/(x^2 + x + 1))*y]), [0], + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(1/(x^2 + x + 1))*y]))
[6nsage: AA
( + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(1/(x^2 + x + 1))*y]), [0], + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(1/(x^2 + x + 1))*y]))
[6nsage: om = AA.omega0.omega
[6nsasage: om
((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx
[6nsage: om.cartier()
((x + 1)/(x*y - y)) dx
[6nsage: om.cartier().expansion_at_infty()
1 + 2*t^2 + t^4 + t^6 + 2*t^8 + O(t^10)
[6nsage: autom(Bcrys[1])
([(1/(x^2 + 2*x))*y] d[x] + V(((x^4 - x^3 - x^2 + x + 1)/(x^2*y + x*y + y)) dx) + dV([((x^6 + 2*x^5 + 2*x^3 + x^2 + x)/(x^2 + x + 1))*y]), [(2/(x + 1))*y] + V((x^4 + x^3 + x^2)*y), [(2/(x^4 + x^3 + 2*x^2 + 2*x))*y] d[x] + V(((-x^7 - x^6 + x^4 - x^3 - x^2 + 1)/(x^6*y - x^5*y - x^4*y - x^3*y - x^2*y - x*y + y)) dx) + dV([((2*x^4 + 2*x^3 + 2*x^2 + x)/(x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 1))*y]))
[6nsage: autom(Bcrys[1]) - Bcrys[0] - Bcrys[1]
( + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y]), [(1/(x^2 + x))*y] + V(((x^5 + x^4 + 2*x^3 + x^2 + 2*x + 1)/(x^2 + x))*y), [((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*y]))
[6nsage: rr = autom(Bcrys[1]) - Bcrys[0] - Bcrys[1]
[6nsage: Bcrys[1]
([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[6nsage: om = Bcrys[1].omega0
[6nsage: om
[(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y])
[6nsage: sage: om1 = Bcrys[1].omega0
[6nsage: om0 = Bcrys[0].omega0
[6nsage: sage: autom(om1)
[(1/(x^2 + 2*x))*y] d[x] + V(((x^4 - x^3 - x^2 + x + 1)/(x^2*y + x*y + y)) dx) + dV([((x^6 + 2*x^5 + 2*x^3 + x^2 + x)/(x^2 + x + 1))*y])
[6nsage: autom(om1) - om1 - om0
+ V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y])
[6nsage: om1
[(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y])
[6nsage: om1.omega
((x^4 + x^2 - 1)/(x^2*y - y)) dx
[6nsage: om1.omega.regular_form()
[6nsage: Bcrys[1]
([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
[6nsage: om1 - C.x.teichmuller()*C.y().teichmuller().diffn()
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [72], in <cell line: 1>()
----> 1 om1 - C.x.teichmuller()*C.y().teichmuller().diffn()
 
TypeError: 'superelliptic_function' object is not callable
[6nsage: om1 - C.x.teichmuller()*C.y.teichmuller().diffn()
V(((x^8 - x^6 + 1)/y) dx)
[6nsage: autom(C.x.teichmuller().diffn())
[1] d[x]dV([x^2 + x])
[6nsage: autom(om1) - om1 - om0
+ V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y])
[6nsage: om1.regular_form()
[0] d[x] + [x] d[y] + V(((x^8 - x^6 + 1)/y) dx) + dV(0)
[6nsage: om0.regular_form()
[0] d[x] + [1] d[y] + V(((x^5 + x^3)/y) dx) + dV(0)
[6nsage: g = (x^8 - x^6)
[6nsage: g(x+1) - g
2*x^7 + x^6 + 2*x^5 + x^4 + x^2 + 2*x
[6nsage: A = autom(om1) - om1 - om0
[6nsage: B = ((C.x^2 sage: B = ((C.x^2 + C.x)*C.y^2*C.y.diffn()).verschiebung() + ((2*C.x^7 + C.x^6 + C.x^5 + C.x^4 + 2*C.x^3+C.x^2+2*C.x)*C.y.diffn()).verschiebung()
[6nssage: A == B
True
[6nsage: A.cartier()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [83], in <cell line: 1>()
----> 1 A.cartier()
 
AttributeError: 'superelliptic_drw_form' object has no attribute 'cartier'
[6nsage: A.omega.cartier()
((x + 1)/(x*y - y)) dx
[6nsage: sage: A
+ V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y])
[6nsage: (x^5 + x^4 + x^2 + x).quo_rem(x^2 + x + 1)
(x^3 + 2*x + 2, 1)
[6nsage: u
1/x
sage: u.expansion_at_infty()
t^2 + 2*t^6 + 2*t^10 + t^14 + 2*t^18 + O(t^22)
sage: v.expansion_at_infty()
t + O(t^21)
sage: A
+ V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y])
[6nsage: A.omega.cartier()
((x + 1)/(x*y - y)) dx
[6nsage: A.omega.cartier().cartier()
((-1)/y) dx
[6nsage: load('init.sage')
[6nsage: om = (C.y)^(-1)*C.dx
[6nsage: inv_cartier(om)
((x^3 - x)/y) dx
[6nsage: inv_cartier(inv_cartier(om))
((x^12 - x^10 - x^6 + x^4)/y) dx
[6nsage: ii = inv_cartier(inv_cartier(om))
[6nsage: ((-C.x^3 +C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx - ii
((-x^14 - x^13 + x^11 + x^10 + x^8 + x^7 - x^5 - x^4 - x^3 + x^2 + x)/(x^2*y + x*y + y)) dx
sage: ii.is_regular_on_U0()
True
sage: (((-C.x^3 +C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx - ii).cartier()
((-x^4 + x^3 + x^2 + 1)/(x*y - y)) dx
sage: (((-C.x^3 +C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx - ii).cartier().cartier()
(1/y) dx
[6nsage: (((-C.x^3 +C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx + ii).cartier()
((x^4 - x^3 - x^2 - x + 1)/(x*y - y)) dx
[6nsage: (((-C.x^3 +C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx + ii).cartier().cartier()
0 dx
[6nsage: (((-C.x^3 +C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx + ii).cartier().cartier()
0 dx
[6nsage: x
x
[6nsasage: G = x^3 + x
sage: G.integral()
x^4 + 2*x^2
sage: G = x^3 + x + x^2
sage: G.integral()
---------------------------------------------------------------------------
ZeroDivisionError Traceback (most recent call last)
Input In [109], in <cell line: 1>()
----> 1 G.integral()
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:3994, in sage.rings.polynomial.polynomial_element.Polynomial.integral()
3992 cdef Py_ssize_t n
3993 zero = Q.zero()
-> 3994 p = [zero] + [cm.bin_op(Q(self.get_unsafe(n)), n + 1, operator.truediv)
3995 if self.get_unsafe(n) else zero for n in range(self.degree() + 1)]
3996 return S(p)
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
1202 self._record_exception()
1203 else:
-> 1204 return PyObject_CallObject(op, xy)
1205
1206 if op is mul:
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
1735 cdef int cl = classify_elements(left, right)
1736 if HAVE_SAME_PARENT(cl):
-> 1737 return (<Element>left)._div_(right)
1738 if BOTH_ARE_ELEMENT(cl):
1739 return coercion_model.bin_op(left, right, truediv)
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
2622 if right_inverse is None:
-> 2623 raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
2624 else:
2625 return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)
 
ZeroDivisionError: inverse of Mod(0, 3) does not exist
[6nsage: load('init.sage')
[6nsage: om = (C.y/C.x).diffn()
[6nsage: om.int()
((x^5 + x)/y) dx
[6nsage: load('init.sage')
[6nsage: om.int()
((x^5 + x)/y) dx
[6nsage: om.int() - (C.y/C.x)
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [115], in <cell line: 1>()
----> 1 om.int() - (C.y/C.x)
 
File <string>:26, in __sub__(self, other)
 
AttributeError: 'superelliptic_function' object has no attribute 'form'
[6nsage: load('init.sage')
[6nsage: om = (C.y/C.x).diffn()
[6nsage: om.int() - (C.y/C.x)
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [118], in <cell line: 1>()
----> 1 om.int() - (C.y/C.x)
 
File <string>:199, in int(self)
 
File <string>:19, in __add__(self, other)
 
AttributeError: 'superelliptic_function' object has no attribute 'form'
[6nsage: om.int()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [119], in <cell line: 1>()
----> 1 om.int()
 
File <string>:199, in int(self)
 
File <string>:19, in __add__(self, other)
 
AttributeError: 'superelliptic_function' object has no attribute 'form'
[6nsage: load('init.sage')
[6nsage: om = (C.y/C.x).diffn()
[6nsage: om.carier()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [122], in <cell line: 1>()
----> 1 om.carier()
 
AttributeError: 'superelliptic_form' object has no attribute 'carier'
[6nsage: om.cartier().expansion_at_infty()
0
[6nsage: om.cartier()
0 dx
[6nsage: om.int() - (C.y/C.x)
((x^5 + 2*x^2 + x + 1)/(x^3 + 2*x))*y
[6nsage: (om.int() - (C.y/C.x)).pth_root()
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [126], in <cell line: 1>()
----> 1 (om.int() - (C.y/C.x)).pth_root()
 
File <string>:168, in pth_root(self)
 
ValueError: Function is not a p-th power.
[6nsage: om = C.dx
[6nsage: om.int()
x
[6nsage: om = C.y.diffn()
[6nsage: om.int()
((x^3 + x)/(x^2 + 2))*y
[6nsage: om.int() - C.y
((x^3 + 2*x^2 + x + 1)/(x^2 + 2))*y
[6nsage: (om.int() - C.y).pth_root()
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [132], in <cell line: 1>()
----> 1 (om.int() - C.y).pth_root()
 
File <string>:168, in pth_root(self)
 
ValueError: Function is not a p-th power.
[6nsage: om.int().diffn()
(x^5/(x^2*y - y)) dx
[6nsage: load('init.sage')
[6nsage: om = C.y.diffn()
[6nsage: om.int().diffn()
(1/y) dx
[6nsage: om = (C.y/C.x).diffn()
[6nsage: om.int().diffn()
((-x^2 - 1)/(x*y)) dx
[6nsage: om.int().diffn() == om
True
[6nsage: om.int()
((x^4 + 1)/(x^5 + x^3 + x))*y
[6nsage: om = C.x*C.y
[6nsage: om = om.diffn()
[6nsage: om.int()
((x^5 + x^3)/(x^4 + x^2 + 1))*y
[6nsage: om.int().diffn()
(x^3/y) dx
[6nsage: decomposition_g0_g8(om.int())
(((x^5 + x^3)/(x^4 + x^2 + 1))*y, 0, 0)
[6nsage:
[6nsage:
sage:
sage: quit()
~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
sage: load('init.sage')
Traceback (most recent call last):
 
File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
exec(code_obj, self.user_global_ns, self.user_ns)
 
Input In [1] in <cell line: 1>
load('init.sage')
 
File sage/misc/persist.pyx:175 in sage.misc.persist.load
sage.repl.load.load(filename, globals())
 
File /ext/sage/9.7/src/sage/repl/load.py:272 in load
exec(preparse_file(f.read()) + "\n", globals)
 
File <string>:21 in <module>
 
File sage/misc/persist.pyx:175 in sage.misc.persist.load
sage.repl.load.load(filename, globals())
 
File /ext/sage/9.7/src/sage/repl/load.py:272 in load
exec(preparse_file(f.read()) + "\n", globals)
 
File <string>:22
if self.dx = _sage_const_0 *C.x and self.y = _sage_const_0 *C.x:
^
SyntaxError: cannot assign to attribute here. Maybe you meant '==' instead of '='?
 
[6nsage: load('init.sage')
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y
[6nsage: om = g.diffn()
[6nsage: om = om.regular_form()
[6nsage: om.int()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [6], in <cell line: 1>()
----> 1 om.int()
 
File <string>:21, in int(self)
 
AttributeError: 'superelliptic_regular_form' object has no attribute 'fct_field'
[6nsage: load('init.sage')
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y
[6nsage: om = om.regular_form()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [9], in <cell line: 1>()
----> 1 om = om.regular_form()
 
AttributeError: 'superelliptic_regular_form' object has no attribute 'regular_form'
[6nsage: om = g.diffn()
[6nsage: om = om.regular_form()
[6nsage: om.int()
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [12], in <cell line: 1>()
----> 1 om.int()
 
File <string>:28, in int(self)
 
ValueError: not enough values to unpack (expected 2, got 1)
[6nsage: sage: Fxy, Rxy, x, y=C.fct_field
[6nsasage: (x^6*y^7).exponents()
[(6, 7)]
[6nsage: i, j = (x^6*y^7).exponents()[0]
[6nsage: load('init.sage')
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y
[6nsage: om = g.diffn()
[6nsage: om = om.regular_form()
[6nsage: om.int()
---------------------------------------------------------------------------
ZeroDivisionError Traceback (most recent call last)
Input In [20], in <cell line: 1>()
----> 1 om.int()
 
File <string>:30, in int(self)
 
File <string>:30, in int(self)
 
[... skipping similar frames: int at line 30 (3 times)]
 
File <string>:30, in int(self)
 
File <string>:29, in int(self)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1739, in sage.structure.element.Element.__truediv__()
1737 return (<Element>left)._div_(right)
1738 if BOTH_ARE_ELEMENT(cl):
-> 1739 return coercion_model.bin_op(left, right, truediv)
1740
1741 try:
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
1202 self._record_exception()
1203 else:
-> 1204 return PyObject_CallObject(op, xy)
1205
1206 if op is mul:
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
1735 cdef int cl = classify_elements(left, right)
1736 if HAVE_SAME_PARENT(cl):
-> 1737 return (<Element>left)._div_(right)
1738 if BOTH_ARE_ELEMENT(cl):
1739 return coercion_model.bin_op(left, right, truediv)
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
2622 if right_inverse is None:
-> 2623 raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
2624 else:
2625 return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)
 
ZeroDivisionError: inverse of Mod(0, 3) does not exist
[6nsage: om
(x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2 dx
[6nsage: load('init.sage')
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y
[6nsage: om = g.diffn()
[6nsage: om = om.regular_form()
[6nsage: om
((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
[6nsage: om.int()
---------------------------------------------------------------------------
ZeroDivisionError Traceback (most recent call last)
Input In [27], in <cell line: 1>()
----> 1 om.int()
 
File <string>:30, in int(self)
 
File <string>:30, in int(self)
 
[... skipping similar frames: int at line 30 (3 times)]
 
File <string>:30, in int(self)
 
File <string>:29, in int(self)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1739, in sage.structure.element.Element.__truediv__()
1737 return (<Element>left)._div_(right)
1738 if BOTH_ARE_ELEMENT(cl):
-> 1739 return coercion_model.bin_op(left, right, truediv)
1740
1741 try:
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
1202 self._record_exception()
1203 else:
-> 1204 return PyObject_CallObject(op, xy)
1205
1206 if op is mul:
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
1735 cdef int cl = classify_elements(left, right)
1736 if HAVE_SAME_PARENT(cl):
-> 1737 return (<Element>left)._div_(right)
1738 if BOTH_ARE_ELEMENT(cl):
1739 return coercion_model.bin_op(left, right, truediv)
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
2622 if right_inverse is None:
-> 2623 raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
2624 else:
2625 return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)
 
ZeroDivisionError: inverse of Mod(0, 3) does not exist
[6nsage: load('init.sage')
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y
[6nsage: om = g.diffn()
[6nsage: om = om.regular_form()
[6nsasage: om
((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
[6nsage: om.int()
int(self) ((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
m dx x^18*y
int(self) ((x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19) dy
m dx x^16*y
int(self) ((2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17) dy
m dx x^12*y
int(self) ((2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13) dy
m dx x^10*y
int(self) (2*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^6
int(self) (2*y + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^4
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
---------------------------------------------------------------------------
ZeroDivisionError Traceback (most recent call last)
Input In [33], in <cell line: 1>()
----> 1 om.int()
 
File <string>:32, in int(self)
 
File <string>:32, in int(self)
 
[... skipping similar frames: int at line 32 (3 times)]
 
File <string>:32, in int(self)
 
File <string>:31, in int(self)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1739, in sage.structure.element.Element.__truediv__()
1737 return (<Element>left)._div_(right)
1738 if BOTH_ARE_ELEMENT(cl):
-> 1739 return coercion_model.bin_op(left, right, truediv)
1740
1741 try:
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
1202 self._record_exception()
1203 else:
-> 1204 return PyObject_CallObject(op, xy)
1205
1206 if op is mul:
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
1735 cdef int cl = classify_elements(left, right)
1736 if HAVE_SAME_PARENT(cl):
-> 1737 return (<Element>left)._div_(right)
1738 if BOTH_ARE_ELEMENT(cl):
1739 return coercion_model.bin_op(left, right, truediv)
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
2622 if right_inverse is None:
-> 2623 raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
2624 else:
2625 return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)
 
ZeroDivisionError: inverse of Mod(0, 3) does not exist
[6nsage: g = C.x^7 * C.y^8
[6nsage: om = g.diffn()
[6nsage: om
(x^18 + x^16 - x^12 - x^10) dx
[6nsage: om.int()
x^19 + 2*x^17 + 2*x^13 + x^11
[6nsage: g = 2*C.x*C.y^3
[6nsage: g.diffn()
((-x^6 - x^4 - x^2)/y) dx
[6nsage: om = g.diffn()
[6nsage: om.int()
(2*x^4 + x^2)*y
[6nsage: g = - C.y
[6nsage: om = g.diffn()
[6nsage: om = om.regular_form()
[6nssage: om
(2) dy
[6nsage: om.int()
int(self) (2) dy
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [46], in <cell line: 1>()
----> 1 om.int()
 
File <string>:23, in int(self)
 
AttributeError: 'superelliptic_regular_form' object has no attribute 'y'
[6nsage: load('init.sage')
[6nsage: g = - C.y
[6nsage: sage: om = g.diffn()
[6nsage: om.int()
((2*x^2 + 2)/(x^4 + x^2 + 1))*y
[6nsage: om = om.regular_form()
[6nsage: om.int()
int(self) (2) dy
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [52], in <cell line: 1>()
----> 1 om.int()
 
File <string>:36, in int(self)
 
NameError: name 'dy' is not defined
[6nsage: load('init.sage')
[6nsage: g = - C.y
[6nsage: om = g.diffn()
[6nsage: om = om.regular_form()
[6nsage: om.int()
int(self) (2) dy
m dx 1
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [57], in <cell line: 1>()
----> 1 om.int()
 
File <string>:38, in int(self)
 
ValueError: not enough values to unpack (expected 2, got 1)
[6nsage: load('init.sage')
[6nsage: g = - C.y
[6nsage: om = g.diffn()
[6nsage: om = om.regular_form()
[6nsage: om.int()
int(self) (2) dy
m dx 1
int(self) ((1/(x^2 + 2))*y + 2) dy
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1009, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
1008 # now try calling the base ring's __call__ methods
-> 1009 element = self.base_ring()(element)
1010 _p = p_NSet(sa2si(element,_ring), _ring)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
 
File /ext/sage/9.7/src/sage/categories/map.pyx:1692, in sage.categories.map.FormalCompositeMap._call_()
1691 for f in self.__list:
-> 1692 x = f._call_(x)
1693 return x
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:12066, in sage.rings.polynomial.polynomial_element.ConstantPolynomialSection._call_()
12065 """
> 12066 cpdef Element _call_(self, x):
12067 """
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:12091, in sage.rings.polynomial.polynomial_element.ConstantPolynomialSection._call_()
12090 else:
> 12091 raise TypeError("not a constant polynomial")
12092
 
TypeError: not a constant polynomial
 
During handling of the above exception, another exception occurred:
 
TypeError Traceback (most recent call last)
Input In [62], in <cell line: 1>()
----> 1 om.int()
 
File <string>:40, in int(self)
 
File <string>:35, in int(self)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
159 print(type(C), C)
160 print(type(C._element_constructor), C._element_constructor)
--> 161 raise
162
163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1013, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
1011 return new_MP(self,_p)
1012 except (TypeError, ValueError):
-> 1013 raise TypeError("Could not find a mapping of the passed element to this ring.")
1014
1015 def _repr_(self):
 
TypeError: Could not find a mapping of the passed element to this ring.
[6nsage: load('init.sage')
[6nsage: g = - C.y
[6nsage: om = g.diffn()
[6nsage: om = om.regular_form()
[6nsage: om.int()
int(self) (2) dy
m dy 1
int(self) (0) dy
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [67], in <cell line: 1>()
----> 1 om.int()
 
File <string>:40, in int(self)
 
File <string>:38, in __add__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
493 """
--> 494 return self.getattr_from_category(name)
495
496 cdef getattr_from_category(self, name):
 
File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
505 else:
506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
508
509 def __dir__(self):
 
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
359 dummy_error_message.cls = type(self)
360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
362 attribute = <object>attr
363 # Check for a descriptor (__get__ in Python)
 
AttributeError: 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular' object has no attribute 'function'
[6nsage: load('init.sage')
[6nsage: g = - C.y
[6nsage: om = g.diffn()
[6nsage: om = om.regular_form()
[6nsage: om.int()
int(self) (2) dy
m dy 1
int(self) (0) dy
2*y
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y
[6nsage: om = g.diffn()
[6nsage: om = om.regular_form()
[6nsage: om.int()
int(self) ((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
m dx x^18*y
int(self) ((x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19) dy
m dx x^16*y
int(self) ((2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17) dy
m dx x^12*y
int(self) ((2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13) dy
m dx x^10*y
int(self) (2*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^6
int(self) (2*y + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^4
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
---------------------------------------------------------------------------
ZeroDivisionError Traceback (most recent call last)
Input In [76], in <cell line: 1>()
----> 1 om.int()
 
File <string>:32, in int(self)
 
File <string>:32, in int(self)
 
[... skipping similar frames: int at line 32 (3 times)]
 
File <string>:32, in int(self)
 
File <string>:31, in int(self)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1739, in sage.structure.element.Element.__truediv__()
1737 return (<Element>left)._div_(right)
1738 if BOTH_ARE_ELEMENT(cl):
-> 1739 return coercion_model.bin_op(left, right, truediv)
1740
1741 try:
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
1202 self._record_exception()
1203 else:
-> 1204 return PyObject_CallObject(op, xy)
1205
1206 if op is mul:
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
1735 cdef int cl = classify_elements(left, right)
1736 if HAVE_SAME_PARENT(cl):
-> 1737 return (<Element>left)._div_(right)
1738 if BOTH_ARE_ELEMENT(cl):
1739 return coercion_model.bin_op(left, right, truediv)
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
2622 if right_inverse is None:
-> 2623 raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
2624 else:
2625 return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)
 
ZeroDivisionError: inverse of Mod(0, 3) does not exist
[6nsage: om
((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
[6nsage: g = 2*C.x*C.y^3
[6nsage: om = g.diffn().regular_form()
[6nsage: om
(2*x^6 + 2*x^4 + 2*x^2) dy
[6nsage: load('init.sage')
[6nsage: sage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y
[6nsage: om = g.diffn().regular_form()
[6nsage: om.int()
int(self) ((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
m dx x^18*y
int(self) ((x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19) dy
m dx x^16*y
int(self) ((2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17) dy
m dx x^12*y
int(self) ((2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13) dy
m dx x^10*y
int(self) (2*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^6
int(self) (2*y + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^4
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dx y
int(self) (2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dx 1
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
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int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [84], in <cell line: 1>()
----> 1 om.int()
 
File <string>:33, in int(self)
 
File <string>:33, in int(self)
 
[... skipping similar frames: int at line 33 (6 times)]
 
File <string>:42, in int(self)
 
[... skipping similar frames: int at line 33 (1 times)]
 
File <string>:42, in int(self)
 
[... skipping similar frames: int at line 33 (159 times), int at line 42 (159 times)]
 
File <string>:33, in int(self)
 
File <string>:42, in int(self)
 
File <string>:27, in int(self)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
1001
1002 try:
-> 1003 return self(str(element))
1004 except TypeError:
1005 pass
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:991, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
989 else:
990 element = element.replace("^","**")
--> 991 element = eval(element, d, {})
992 except (SyntaxError, NameError):
993 raise TypeError("Could not find a mapping of the passed element to this ring.")
 
File <string>:1, in <module>
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: load('init.sage')
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y
[6nsage: sage: om = g.diffn().regular_form()
[6nsage: om.int()
int(self) ((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
m dx x^12*y
int(self) ((x^18 + x^16 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (x^13) dy
m dx x^4
int(self) ((x^18 + x^16 + 2*x^10 + 2)*y + 2*x^6 + 2*x^2 + 2) dx + (x^13) dy
m dx x^18*y
int(self) ((x^16 + 2*x^10 + 2)*y + 2*x^6 + 2*x^2 + 2) dx + (2*x^19 + x^13) dy
m dx y
int(self) ((x^16 + 2*x^10)*y + 2*x^6 + 2*x^2 + 2) dx + (2*x^19 + x^13 + x) dy
m dx x^16*y
int(self) (2*x^10*y + 2*x^6 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^6
int(self) (2*x^10*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^10*y
int(self) (2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) (x^16*y + 2*x^2 + 2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx 1
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^11
int(self) ((2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + x^13) dy
m dx x^2
m dy x^17
int(self) ((x^16 + 2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^13) dy
m dx x^2
m dy x^13
int(self) ((x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx + (2*x^19) dy
m dx x^2
m dy x^19
int(self) ((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx
m dx y
int(self) ((x^18 + x^16 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (x) dy
m dx x^10*y
int(self) ((x^18 + x^16 + 2*x^12)*y + 2*x^2) dx + (2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((x^18 + x^16 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (x) dy
m dx x^16*y
int(self) ((x^18 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (x^17 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx
m dx x^10*y
int(self) ((x^18 + x^16 + 2*x^12 + 2)*y + 2*x^2) dx + (2*x^11) dy
m dx y
int(self) ((x^18 + x^16 + 2*x^12)*y + 2*x^2) dx + (2*x^11 + x) dy
m dx x^12*y
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^11
int(self) ((x^18 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17 + x^13) dy
m dx y
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17 + x^13) dy
m dx y
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16 + 2*x^10)*y + 2*x^2) dx + (x^13 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + x^16 + 2*x^10 + 2)*y + 2*x^2) dx + (x^13) dy
m dx x^2
m dy x^13
int(self) ((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx
m dx y
int(self) ((x^18 + x^16 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (x) dy
m dx x^10*y
int(self) ((x^18 + x^16 + 2*x^12)*y + 2*x^2) dx + (2*x^11 + x) dy
m dx x^16*y
int(self) ((x^18 + 2*x^12)*y + 2*x^2) dx + (x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^10*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) ((x^18 + 2*x^12)*y + 2*x^2) dx + (x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16 + 2*x^10)*y + 2*x^2) dx + (x^13 + x) dy
m dx x^18*y
int(self) ((x^16 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^13 + x) dy
m dx x^10*y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x
int(self) ((2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + x^13) dy
m dx x^2
m dy x^17
int(self) ((x^16 + 2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^13) dy
m dx x^16*y
int(self) ((2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + x^13) dy
m dx x^10*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^11
int(self) ((2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + x^13) dy
m dx x^2
m dy x^13
int(self) ((2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17) dy
m dx y
int(self) ((x^18 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (x^17 + x) dy
m dx x^10*y
int(self) ((x^18 + 2*x^12)*y + 2*x^2) dx + (x^17 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16 + 2*x^12)*y + 2*x^2) dx + (2*x^11 + x) dy
m dx x^12*y
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((x^18 + x^16 + 2*x^10)*y + 2*x^2) dx + (x^13 + x) dy
m dx x^18*y
int(self) ((x^16 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^13 + x) dy
m dx x^10*y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((x^16 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^13 + x) dy
m dx x^2
m dy x^13
int(self) ((x^16 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x) dy
m dx x^16*y
int(self) ((2*x^12 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^17 + x) dy
m dx x^10*y
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^17
int(self) ((x^16 + 2)*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11) dy
m dx y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) ((x^18 + 2*x^12)*y + 2*x^2) dx + (x^17 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) ((x^18 + 2*x^12)*y + 2*x^2) dx + (x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) ((x^18 + 2*x^12)*y + 2*x^2) dx + (x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^2
m dy x^13
int(self) ((x^18 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (x^17 + x) dy
m dx x^12*y
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^10*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^13
int(self) ((2*x^12 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11) dy
m dx y
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^13
int(self) ((x^18 + 2*x^12 + 2)*y + 2*x^2) dx + (x^17 + 2*x^11) dy
m dx y
int(self) ((x^18 + 2*x^12)*y + 2*x^2) dx + (x^17 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((x^18 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (x^17 + x) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (x) dy
m dx x^16*y
int(self) ((x^18 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (x^17 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17) dy
m dx x^10*y
int(self) ((x^18 + 2*x^12 + 2)*y + 2*x^2) dx + (x^17 + 2*x^11) dy
m dx y
int(self) ((x^18 + 2*x^12)*y + 2*x^2) dx + (x^17 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16 + 2*x^12)*y + 2*x^2) dx + (2*x^11 + x) dy
m dx x^18*y
int(self) ((x^16 + 2*x^12)*y + 2*x^2) dx + (2*x^19 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((x^16 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x) dy
m dx x^2
m dy x
int(self) ((x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx + (2*x^19) dy
m dx x^10*y
int(self) ((x^16 + 2*x^12 + 2)*y + 2*x^2) dx + (2*x^19 + 2*x^11) dy
m dx x^12*y
int(self) ((x^16 + 2)*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11) dy
m dx x^16*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^11
int(self) ((2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + x^13) dy
m dx y
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x^13
int(self) ((2*x^12 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^17 + x) dy
m dx x^12*y
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^18*y
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x
int(self) ((2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + x^13) dy
m dx x^10*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x
int(self) ((2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + x^13) dy
m dx x^10*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x^17
int(self) ((x^16 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^13 + x) dy
m dx x^10*y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^10*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x
int(self) ((2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + x^13) dy
m dx y
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x^17
int(self) ((x^16 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^13 + x) dy
m dx x^10*y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((x^18 + x^16 + 2*x^10)*y + 2*x^2) dx + (x^13 + x) dy
m dx x^10*y
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^10*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^18*y
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17 + x^13) dy
m dx x^10*y
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x^17
int(self) ((x^16 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^13 + x) dy
m dx x^2
m dy x^19
int(self) ((x^18 + x^16 + 2*x^10)*y + 2*x^2) dx + (x^13 + x) dy
m dx x^10*y
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((x^18 + x^16 + 2*x^10)*y + 2*x^2) dx + (x^13 + x) dy
m dx x^10*y
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^10*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) ((x^16 + 2*x^12)*y + 2*x^2) dx + (2*x^19 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((2*x^12 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^17 + x) dy
m dx x^2
m dy x
int(self) ((2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17) dy
m dx y
int(self) ((2*x^12 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^17 + x) dy
m dx x^2
m dy x^17
int(self) ((x^16 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x) dy
m dx x^16*y
int(self) ((2*x^12 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^17 + x) dy
m dx x^10*y
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x^13
int(self) ((2*x^12 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^17 + x) dy
m dx x^12*y
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x^17
int(self) ((x^16 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^13 + x) dy
m dx x^16*y
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^10*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^10*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) ((2*x^12 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11) dy
m dx x^2
m dy x^17
int(self) ((x^16 + 2*x^12 + 2)*y + 2*x^2) dx + (2*x^19 + 2*x^11) dy
m dx x^2
m dy x^11
int(self) ((x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx + (2*x^19) dy
m dx y
int(self) ((x^16 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x) dy
m dx x^12*y
int(self) ((x^16 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^13 + x) dy
m dx x^10*y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((x^18 + x^16 + 2*x^10)*y + 2*x^2) dx + (x^13 + x) dy
m dx x^16*y
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^10*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^13
int(self) ((x^18 + 2*x^12 + 2)*y + 2*x^2) dx + (x^17 + 2*x^11) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16 + 2*x^12 + 2)*y + 2*x^2) dx + (2*x^11) dy
m dx y
int(self) ((x^18 + x^16 + 2*x^12)*y + 2*x^2) dx + (2*x^11 + x) dy
m dx x^18*y
int(self) ((x^16 + 2*x^12)*y + 2*x^2) dx + (2*x^19 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) ((x^16 + 2*x^12)*y + 2*x^2) dx + (2*x^19 + 2*x^11 + x) dy
m dx x^12*y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) ((x^18 + x^16 + 2*x^12)*y + 2*x^2) dx + (2*x^11 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + x^16 + 2*x^12 + 2)*y + 2*x^2) dx + (2*x^11) dy
m dx x^2
m dy x^11
int(self) ((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx
m dx x^18*y
int(self) ((x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx + (2*x^19) dy
m dx y
int(self) ((x^16 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x) dy
m dx x^12*y
int(self) ((x^16 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^13 + x) dy
m dx x^2
m dy x
int(self) ((x^16 + 2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^13) dy
m dx y
int(self) ((x^16 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^13 + x) dy
m dx x^2
m dy x^19
int(self) ((x^18 + x^16 + 2*x^10)*y + 2*x^2) dx + (x^13 + x) dy
m dx x^18*y
int(self) ((x^16 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^13 + x) dy
m dx x^10*y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^10*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) ((x^16 + 2*x^12)*y + 2*x^2) dx + (2*x^19 + 2*x^11 + x) dy
m dx x^12*y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) ((x^16 + 2*x^12)*y + 2*x^2) dx + (2*x^19 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16 + 2)*y + 2*x^2) dx + (x^13 + 2*x^11) dy
m dx x^18*y
int(self) ((x^16 + 2)*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11) dy
m dx x^2
m dy x^11
int(self) ((x^16 + 2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^13) dy
m dx x^10*y
int(self) ((x^16 + 2)*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11) dy
m dx y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) ((2*x^12 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11) dy
m dx x^2
m dy x^11
int(self) ((2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17) dy
m dx x^12*y
int(self) ((x^18 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17 + x^13) dy
m dx x^10*y
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((2*x^12 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^17 + x) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (x^17 + x) dy
m dx x^12*y
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^10*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + x^16 + 2)*y + 2*x^2) dx + (x^13 + 2*x^11) dy
m dx x^16*y
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^13
int(self) ((2*x^12 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2*x^12 + 2)*y + 2*x^2) dx + (x^17 + 2*x^11) dy
m dx x^2
m dy x^11
int(self) ((x^18 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17) dy
m dx y
int(self) ((x^18 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (x^17 + x) dy
m dx x^10*y
int(self) ((x^18 + 2*x^12)*y + 2*x^2) dx + (x^17 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + 2*x^12 + 2)*y + 2*x^2) dx + (x^17 + 2*x^11) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16 + 2*x^12 + 2)*y + 2*x^2) dx + (2*x^11) dy
m dx x^12*y
int(self) ((x^18 + x^16 + 2)*y + 2*x^2) dx + (x^13 + 2*x^11) dy
m dx x^16*y
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16 + 2)*y + 2*x^2) dx + (x^13 + 2*x^11) dy
m dx y
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + x^16 + 2)*y + 2*x^2) dx + (x^13 + 2*x^11) dy
m dx x^18*y
int(self) ((x^16 + 2)*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11) dy
m dx y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) ((x^16 + 2)*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11) dy
m dx x^16*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x^17
int(self) ((x^16 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^13 + x) dy
m dx x^10*y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((x^16 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^13 + x) dy
m dx x^16*y
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^10*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((2*x^12 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^17 + x) dy
m dx x^10*y
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) ((2*x^12 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11) dy
m dx y
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^10*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x
int(self) ((2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + x^13) dy
m dx y
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x
int(self) ((2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + x^13) dy
m dx x^10*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^11
int(self) ((2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + x^13) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17 + x^13) dy
m dx x^18*y
int(self) ((2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + x^13) dy
m dx x^10*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^10*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) ((x^16 + 2*x^12)*y + 2*x^2) dx + (2*x^19 + 2*x^11 + x) dy
m dx x^12*y
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^13
int(self) ((2*x^12 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11) dy
m dx x^12*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^11
int(self) ((2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + x^13) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17 + x^13) dy
m dx x^18*y
int(self) ((2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + x^13) dy
m dx x^2
m dy x^17
int(self) ((x^16 + 2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^13) dy
m dx x^10*y
int(self) ((x^16 + 2)*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + x^16 + 2)*y + 2*x^2) dx + (x^13 + 2*x^11) dy
m dx x^16*y
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^11
int(self) ((2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + x^13) dy
m dx y
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x^13
int(self) ((2*x^12 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^17 + x) dy
m dx x^10*y
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) ((x^18 + 2*x^12)*y + 2*x^2) dx + (x^17 + 2*x^11 + x) dy
m dx x^12*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^10*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^13
int(self) ((2*x^12 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11) dy
m dx x^12*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17 + x^13) dy
m dx y
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17 + x^13) dy
m dx x^2
m dy x^13
int(self) ((x^18 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx
m dx x^10*y
int(self) ((x^18 + x^16 + 2*x^12 + 2)*y + 2*x^2) dx + (2*x^11) dy
m dx x^18*y
int(self) ((x^16 + 2*x^12 + 2)*y + 2*x^2) dx + (2*x^19 + 2*x^11) dy
m dx x^12*y
int(self) ((x^16 + 2)*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11) dy
m dx x^16*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^17
int(self) ((x^16 + 2)*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + x^16 + 2)*y + 2*x^2) dx + (x^13 + 2*x^11) dy
m dx x^2
m dy x^11
int(self) ((x^18 + x^16 + 2*x^10 + 2)*y + 2*x^2) dx + (x^13) dy
m dx x^18*y
int(self) ((x^16 + 2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^13) dy
m dx y
int(self) ((x^16 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^13 + x) dy
m dx x^16*y
int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17 + x^13) dy
m dx y
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^2
m dy x^17
int(self) ((x^18 + x^16 + 2*x^10)*y + 2*x^2) dx + (x^13 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + x^16 + 2*x^10 + 2)*y + 2*x^2) dx + (x^13) dy
m dx x^2
m dy x^13
int(self) ((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx
m dx y
int(self) ((x^18 + x^16 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (x) dy
m dx x^12*y
int(self) ((x^18 + x^16 + 2*x^10)*y + 2*x^2) dx + (x^13 + x) dy
m dx x^10*y
int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^11
int(self) ((x^18 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17 + x^13) dy
m dx x^10*y
int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
m dx y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^11
int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
m dx x^10*y
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^17
int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
m dx x^16*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^13
int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
m dx x^2
m dy x
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [88], in <cell line: 1>()
----> 1 om.int()
 
File <string>:34, in int(self)
 
File <string>:34, in int(self)
 
[... skipping similar frames: int at line 34 (5 times)]
 
File <string>:43, in int(self)
 
[... skipping similar frames: int at line 34 (2 times)]
 
File <string>:43, in int(self)
 
[... skipping similar frames: int at line 34 (229 times), int at line 43 (229 times)]
 
File <string>:34, in int(self)
 
File <string>:43, in int(self)
 
File <string>:42, in int(self)
 
File <string>:51, in __sub__(self, other)
 
File <string>:224, in reduction(C, g)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
1514 return (<Element>left)._mul_(right)
1515 if BOTH_ARE_ELEMENT(cl):
-> 1516 return coercion_model.bin_op(left, right, mul)
1517
1518 cdef long value
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1200, in sage.structure.coerce.CoercionModel.bin_op()
1198 # Now coerce to a common parent and do the operation there
1199 try:
-> 1200 xy = self.canonical_coercion(x, y)
1201 except TypeError:
1202 self._record_exception()
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1311, in sage.structure.coerce.CoercionModel.canonical_coercion()
1309 x_map, y_map = coercions
1310 if x_map is not None:
-> 1311 x_elt = (<Map>x_map)._call_(x)
1312 else:
1313 x_elt = x
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
285 raise TypeError("Cannot coerce {} to {}".format(x, C))
286 cdef Map m
--> 287 cdef Element e = method(C)
288 if e is None:
289 raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x)))
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:198, in sage.rings.polynomial.multi_polynomial.MPolynomial._polynomial_()
196 var = R.variable_name()
197 if var in self._parent.variable_names():
--> 198 return R(self.polynomial(self._parent(var)))
199 else:
200 return R([self])
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:419, in sage.rings.polynomial.multi_polynomial.MPolynomial.polynomial()
417 w = {remove_from_tuple(e, ind): val
418 for e, val in self.dict().iteritems() if not e[ind]}
--> 419 v = [B(w)] # coefficients that don't involve var
420 z = var
421 for i in range(1,d+1):
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:462, in PolynomialRing_general._element_constructor_(self, x, check, is_gen, construct, **kwds)
460 if x.type() != 't_POL':
461 x = x.Polrev()
--> 462 elif isinstance(x, FiniteRingElement):
463 try:
464 return self(x.polynomial())
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: load('init.sage')
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y
[6nsage: om = g.diffn().regular_form()
[6nsage: om.int()
int(self) ((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [92], in <cell line: 1>()
----> 1 om.int()
 
File <string>:26, in int(self)
 
NameError: name 'random_choice' is not defined
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y
[6nsage: load('init.sage')
^[[A[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y
[6nsage: om = g.diffn().regular_form()
[6nsage: om.int()
int(self) ((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
---------------------------------------------------------------------------
IndexError Traceback (most recent call last)
Input In [97], in <cell line: 1>()
----> 1 om.int()
 
File <string>:38, in int(self)
 
File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/random.py:378, in Random.choice(self, seq)
376 """Choose a random element from a non-empty sequence."""
377 # raises IndexError if seq is empty
--> 378 return seq[self._randbelow(len(seq))]
 
IndexError: list index out of range
[6nsage: load('init.sage')
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y
[6nsage: om = g.diffn().regular_form().int()
int(self) ((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
m dx x^18*y
int(self) ((x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19) dy
m dx x^16*y
int(self) ((2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17) dy
m dx x^12*y
int(self) ((2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13) dy
m dx x^10*y
int(self) (2*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^6
int(self) (2*y + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^4
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dy x^19
int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
m dx x^18*y
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
File <string>:60, in __mul__(self, other)
 
File <string>:14, in __init__(self, C, g)
 
File <string>:220, in reduction(C, g)
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:632, in PolynomialRing(base_ring, *args, **kwds)
630 raise TypeError("you must specify the names of the variables")
--> 632 names = normalize_names(n, names)
634 # At this point, we have only handled the "names" keyword if it was
635 # needed. Since we know the variable names, it would logically be
636 # an error to specify an additional "names" keyword. However,
(...)
639 # and we allow this for historical reasons. However, the names
640 # must be consistent!
 
File /ext/sage/9.7/src/sage/structure/category_object.pyx:900, in sage.structure.category_object.normalize_names()
899
--> 900 cpdef normalize_names(Py_ssize_t ngens, names):
901 r"""
 
File /ext/sage/9.7/src/sage/structure/category_object.pyx:993, in sage.structure.category_object.normalize_names()
992 # Convert names to strings and strip whitespace
--> 993 names = [str(x).strip() for x in names]
994 else:
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
 
During handling of the above exception, another exception occurred:
 
AttributeError Traceback (most recent call last)
Input In [100], in <cell line: 1>()
----> 1 om = g.diffn().regular_form().int()
 
File <string>:35, in int(self)
 
File <string>:35, in int(self)
 
[... skipping similar frames: int at line 35 (4 times)]
 
File <string>:44, in int(self)
 
[... skipping similar frames: int at line 35 (1 times)]
 
File <string>:44, in int(self)
 
[... skipping similar frames: int at line 35 (219 times), int at line 44 (219 times)]
 
File <string>:35, in int(self)
 
File <string>:44, in int(self)
 
File <string>:34, in int(self)
 
File <string>:63, in __mul__(self, other)
 
AttributeError: 'superelliptic_function' object has no attribute 'form'
[6nsage: load('init.sage')
Traceback (most recent call last):
 
File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
exec(code_obj, self.user_global_ns, self.user_ns)
 
Input In [101] in <cell line: 1>
load('init.sage')
 
File sage/misc/persist.pyx:175 in sage.misc.persist.load
sage.repl.load.load(filename, globals())
 
File /ext/sage/9.7/src/sage/repl/load.py:272 in load
exec(preparse_file(f.read()) + "\n", globals)
 
File <string>:21 in <module>
 
File sage/misc/persist.pyx:175 in sage.misc.persist.load
sage.repl.load.load(filename, globals())
 
File /ext/sage/9.7/src/sage/repl/load.py:272 in load
exec(preparse_file(f.read()) + "\n", globals)
 
File <string>:30
print('m dx', m)
^
IndentationError: expected an indented block after 'for' statement on line 29
 
[6nsage: load('init.sage')
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [102], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:30, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:21, in <module>
 
File <string>:73, in diffn(self, dy_w)
 
File <string>:177, in dy_w(C)
 
File /ext/sage/9.7/src/sage/rings/rational.pyx:2414, in sage.rings.rational.Rational.__mul__()
2412 return x
2413
-> 2414 return coercion_model.bin_op(left, right, operator.mul)
2415
2416 cpdef _mul_(self, right):
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:48, in __rmul__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
1526 if not err:
1527 return (<Element>right)._mul_long(value)
-> 1528 return coercion_model.bin_op(left, right, mul)
1529 except TypeError:
1530 return NotImplemented
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:43, in __rmul__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
1526 if not err:
1527 return (<Element>right)._mul_long(value)
-> 1528 return coercion_model.bin_op(left, right, mul)
1529 except TypeError:
1530 return NotImplemented
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:43, in __rmul__(self, other)
 
[... skipping similar frames: sage.structure.coerce.CoercionModel.bin_op at line 1242 (3 times), sage.structure.element.Element.__mul__ at line 1528 (3 times), __rmul__ at line 43 (2 times)]
 
File <string>:43, in __rmul__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
1526 if not err:
1527 return (<Element>right)._mul_long(value)
-> 1528 return coercion_model.bin_op(left, right, mul)
1529 except TypeError:
1530 return NotImplemented
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:41, in __rmul__(self, other)
 
File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
1962 return y
1963
-> 1964 return coercion_model.bin_op(left, right, operator.mul)
1965
1966 cpdef _mul_(self, right):
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:70, in __rmul__(self, constant)
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: load('init.sage')
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y
[6nsage: om = g.diffn().regular_form().int()
int(self) ((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
m dx x^18*y
int(self) ((x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19) dy
m dx x^16*y
int(self) ((2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17) dy
m dx x^12*y
int(self) ((2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13) dy
m dx x^10*y
int(self) (2*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^6
int(self) (2*y + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^4
int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
m dx x^2
m dx y
int(self) (2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dx 1
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
m dx x^2
m dy x^19
int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
m dx x^18*y
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [105], in <cell line: 1>()
----> 1 om = g.diffn().regular_form().int()
 
File <string>:35, in int(self)
 
File <string>:35, in int(self)
 
[... skipping similar frames: int at line 35 (6 times)]
 
File <string>:44, in int(self)
 
[... skipping similar frames: int at line 35 (1 times)]
 
File <string>:44, in int(self)
 
[... skipping similar frames: int at line 35 (70 times), int at line 44 (70 times)]
 
File <string>:35, in int(self)
 
File <string>:44, in int(self)
 
File <string>:34, in int(self)
 
File <string>:82, in __pow__(self, exp)
 
File <string>:7, in __init__(self, C, g)
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:632, in PolynomialRing(base_ring, *args, **kwds)
629 except KeyError:
630 raise TypeError("you must specify the names of the variables")
--> 632 names = normalize_names(n, names)
634 # At this point, we have only handled the "names" keyword if it was
635 # needed. Since we know the variable names, it would logically be
636 # an error to specify an additional "names" keyword. However,
(...)
639 # and we allow this for historical reasons. However, the names
640 # must be consistent!
641 if "names" in kwds:
 
File /ext/sage/9.7/src/sage/structure/category_object.pyx:900, in sage.structure.category_object.normalize_names()
898 return dir_with_other_class(self, self.category().parent_class)
899
--> 900 cpdef normalize_names(Py_ssize_t ngens, names):
901 r"""
902 Return a tuple of strings of variable names of length ngens given
 
File /ext/sage/9.7/src/sage/structure/category_object.pyx:993, in sage.structure.category_object.normalize_names()
991 if isinstance(names, (tuple, list)):
992 # Convert names to strings and strip whitespace
--> 993 names = [str(x).strip() for x in names]
994 else:
995 # Interpret names as string and convert to tuple of strings
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: g
(2*x^4 + x^2 + 2)*y + x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
[6nsage: g.diffn()
((x^18*y + x^16*y - x^12*y - x^10*y - x^6 - x^4 - x^2 - y - 1)/y) dx
[6nsage: g.diffn().regular_form()
((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
[6nsage: g = 2*C.x*C.y^3
[6nsage: om = g.diffn().regular_form()
[6nsage: om
(2*x^6 + 2*x^4 + 2*x^2) dy
[6nssage: g = C.x^7 * C.y^8
[6nsage: om = g.diffn().regular_form(); om
(x^18 + x^16 + 2*x^12 + 2*x^10) dx
[6nsage: g
x^19 + 2*x^17 + 2*x^13 + x^11
[6nsage: om.int()
int(self) (x^18 + x^16 + 2*x^12 + 2*x^10) dx
m dx x^18
int(self) (x^16 + 2*x^12 + 2*x^10) dx
m dx x^16
int(self) (2*x^12 + 2*x^10) dx
m dx x^12
int(self) (2*x^10) dx
m dx x^10
int(self) (0) dy
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [115], in <cell line: 1>()
----> 1 om.int()
 
File <string>:35, in int(self)
 
File <string>:35, in int(self)
 
[... skipping similar frames: int at line 35 (1 times)]
 
File <string>:35, in int(self)
 
File <string>:38, in __add__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
493 """
--> 494 return self.getattr_from_category(name)
495
496 cdef getattr_from_category(self, name):
 
File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
505 else:
506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
508
509 def __dir__(self):
 
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
359 dummy_error_message.cls = type(self)
360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
362 attribute = <object>attr
363 # Check for a descriptor (__get__ in Python)
 
AttributeError: 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular' object has no attribute 'function'
[6nsage: load('init.sage')
[6nsage: g = C.x^7 * C.y^8
[6nsage: om = g.diffn().regular_form(); om
(x^18 + x^16 + 2*x^12 + 2*x^10) dx
[6nsage: om.int()
int(self) (x^18 + x^16 + 2*x^12 + 2*x^10) dx
m dx x^18
int(self) (x^16 + 2*x^12 + 2*x^10) dx
m dx x^16
int(self) (2*x^12 + 2*x^10) dx
m dx x^12
int(self) (2*x^10) dx
m dx x^10
int(self) (0) dy
x^19 + 2*x^17 + 2*x^13 + x^11
[6nsage: g - om.int()
int(self) (x^18 + x^16 + 2*x^12 + 2*x^10) dx
m dx x^18
int(self) (x^16 + 2*x^12 + 2*x^10) dx
m dx x^16
int(self) (2*x^12 + 2*x^10) dx
m dx x^12
int(self) (2*x^10) dx
m dx x^10
int(self) (0) dy
0
[6nssage: g = 2*C.x*C.y^3
[6nssage: om = g.diffn().regular_form(); om
(2*x^6 + 2*x^4 + 2*x^2) dy
[6nsage: om.int()
int(self) (2*x^6 + 2*x^4 + 2*x^2) dy
m dy x^6
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2) dy
m dy x^4
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [123], in <cell line: 1>()
----> 1 om.int()
 
File <string>:44, in int(self)
 
File <string>:44, in int(self)
 
File <string>:35, in int(self)
 
[... skipping similar frames: int at line 44 (1 times)]
 
File <string>:35, in int(self)
 
[... skipping similar frames: int at line 44 (84 times), int at line 35 (84 times)]
 
File <string>:44, in int(self)
 
File <string>:35, in int(self)
 
File <string>:43, in int(self)
 
File <string>:52, in __sub__(self, other)
 
File <string>:14, in __init__(self, C, g)
 
File <string>:223, in reduction(C, g)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
285 raise TypeError("Cannot coerce {} to {}".format(x, C))
286 cdef Map m
--> 287 cdef Element e = method(C)
288 if e is None:
289 raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x)))
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:198, in sage.rings.polynomial.multi_polynomial.MPolynomial._polynomial_()
196 var = R.variable_name()
197 if var in self._parent.variable_names():
--> 198 return R(self.polynomial(self._parent(var)))
199 else:
200 return R([self])
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:411, in sage.rings.polynomial.multi_polynomial.MPolynomial.polynomial()
409 # Make polynomial ring over all variables except var.
410 S = R.base_ring()[tuple(Z)]
--> 411 ring = S[var]
412 if not self:
413 return ring(0)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:1275, in sage.structure.parent.Parent.__getitem__()
1273 except AttributeError:
1274 return self.list()[n]
-> 1275 return meth(n)
1276
1277 #########################################################################
 
File /ext/sage/9.7/src/sage/categories/rings.py:1176, in Rings.ParentMethods.__getitem__(self, arg)
1173 # 2. Otherwise, try to return a polynomial ring
1175 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-> 1176 return PolynomialRing(self, elts)
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:561, in PolynomialRing(base_ring, *args, **kwds)
557 names = None # Unknown variable names
559 # Use a single-variate ring by default unless the "singular"
560 # implementation is asked.
--> 561 multivariate = kwds.get("implementation") == "singular"
563 # Check specifically for None because it is an easy mistake to
564 # make and Integer(None) returns 0, so we wouldn't catch this
565 # otherwise.
566 if any(arg is None for arg in args):
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: sage: (2*x^4 + 2*x^2).quo_rem(x^3 - x)
(2*x, x^2)
[6nsasage: om = (2*C.x^4 + 2*C.x^2)*C.y.diffn()
[6nsage: om.cartier()
0 dx
[6nsage: om.int()
((x^6 + x^2)/(x^4 + x^2 + 1))*y
[6nsagesage: C.y*C.y.diffn()
1 dx
[6nsasage: g = 2*C.x*C.y^3
[6nsage: om = g.diffn().regular_form()
[6nsage: om = g.diffn()
[6nsage: om1 = om.regular_form()
[6nsage: om1.form() == om
True
[6nsage: om1
(2*x^6 + 2*x^4 + 2*x^2) dy
[6nsage: om
((-x^6 - x^4 - x^2)/y) dx
[6nsage: g
(2*x^4 + x^2)*y
[6nsage: om2 = (C.y*(2*C.x^3 + 2*C.x)+(2*C.x^4 - 2*C.x^2))*C.y.diffn()
[6nsage: om2 == om1
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [138], in <cell line: 1>()
----> 1 om2 == om1
 
File <string>:12, in __eq__(self, other)
 
AttributeError: 'superelliptic_regular_form' object has no attribute 'reduce'
[6nsage: om2 == om
False
[6nsage: om2 - om
((x^6 - x^3*y - x^2 - x*y)/y) dx
[6nsage: (om2 - om).regular_form()
((2*x^3 + 2*x)*y + x^6 + 2*x^2) dx
[6nsage: g
(2*x^4 + x^2)*y
[6nsage: g.diffn().regular_form()
(2*x^6 + 2*x^4 + 2*x^2) dy
[6nsage: g.diffn()
((-x^6 - x^4 - x^2)/y) dx
[6nsage: g.regular_form()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [145], in <cell line: 1>()
----> 1 g.regular_form()
 
AttributeError: 'superelliptic_function' object has no attribute 'regular_form'
[6nsage: g.diffn().regular_form()
(2*x^6 + 2*x^4 + 2*x^2) dy
[6nssage: g.diffn()
((-x^6 - x^4 - x^2)/y) dx
[6nsage: g.diffn().int()
(2*x^4 + x^2)*y
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y
[6nsage: om = g.diffn()
[6nsage: om.int()
((2*x^8 + 2)/(x^4 + x^2 + 1))*y + x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
[6nsage: om
((x^18*y + x^16*y - x^12*y - x^10*y - x^6 - x^4 - x^2 - y - 1)/y) dx
[6nsage: om.regular_form()
((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
[6nsage: om.regular_form().form()
((x^21 - x^17 - x^15 + x^11 - x^6*y - x^4*y - x^3 - x^2*y + x - y)/y) dx
[6nsage: om.regular_form().form().int()
---------------------------------------------------------------------------
ZeroDivisionError Traceback (most recent call last)
Input In [155], in <cell line: 1>()
----> 1 om.regular_form().form().int()
 
File <string>:199, in int(self)
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:3994, in sage.rings.polynomial.polynomial_element.Polynomial.integral()
3992 cdef Py_ssize_t n
3993 zero = Q.zero()
-> 3994 p = [zero] + [cm.bin_op(Q(self.get_unsafe(n)), n + 1, operator.truediv)
3995 if self.get_unsafe(n) else zero for n in range(self.degree() + 1)]
3996 return S(p)
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
1202 self._record_exception()
1203 else:
-> 1204 return PyObject_CallObject(op, xy)
1205
1206 if op is mul:
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
1735 cdef int cl = classify_elements(left, right)
1736 if HAVE_SAME_PARENT(cl):
-> 1737 return (<Element>left)._div_(right)
1738 if BOTH_ARE_ELEMENT(cl):
1739 return coercion_model.bin_op(left, right, truediv)
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
2622 if right_inverse is None:
-> 2623 raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
2624 else:
2625 return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)
 
ZeroDivisionError: inverse of Mod(0, 3) does not exist
[6nsage: om.regular_form().form() == om
False
[6nsage: om
((x^18*y + x^16*y - x^12*y - x^10*y - x^6 - x^4 - x^2 - y - 1)/y) dx
[6nsage: om.regular_form().form() == om
False
[6nsage: om
((x^18*y + x^16*y - x^12*y - x^10*y - x^6 - x^4 - x^2 - y - 1)/y) dx
[6nsage: om.regular_form().form() - om
((x^21 - x^18*y - x^17 - x^16*y - x^15 + x^12*y + x^11 + x^10*y - x^6*y + x^6 - x^4*y + x^4 - x^3 - x^2*y + x^2 + x + 1)/y) dx
[6nsage: om.regular_form().form()
((x^21 - x^17 - x^15 + x^11 - x^6*y - x^4*y - x^3 - x^2*y + x - y)/y) dx
~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
[22;0t[6nsage: lo
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [1], in <cell line: 1>()
----> 1 lo
 
NameError: name 'lo' is not defined
[6nsage: load('init.sage')
[6nsage: g = C.x*C.y
[6nsage: om = g.diffn()
[6nsage: om.regular_form().form() == om
True
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y
[6nsage: om = g.diffn()
[6nsage: om.regular_form().form() == om
False
[6nsage: om
((x^18*y + x^16*y - x^12*y - x^10*y - x^6 - x^4 - x^2 - y - 1)/y) dx
[6nsage: om.regular_form()
((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
[6nsage: om.regular_form().form()
((x^21 - x^17 - x^15 + x^11 - x^6*y - x^4*y - x^3 - x^2*y + x - y)/y) dx
[6nsage: load('init.sage')
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y
[6nsage: om = g.diffn()
[6nsage: om.regular_form().form()
if fct.denominator() == y:
if fct.denominator() == 1:
((x^21 - x^17 - x^15 + x^11 - x^6*y - x^4*y - x^3 - x^2*y + x - y)/y) dx
[6nsage: load('init.sage')
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y
[6nsage: om = g.diffn()
[6nsage: om.regular_form().form()
if fct.denominator() == y:
fct, fct.numerator() x^18*y + x^16*y - x^12*y - x^10*y - x^6 - x^4 - x^2 - y - 1 x^18*y + x^16*y - x^12*y - x^10*y - x^6 - x^4 - x^2 - y - 1
if fct.denominator() == 1:
((x^21 - x^17 - x^15 + x^11 - x^6*y - x^4*y - x^3 - x^2*y + x - y)/y) dx
[6nsage: load('init.sage')
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y
[6nsage: om = g.diffn()
[6nsage: om.regular_form().form() == om
if fct.denominator() == y:
True
[6nsage: load('init.sage')
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y
[6nsage: om = g.diffn()
[6nsage: om.regular_form().form() == om
True
[6nsage: om.regular_form().int()
int(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
m dx x^18
int(self) (x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
m dx x^16
int(self) (2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
m dx x^12
int(self) (2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
m dx x^10
int(self) (2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
m dx 1
int(self) (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
m dy x^6
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
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int(self) (2*x^4 + 2*x^2 + 2) dy
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^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
File <string>:59, in __mul__(self, other)
 
File <string>:222, in reduction(C, g)
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
 
During handling of the above exception, another exception occurred:
 
AttributeError Traceback (most recent call last)
Input In [28], in <cell line: 1>()
----> 1 om.regular_form().int()
 
File <string>:35, in int(self)
 
File <string>:35, in int(self)
 
[... skipping similar frames: int at line 35 (3 times)]
 
File <string>:44, in int(self)
 
File <string>:44, in int(self)
 
[... skipping similar frames: int at line 35 (124 times), int at line 44 (124 times)]
 
File <string>:35, in int(self)
 
File <string>:44, in int(self)
 
File <string>:34, in int(self)
 
File <string>:63, in __mul__(self, other)
 
AttributeError: 'superelliptic_function' object has no attribute 'form'
[6nsasage: Fxy, Rxy, x, y=C.fct_field
sage: om = superelliptic_regular_form(0*C.x, C.x^3 + 2*C.x^2 + 2*C.one)
 
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [30], in <cell line: 1>()
----> 1 om = superelliptic_regular_form(Integer(0)*C.x, C.x**Integer(3) + Integer(2)*C.x**Integer(2) + Integer(2)*C.one)
 
File <string>:39, in __add__(self, other)
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: om = superelliptic_regular_form(0*C.x, C.x^3 + 2*C.x^2 + 2*C.one)
[6nsage: om
(x^3 + 2*x^2 + 2) dy
[6nsage: om.int()
int(self) (x^3 + 2*x^2 + 2) dy
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int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [33], in <cell line: 1>()
----> 1 om.int()
 
File <string>:44, in int(self)
 
File <string>:44, in int(self)
 
File <string>:35, in int(self)
 
[... skipping similar frames: int at line 44 (1 times)]
 
File <string>:35, in int(self)
 
[... skipping similar frames: int at line 44 (108 times), int at line 35 (108 times)]
 
File <string>:44, in int(self)
 
File <string>:35, in int(self)
 
File <string>:43, in int(self)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
1526 if not err:
1527 return (<Element>right)._mul_long(value)
-> 1528 return coercion_model.bin_op(left, right, mul)
1529 except TypeError:
1530 return NotImplemented
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:70, in __rmul__(self, constant)
 
File <string>:14, in __init__(self, C, g)
 
File <string>:223, in reduction(C, g)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
285 raise TypeError("Cannot coerce {} to {}".format(x, C))
286 cdef Map m
--> 287 cdef Element e = method(C)
288 if e is None:
289 raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x)))
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:198, in sage.rings.polynomial.multi_polynomial.MPolynomial._polynomial_()
196 var = R.variable_name()
197 if var in self._parent.variable_names():
--> 198 return R(self.polynomial(self._parent(var)))
199 else:
200 return R([self])
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:410, in sage.rings.polynomial.multi_polynomial.MPolynomial.polynomial()
408
409 # Make polynomial ring over all variables except var.
--> 410 S = R.base_ring()[tuple(Z)]
411 ring = S[var]
412 if not self:
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:1275, in sage.structure.parent.Parent.__getitem__()
1273 except AttributeError:
1274 return self.list()[n]
-> 1275 return meth(n)
1276
1277 #########################################################################
 
File /ext/sage/9.7/src/sage/categories/rings.py:1176, in Rings.ParentMethods.__getitem__(self, arg)
1173 # 2. Otherwise, try to return a polynomial ring
1175 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-> 1176 return PolynomialRing(self, elts)
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:51, in PolynomialRing(base_ring, *args, **kwds)
45 _cache = sage.misc.weak_dict.WeakValueDictionary()
48 # The signature for this function is too complicated to express sensibly
49 # in any other way besides *args and **kwds (in Python 3 or Cython, we
50 # could probably do better thanks to PEP 3102).
---> 51 def PolynomialRing(base_ring, *args, **kwds):
52 r"""
53 Return the globally unique univariate or multivariate polynomial
54 ring with given properties and variable name or names.
(...)
551 TypeError: unable to convert 'x' to an integer
552 """
553 if not ring.is_Ring(base_ring):
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: om = superelliptic_regular_form(0*C.x, C.y^2 + C.x + 2*C.x^2 + 2*C.one)
[6nsage: om.int()
int(self) (x^3 + 2*x^2 + 2) dy
m dy x^3
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
int(self) (2*x*y) dx + (2) dy
m dx x*y
int(self) (2*x^2 + 2) dy
m dy x^2
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [35], in <cell line: 1>()
----> 1 om.int()
 
File <string>:44, in int(self)
 
File <string>:44, in int(self)
 
File <string>:35, in int(self)
 
[... skipping similar frames: int at line 44 (1 times)]
 
File <string>:35, in int(self)
 
[... skipping similar frames: int at line 44 (58 times), int at line 35 (58 times)]
 
File <string>:44, in int(self)
 
File <string>:35, in int(self)
 
File <string>:43, in int(self)
 
File <string>:51, in __sub__(self, other)
 
File <string>:216, in reduction(C, g)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
636 ring_one = self.ring().one()
637 try:
--> 638 return self._element_class(self, x, ring_one, coerce=coerce)
639 except (TypeError, ValueError):
640 pass
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:115, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
113 if coerce:
114 self.__numerator = parent.ring()(numerator)
--> 115 self.__denominator = parent.ring()(denominator)
116 else:
117 self.__numerator = numerator
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:506, in FractionField_generic.ring(self)
503 s = 'FieldOfFractions(%s)' % self.ring()._magma_init_(magma)
504 return magma._with_names(s, self.variable_names())
--> 506 def ring(self):
507 """
508 Return the ring that this is the fraction field of.
509
(...)
516 Multivariate Polynomial Ring in x, y over Rational Field
517 """
518 return self._R
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: om.form().int()
---------------------------------------------------------------------------
ZeroDivisionError Traceback (most recent call last)
Input In [36], in <cell line: 1>()
----> 1 om.form().int()
 
File <string>:199, in int(self)
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:3994, in sage.rings.polynomial.polynomial_element.Polynomial.integral()
3992 cdef Py_ssize_t n
3993 zero = Q.zero()
-> 3994 p = [zero] + [cm.bin_op(Q(self.get_unsafe(n)), n + 1, operator.truediv)
3995 if self.get_unsafe(n) else zero for n in range(self.degree() + 1)]
3996 return S(p)
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
1202 self._record_exception()
1203 else:
-> 1204 return PyObject_CallObject(op, xy)
1205
1206 if op is mul:
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
1735 cdef int cl = classify_elements(left, right)
1736 if HAVE_SAME_PARENT(cl):
-> 1737 return (<Element>left)._div_(right)
1738 if BOTH_ARE_ELEMENT(cl):
1739 return coercion_model.bin_op(left, right, truediv)
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
2622 if right_inverse is None:
-> 2623 raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
2624 else:
2625 return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)
 
ZeroDivisionError: inverse of Mod(0, 3) does not exist
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y
[6nsage: om.form().int()
---------------------------------------------------------------------------
ZeroDivisionError Traceback (most recent call last)
Input In [38], in <cell line: 1>()
----> 1 om.form().int()
 
File <string>:199, in int(self)
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:3994, in sage.rings.polynomial.polynomial_element.Polynomial.integral()
3992 cdef Py_ssize_t n
3993 zero = Q.zero()
-> 3994 p = [zero] + [cm.bin_op(Q(self.get_unsafe(n)), n + 1, operator.truediv)
3995 if self.get_unsafe(n) else zero for n in range(self.degree() + 1)]
3996 return S(p)
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
1202 self._record_exception()
1203 else:
-> 1204 return PyObject_CallObject(op, xy)
1205
1206 if op is mul:
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
1735 cdef int cl = classify_elements(left, right)
1736 if HAVE_SAME_PARENT(cl):
-> 1737 return (<Element>left)._div_(right)
1738 if BOTH_ARE_ELEMENT(cl):
1739 return coercion_model.bin_op(left, right, truediv)
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
2622 if right_inverse is None:
-> 2623 raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
2624 else:
2625 return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)
 
ZeroDivisionError: inverse of Mod(0, 3) does not exist
[6nsagsage: om == g.diffn()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [39], in <cell line: 1>()
----> 1 om == g.diffn()
 
File <string>:12, in __eq__(self, other)
 
AttributeError: 'superelliptic_regular_form' object has no attribute 'reduce'
[6nsage: om.form() == g.diffn()
False
[6nsage: sage: g
(2*x^4 + x^2 + 2)*y + x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
[6nsage:
[6nssage: om = g.diffn()
[6nsage: om.regular_form().form() == om
True
[6nsage: om.int()
((2*x^8 + 2)/(x^4 + x^2 + 1))*y + x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
[6nsage: om.regular_form().int()
int(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
m dx x^18
int(self) (x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
m dx x^16
int(self) (2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
m dx x^12
int(self) (2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
m dx x^10
int(self) (2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
m dx 1
int(self) (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
m dy x^6
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
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^Cint(self) (2*x^4 + 2*x^2 + 2) dy
---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [45], in <cell line: 1>()
----> 1 om.regular_form().int()
 
File <string>:35, in int(self)
 
File <string>:35, in int(self)
 
[... skipping similar frames: int at line 35 (3 times)]
 
File <string>:44, in int(self)
 
File <string>:44, in int(self)
 
[... skipping similar frames: int at line 35 (70 times), int at line 44 (69 times)]
 
File <string>:44, in int(self)
 
File <string>:35, in int(self)
 
File <string>:21, in int(self)
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: om1 = (2*C.x^4 + 2*C.x^2 + 2*C.one)*C.y.diffn()
[6nsage: om1.int()
(x^2 + 2)*y
[6nsage: g
(2*x^4 + x^2 + 2)*y + x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
[6nsage: om1.regular_form().int()
int(self) (2*x^4 + 2*x^2 + 2) dy
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int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
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int(self) (x^3*y) dx + (2*x^2 + 2) dy
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int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
m dx x^3*y
int(self) (2*x^4 + 2*x^2 + 2) dy
m dy x^4
int(self) (x^3*y) dx + (2*x^2 + 2) dy
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [49], in <cell line: 1>()
----> 1 om1.regular_form().int()
 
File <string>:44, in int(self)
 
File <string>:35, in int(self)
 
File <string>:44, in int(self)
 
File <string>:35, in int(self)
 
[... skipping similar frames: int at line 44 (68 times), int at line 35 (67 times)]
 
File <string>:35, in int(self)
 
File <string>:44, in int(self)
 
File <string>:24, in int(self)
 
File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
1962 return y
1963
-> 1964 return coercion_model.bin_op(left, right, operator.mul)
1965
1966 cpdef _mul_(self, right):
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:70, in __rmul__(self, constant)
 
File <string>:14, in __init__(self, C, g)
 
File <string>:214, in reduction(C, g)
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: om.int()
((2*x^8 + 2)/(x^4 + x^2 + 1))*y + x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
[6nsage: om1.int()
(x^2 + 2)*y
[6nsage: om1
((-x^4 - x^2 - 1)/y) dx
[6nsage: om1
((-x^4 - x^2 - 1)/y) dx
[6nsage: om1.int().diffn() == om1
True
[6nsage: om1.int().diffn()
((-x^4 - x^2 - 1)/y) dx
[6nsage: C.polynomial
x^3 + 2*x
[6nsage: (C.polynomial)^2
x^6 + x^4 + x^2
[6nsage: autom(C.crystalline_cohomology_basis()[1]).coordinates()
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
coordinates of form self (1/y) dx
(1, 1)
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
( + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y]), [(1/(x^2 + x))*y] + V(((x^5 + x^4 + 2*x^3 + x^2 + 2*x + 1)/(x^2 + x))*y), [((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*y]))
[6nsage: load('init.sage')
Traceback (most recent call last):
 
File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
exec(code_obj, self.user_global_ns, self.user_ns)
 
Input In [59] in <cell line: 1>
load('init.sage')
 
File sage/misc/persist.pyx:175 in sage.misc.persist.load
sage.repl.load.load(filename, globals())
 
File /ext/sage/9.7/src/sage/repl/load.py:272 in load
exec(preparse_file(f.read()) + "\n", globals)
 
File <string>:3 in <module>
 
File sage/misc/persist.pyx:175 in sage.misc.persist.load
sage.repl.load.load(filename, globals())
 
File /ext/sage/9.7/src/sage/repl/load.py:272 in load
exec(preparse_file(f.read()) + "\n", globals)
 
File <string>:203
"If omega is regular, return form eta such that Cartier(eta) = omega"
^
IndentationError: expected an indented block after function definition on line 202
 
[6nsage: load('init.sage')
[6nsage: autom(C.crystalline_cohomology_basis()[1]).coordinates()
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
coordinates of form self (1/y) dx
(1, 1)
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [61], in <cell line: 1>()
----> 1 autom(C.crystalline_cohomology_basis()[Integer(1)]).coordinates()
 
File <string>:78, in coordinates(self, basis)
 
File <string>:207, in inv_cartier(omega)
 
AttributeError: 'NoneType' object has no attribute 'dx'
[6nsage: load('init.sage')
[6nsage: autom(C.crystalline_cohomology_basis()[1]).coordinates()
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
coordinates of form self (1/y) dx
(1, 1)
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega, omega_regular ((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx None
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [63], in <cell line: 1>()
----> 1 autom(C.crystalline_cohomology_basis()[Integer(1)]).coordinates()
 
File <string>:78, in coordinates(self, basis)
 
File <string>:208, in inv_cartier(omega)
 
AttributeError: 'NoneType' object has no attribute 'dx'
[6nsage: load('init.sage')
[6nsage: autom(C.crystalline_cohomology_basis()[1]).coordinates()
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
coordinates of form self (1/y) dx
(1, 1)
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega, omega_regular ((-1)/y) dx (2) dy
omega, omega_regular ((-x^3 + x)/y) dx (2*x^3 + x) dy
fct ((x^2 + 2*x + 1)/(x + 2))*y
aux (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), [0], V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
aux_divided_by_p (((x + 1)/(x*y - y)) dx, 0, ((x + 1)/(x*y - y)) dx)
aux_divided_by_p.omega8 == aux.omega8.omega.cartier() True
coordinates of form self ((x + 1)/(x*y - y)) dx
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [65], in <cell line: 1>()
----> 1 autom(C.crystalline_cohomology_basis()[Integer(1)]).coordinates()
 
File <string>:92, in coordinates(self, basis)
 
File <string>:56, in coordinates(self)
 
File <string>:94, in coordinates(self, basis)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
786 return self._call_with_args(x, args, kwds)
787
--> 788 cpdef Element _call_(self, x):
789 """
790 Call method with a single argument, not implemented in the base class.
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
1249 return num
1250 if check and not den.is_unit():
1251 # This should probably be a ValueError.
1252 # However, too much existing code is expecting this to throw a
1253 # TypeError, so we decided to keep it for the time being.
-> 1254 raise TypeError("fraction must have unit denominator")
1255 return num * den.inverse_of_unit()
 
TypeError: fraction must have unit denominator
[6nsasage: ff = ((C.x^2 + 2*C.x + C.one)/(C.x + 2*C.one))*C.y
[6nsage: ff.diffn()
((x^4 - x^3 - x^2 - x + 1)/(x*y - y)) dx
[6nsage: sage:
[6nsage: om = ff.diffn()
sage: om.is_regular_on_U0()
False
sage: load('init.sage')
sage: autom(C.crystalline_cohomology_basis()[1]).coordinates()
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
coordinates of form self (1/y) dx
(1, 1)
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega, omega_regular ((-1)/y) dx (2) dy
omega, omega_regular ((-x^3 + x)/y) dx (2*x^3 + x) dy
aux.omega0.omega ((-x^12 + x^10 + x^6 - x^4)/y) dx
aux.omega0.h2 (x^6 + 2*x^4 + x^3 + 2*x)*y
aux (V(((-x^12 + x^10 + x^6 - x^4)/y) dx), V(((2*x^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
aux_divided_by_p (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
aux_divided_by_p.omega8 == aux.omega8.omega.cartier() True
sage/rings/polynomial/polynomial_zmod_flint.pyx:7: DeprecationWarning: invalid escape sequence '\Z'
"""
sage/rings/polynomial/polynomial_zmod_flint.pyx:7: DeprecationWarning: invalid escape sequence '\Z'
"""
---------------------------------------------------------------------------
RecursionError Traceback (most recent call last)
Input In [71], in <cell line: 1>()
----> 1 autom(C.crystalline_cohomology_basis()[Integer(1)]).coordinates()
 
File <string>:95, in coordinates(self, basis)
 
File <string>:70, in coordinates(self)
 
File <string>:70, in coordinates(self)
 
[... skipping similar frames: coordinates at line 70 (2941 times)]
 
File <string>:70, in coordinates(self)
 
File <string>:50, in coordinates(self)
 
File <string>:98, in de_rham_basis(self)
 
File <string>:91, in basis_de_rham_degrees(self)
 
File <string>:5, in __init__(self, C, omega, fct)
 
File <string>:95, in diffn(self)
 
File <string>:7, in __init__(self, C, g)
 
File <string>:259, in reduction_form(C, g)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
159 print(type(C), C)
160 print(type(C._element_constructor), C._element_constructor)
--> 161 raise
162
163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
636 ring_one = self.ring().one()
637 try:
--> 638 return self._element_class(self, x, ring_one, coerce=coerce)
639 except (TypeError, ValueError):
640 pass
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
112 FieldElement.__init__(self, parent)
113 if coerce:
--> 114 self.__numerator = parent.ring()(numerator)
115 self.__denominator = parent.ring()(denominator)
116 else:
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
159 print(type(C), C)
160 print(type(C._element_constructor), C._element_constructor)
--> 161 raise
162
163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1009, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
1007 try:
1008 # now try calling the base ring's __call__ methods
-> 1009 element = self.base_ring()(element)
1010 _p = p_NSet(sa2si(element,_ring), _ring)
1011 return new_MP(self,_p)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
159 print(type(C), C)
160 print(type(C._element_constructor), C._element_constructor)
--> 161 raise
162
163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x)
1143 """
1144 TESTS::
1145
(...)
1182 True
1183 """
1184 try:
-> 1185 return integer_mod.IntegerMod(self, x)
1186 except (NotImplementedError, PariError):
1187 raise TypeError("error coercing to finite field")
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod()
199 return a
200 t = modulus.element_class()
--> 201 return t(parent, value)
202
203
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:380, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
378 else:
379 try:
--> 380 z = integer_ring.Z(value)
381 except (TypeError, ValueError):
382 from sage.structure.element import Expression
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
285 raise TypeError("Cannot coerce {} to {}".format(x, C))
286 cdef Map m
--> 287 cdef Element e = method(C)
288 if e is None:
289 raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x)))
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:831, in sage.rings.fraction_field_element.FractionFieldElement._conversion()
829 return R(self.__numerator)
830 else:
--> 831 self.reduce()
832 num = R(self.__numerator)
833 inv_den = R(self.__denominator).inverse_of_unit()
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:1239, in sage.rings.fraction_field_element.FractionFieldElement_1poly_field.reduce()
1237 if self._is_reduced:
1238 return
-> 1239 super(self.__class__, self).reduce()
1240 self.normalize_leading_coefficients()
1241
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:164, in sage.rings.fraction_field_element.FractionFieldElement.reduce()
162 return codomain.coerce(nnum/nden)
163
--> 164 cpdef reduce(self):
165 """
166 Reduce this fraction.
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:197, in sage.rings.fraction_field_element.FractionFieldElement.reduce()
195 return
196 try:
--> 197 g = self.__numerator.gcd(self.__denominator)
198 if not g.is_unit():
199 self.__numerator //= g
 
File /ext/sage/9.7/src/sage/structure/element.pyx:4494, in sage.structure.element.coerce_binop.new_method()
4492 def new_method(self, other, *args, **kwargs):
4493 if have_same_parent(self, other):
-> 4494 return method(self, other, *args, **kwargs)
4495 else:
4496 a, b = coercion_model.canonical_coercion(self, other)
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:4913, in sage.rings.polynomial.polynomial_element.Polynomial.gcd()
4911 raise NotImplementedError("%s does not provide a gcd implementation for univariate polynomials"%self._parent._base)
4912 else:
-> 4913 return doit(self, other)
4914
4915 @coerce_binop
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:946, in FractionField_generic._gcd_univariate_polynomial(self, f, g)
944 f1 = Num(f.numerator())
945 g1 = Num(g.numerator())
--> 946 return Pol(f1.gcd(g1)).monic()
 
File /ext/sage/9.7/src/sage/structure/element.pyx:4494, in sage.structure.element.coerce_binop.new_method()
4492 def new_method(self, other, *args, **kwargs):
4493 if have_same_parent(self, other):
-> 4494 return method(self, other, *args, **kwargs)
4495 else:
4496 a, b = coercion_model.canonical_coercion(self, other)
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:4907, in sage.rings.polynomial.polynomial_element.Polynomial.gcd()
4905 if tgt.ngens() > 1 and tgt._has_singular:
4906 g = flatten(self).gcd(flatten(other))
-> 4907 return flatten.section()(g)
4908 try:
4909 doit = self._parent._base._gcd_univariate_polynomial
 
File /ext/sage/9.7/src/sage/categories/map.pyx:769, in sage.categories.map.Map.__call__()
767 if P is D: # we certainly want to call _call_/with_args
768 if not args and not kwds:
--> 769 return self._call_(x)
770 return self._call_with_args(x, args, kwds)
771 # Is there coercion?
 
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
786 return self._call_with_args(x, args, kwds)
787
--> 788 cpdef Element _call_(self, x):
789 """
790 Call method with a single argument, not implemented in the base class.
 
File /ext/sage/9.7/src/sage/rings/polynomial/flatten.py:397, in UnflatteningMorphism._call_(self, p)
395 newpol[l - 1] = {}
396 if (i == len(expo) - 1 or expo[i + 1][idx:] != cur_exp[idx:]):
--> 397 newpol[l] = R(newpol[l], check=False)
398 else:
399 break
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:899, in sage.structure.parent.Parent.__call__()
897 return mor._call_(x)
898 else:
--> 899 return mor._call_with_args(x, args, kwds)
900
901 raise TypeError(_LazyString("No conversion defined from %s to %s", (R, self), {}))
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:180, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args()
178 print(type(C), C)
179 print(type(C._element_constructor), C._element_constructor)
--> 180 raise
181
182
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:170, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args()
168 return C._element_constructor(x)
169 else:
--> 170 return C._element_constructor(x, **kwds)
171 else:
172 if len(kwds) == 0:
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:469, in PolynomialRing_general._element_constructor_(self, x, check, is_gen, construct, **kwds)
467 elif isinstance(x, sage.rings.power_series_ring_element.PowerSeries):
468 x = x.truncate()
--> 469 return C(self, x, check, is_gen, construct=construct, **kwds)
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zmod_flint.pyx:129, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint.__init__()
127 except AttributeError:
128 pass
--> 129 Polynomial_template.__init__(self, parent, x, check, is_gen, construct)
130
131 cdef Polynomial_template _new(self):
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_template.pxi:158, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_template.__init__()
156 for deg, coef in x.iteritems():
157 celement_pow(monomial, gen, deg, NULL, (<Polynomial_template>self)._cparent)
--> 158 celement_mul(monomial, &(<Polynomial_template>self.__class__(parent, coef)).x, monomial, (<Polynomial_template>self)._cparent)
159 celement_add(&self.x, &self.x, monomial, (<Polynomial_template>self)._cparent)
160
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zmod_flint.pyx:129, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint.__init__()
127 except AttributeError:
128 pass
--> 129 Polynomial_template.__init__(self, parent, x, check, is_gen, construct)
130
131 cdef Polynomial_template _new(self):
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_template.pxi:107, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_template.__init__()
105 cdef Py_ssize_t deg
106
--> 107 Polynomial.__init__(self, parent, is_gen=is_gen)
108
109 (<Polynomial_template>self)._cparent = get_cparent(self._parent)
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:233, in sage.rings.polynomial.polynomial_element.Polynomial.__init__()
231 True
232 """
--> 233 CommutativeAlgebraElement.__init__(self, parent)
234 self._is_gen = is_gen
235
 
RecursionError: maximum recursion depth exceeded while calling a Python object
[6nsage: load('init.sage')
[6nsage: B = (sage: B = C.crystalline_cohomology_basis()
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
[6nsage: autom(B[1]).coordinates(basis = B)
coordinates of form self (1/y) dx
(1, 1)
omega, omega_regular ((-1)/y) dx (2) dy
omega, omega_regular ((-x^3 + x)/y) dx (2*x^3 + x) dy
aux.omega0.omega ((-x^12 + x^10 + x^6 - x^4)/y) dx
aux.omega0.h2 (x^6 + 2*x^4 + x^3 + 2*x)*y
aux (V(((-x^12 + x^10 + x^6 - x^4)/y) dx), V(((2*x^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [74], in <cell line: 1>()
----> 1 autom(B[Integer(1)]).coordinates(basis = B)
 
File <string>:100, in coordinates(self, basis)
 
File <string>:70, in coordinates(self)
 
File <string>:70, in coordinates(self)
 
[... skipping similar frames: coordinates at line 70 (940 times)]
 
File <string>:70, in coordinates(self)
 
File <string>:60, in coordinates(self)
 
File <string>:107, in coordinates(self, basis, basis_holo, prec)
 
File <string>:79, in serre_duality_pairing(self, fct, prec)
 
File <string>:143, in expansion_at_infty(self, place, prec)
 
File <string>:135, in expansion_at_infty(self, place, prec)
 
File <string>:18, in naive_hensel(fct, F, start, prec)
 
File /ext/sage/9.7/src/sage/rings/big_oh.py:141, in O(*x, **kwds)
138 return x.parent().completion(x.parent().gen())(0, x.degree(), **kwds)
140 elif isinstance(x, laurent_series_ring_element.LaurentSeries):
--> 141 return laurent_series_ring_element.LaurentSeries(x.parent(), 0).\
142 add_bigoh(x.valuation(), **kwds)
144 elif isinstance(x, PuiseuxSeries):
145 return x.add_bigoh(x.valuation(), **kwds)
 
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:148, in sage.rings.laurent_series_ring_element.LaurentSeries.__init__()
146 f = parent._power_series_ring(f)
147 elif not isinstance(f, PowerSeries):
--> 148 f = parent._power_series_ring(f)
149 ## now this is a power series, over a different ring ...
150 ## requires that power series rings with same vars over the
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/power_series_ring.py:823, in PowerSeriesRing_generic._element_constructor_(self, f, prec, check)
821 else:
822 raise TypeError("Can only convert series into ring with same variable name.")
--> 823 return self.element_class(self, f, prec, check=check)
 
File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:44, in sage.rings.power_series_poly.PowerSeries_poly.__init__()
42 ValueError: series has negative valuation
43 """
---> 44 R = parent._poly_ring()
45 if isinstance(f, Element):
46 if (<Element>f)._parent is R:
 
File /ext/sage/9.7/src/sage/rings/power_series_ring.py:961, in PowerSeriesRing_generic._poly_ring(self)
958 pass
959 return False
--> 961 def _poly_ring(self):
962 """
963 Return the underlying polynomial ring used to represent elements of
964 this power series ring.
(...)
970 Univariate Polynomial Ring in t over Integer Ring
971 """
972 return self.__poly_ring
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: gg = ((2*C.x^8 + 2*C.x^7 + C.x^5 + C.x^4 + 2*C.x^2 + 2*C.x)/(C.x^2 + C.x + C.one))*C.y
[6nsage: gg.pth_root()
((2*x^2 + x + 2)/(x + 2))*y
[6nssage: om1 = ((-C.x^12 + C.x^10 + C.x^6 - C.x^4)/C.y)* C.dx
[6nsage: om2 = ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))* C.dx
[6nsasage: R = om1.cartier() - om2.cartier()
[6nsage: R == gg.pth_root()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [80], in <cell line: 1>()
----> 1 R == gg.pth_root()
 
File <string>:12, in __eq__(self, other)
 
AttributeError: 'superelliptic_function' object has no attribute 'reduce'
[6nsage: R == gg.pth_root().diffn()
True
[6nsage: xi = superelliptic_cech(C, om1.cartier(), gg.pth_root())
[6nsage: xi.coordinates()
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [83], in <cell line: 1>()
----> 1 xi.coordinates()
 
File <string>:70, in coordinates(self)
 
File <string>:70, in coordinates(self)
 
[... skipping similar frames: coordinates at line 70 (91 times)]
 
File <string>:70, in coordinates(self)
 
File <string>:66, in coordinates(self)
 
File <string>:7, in decomposition_g0_g8(fct, prec)
 
File <string>:107, in coordinates(self, basis, basis_holo, prec)
 
File <string>:79, in serre_duality_pairing(self, fct, prec)
 
File <string>:142, in expansion_at_infty(self, place, prec)
 
File <string>:137, in expansion_at_infty(self, place, prec)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__()
1512 cdef int cl = classify_elements(left, right)
1513 if HAVE_SAME_PARENT(cl):
-> 1514 return (<Element>left)._mul_(right)
1515 if BOTH_ARE_ELEMENT(cl):
1516 return coercion_model.bin_op(left, right, mul)
 
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:913, in sage.rings.laurent_series_ring_element.LaurentSeries._mul_()
911 cdef LaurentSeries right = <LaurentSeries>right_r
912 return type(self)(self._parent,
--> 913 self.__u * right.__u,
914 self.__n + right.__n)
915
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__()
1512 cdef int cl = classify_elements(left, right)
1513 if HAVE_SAME_PARENT(cl):
-> 1514 return (<Element>left)._mul_(right)
1515 if BOTH_ARE_ELEMENT(cl):
1516 return coercion_model.bin_op(left, right, mul)
 
File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:540, in sage.rings.power_series_poly.PowerSeries_poly._mul_()
538 """
539 prec = self._mul_prec(right_r)
--> 540 return PowerSeries_poly(self._parent,
541 self.__f * (<PowerSeries_poly>right_r).__f,
542 prec=prec,
 
File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:44, in sage.rings.power_series_poly.PowerSeries_poly.__init__()
42 ValueError: series has negative valuation
43 """
---> 44 R = parent._poly_ring()
45 if isinstance(f, Element):
46 if (<Element>f)._parent is R:
 
File /ext/sage/9.7/src/sage/rings/power_series_ring.py:961, in PowerSeriesRing_generic._poly_ring(self)
958 pass
959 return False
--> 961 def _poly_ring(self):
962 """
963 Return the underlying polynomial ring used to represent elements of
964 this power series ring.
(...)
970 Univariate Polynomial Ring in t over Integer Ring
971 """
972 return self.__poly_ring
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: xi1
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [84], in <cell line: 1>()
----> 1 xi1
 
NameError: name 'xi1' is not defined
[6nsage: xi
(((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
[6nsage: xi
(((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
[6nsage: xi.coordinates()
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [87], in <cell line: 1>()
----> 1 xi.coordinates()
 
File <string>:50, in coordinates(self)
 
File <string>:98, in de_rham_basis(self)
 
File <string>:76, in basis_de_rham_degrees(self)
 
File <string>:60, in holomorphic_differentials_basis(self)
 
File <string>:52, in basis_holomorphic_differentials_degree(self)
 
File <string>:7, in __init__(self, C, g)
 
File <string>:259, in reduction_form(C, g)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:711, in FractionField_generic._element_constructor_(self, x, y, coerce)
708 raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
709 x0, y0, self))
710 try:
--> 711 return self._element_class(self, x, y, coerce=coerce)
712 except TypeError:
713 if parent(x) is parent(x0):
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:115, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
113 if coerce:
114 self.__numerator = parent.ring()(numerator)
--> 115 self.__denominator = parent.ring()(denominator)
116 else:
117 self.__numerator = numerator
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
1001
1002 try:
-> 1003 return self(str(element))
1004 except TypeError:
1005 pass
 
File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
192 except AttributeError:
193 return super().__repr__()
--> 194 result = reprfunc()
195 if isinstance(result, str):
196 return result
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_()
2688 NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3
2689 """
-> 2690 return self._repr()
2691
2692 def _latex_(self, name=None):
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2656, in sage.rings.polynomial.polynomial_element.Polynomial._repr()
2654 if n != m-1:
2655 s += " + "
-> 2656 x = y = repr(x)
2657 if y.find("-") == 0:
2658 y = y[1:]
 
File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
192 except AttributeError:
193 return super().__repr__()
--> 194 result = reprfunc()
195 if isinstance(result, str):
196 return result
 
File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:338, in sage.rings.fraction_field_FpT.FpTElement._repr_()
336 """
337 if nmod_poly_degree(self._denom) == 0 and nmod_poly_get_coeff_ui(self._denom, 0) == 1:
--> 338 return repr(self.numer())
339 else:
340 numer_s = repr(self.numer())
 
File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
192 except AttributeError:
193 return super().__repr__()
--> 194 result = reprfunc()
195 if isinstance(result, str):
196 return result
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_()
2688 NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3
2689 """
-> 2690 return self._repr()
2691
2692 def _latex_(self, name=None):
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2656, in sage.rings.polynomial.polynomial_element.Polynomial._repr()
2654 if n != m-1:
2655 s += " + "
-> 2656 x = y = repr(x)
2657 if y.find("-") == 0:
2658 y = y[1:]
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: load('init.sage')
[6nsage: B = C.crystalline_cohomology_basis()
fomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
[6nsasage: autom(B[1]).coordinates(basis = B)
coordinates of form self (1/y) dx
(1, 1)
omega, omega_regular ((-1)/y) dx (2) dy
omega, omega_regular ((-x^3 + x)/y) dx (2*x^3 + x) dy
aux.omega0.omega ((-x^12 + x^10 + x^6 - x^4)/y) dx
aux.omega0.h2 (x^6 + 2*x^4 + x^3 + 2*x)*y
aux (V(((-x^12 + x^10 + x^6 - x^4)/y) dx), V(((2*x^8 + 2*x^7 + x^6 + x^5 + 2*x^2 + 2*x + 1)/(x^2 + x))*y), + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(2/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [90], in <cell line: 1>()
----> 1 autom(B[Integer(1)]).coordinates(basis = B)
 
File <string>:99, in coordinates(self, basis)
 
File <string>:85, in div_by_p(self)
 
File <string>:168, in pth_root(self)
 
ValueError: Function is not a p-th power.
[6nsage: ((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx
Input In [91]
((-x**Integer(3) + x**Integer(2) + x)/(x**Integer(2)*y + x*y + y)) dx
^
SyntaxError: invalid syntax
 
[6nsage: om2 = ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))* C.dx
[6nsage: om2
((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx
sage: om2.expansion_at_infty()
2*t^-2 + 2 + 2*t^4 + t^6 + O(t^8)
sage: load('init.sage')
sage: B = C.crystalline_cohomology_basis()
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
[6nsage: autom(B[1]).coordinates(basis = B)
coordinates of form self (1/y) dx
(1, 1)
aux 0 ( + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y]), V(((x^5 + x^4 + 2*x^3 + x^2 + 2*x + 1)/(x^2 + x))*y), + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(2/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
omega, omega_regular ((-1)/y) dx (2) dy
omega, omega_regular ((-x^3 + x)/y) dx (2*x^3 + x) dy
aux.omega0.omega ((-x^12 + x^10 + x^6 - x^4)/y) dx
aux.omega0.h2 (x^6 + 2*x^4 + x^3 + 2*x)*y
aux (V(((-x^12 + x^10 + x^6 - x^4)/y) dx), V(((2*x^8 + 2*x^7 + x^6 + x^5 + 2*x^2 + 2*x + 1)/(x^2 + x))*y), + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(2/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [97], in <cell line: 1>()
----> 1 autom(B[Integer(1)]).coordinates(basis = B)
 
File <string>:100, in coordinates(self, basis)
 
File <string>:86, in div_by_p(self)
 
File <string>:168, in pth_root(self)
 
ValueError: Function is not a p-th power.
[6nsage: load('init.sage')
[6nsage: B = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
^C---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
File /ext/sage/9.7/src/sage/categories/rings.py:1129, in Rings.ParentMethods.__getitem__(self, arg)
1128 try:
-> 1129 minpolys = [a.minpoly() for a in elts]
1130 except (AttributeError, NotImplementedError, ValueError, TypeError):
 
File /ext/sage/9.7/src/sage/categories/rings.py:1129, in <listcomp>(.0)
1128 try:
-> 1129 minpolys = [a.minpoly() for a in elts]
1130 except (AttributeError, NotImplementedError, ValueError, TypeError):
 
File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
493 """
--> 494 return self.getattr_from_category(name)
495
 
File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
508
 
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
362 attribute = <object>attr
 
AttributeError: 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular' object has no attribute 'minpoly'
 
During handling of the above exception, another exception occurred:
 
KeyboardInterrupt Traceback (most recent call last)
Input In [99], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis(); autom(B[Integer(1)]).coordinates(basis = B)
 
File <string>:53, in crystalline_cohomology_basis(self, prec)
 
File <string>:24, in de_rham_witt_lift(cech_class, prec)
 
File <string>:6, in de_rham_witt_lift_form0(omega)
 
File <string>:99, in diffn(self, dy_w)
 
File <string>:73, in diffn(self, dy_w)
 
File <string>:177, in dy_w(C)
 
File <string>:149, in auxilliary_derivative(P)
 
File <string>:55, in __rmul__(self, other)
 
File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
1962 return y
1963
-> 1964 return coercion_model.bin_op(left, right, operator.mul)
1965
1966 cpdef _mul_(self, right):
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:55, in __rmul__(self, other)
 
File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
1962 return y
1963
-> 1964 return coercion_model.bin_op(left, right, operator.mul)
1965
1966 cpdef _mul_(self, right):
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:55, in __rmul__(self, other)
 
File <string>:84, in __add__(self, other)
 
File <string>:31, in __add__(self, other)
 
File /ext/sage/9.7/src/sage/rings/rational.pyx:2414, in sage.rings.rational.Rational.__mul__()
2412 return x
2413
-> 2414 return coercion_model.bin_op(left, right, operator.mul)
2415
2416 cpdef _mul_(self, right):
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:70, in __rmul__(self, constant)
 
File <string>:14, in __init__(self, C, g)
 
File <string>:223, in reduction(C, g)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
285 raise TypeError("Cannot coerce {} to {}".format(x, C))
286 cdef Map m
--> 287 cdef Element e = method(C)
288 if e is None:
289 raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x)))
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:198, in sage.rings.polynomial.multi_polynomial.MPolynomial._polynomial_()
196 var = R.variable_name()
197 if var in self._parent.variable_names():
--> 198 return R(self.polynomial(self._parent(var)))
199 else:
200 return R([self])
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:411, in sage.rings.polynomial.multi_polynomial.MPolynomial.polynomial()
409 # Make polynomial ring over all variables except var.
410 S = R.base_ring()[tuple(Z)]
--> 411 ring = S[var]
412 if not self:
413 return ring(0)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:1275, in sage.structure.parent.Parent.__getitem__()
1273 except AttributeError:
1274 return self.list()[n]
-> 1275 return meth(n)
1276
1277 #########################################################################
 
File /ext/sage/9.7/src/sage/categories/rings.py:1129, in Rings.ParentMethods.__getitem__(self, arg)
1126 elts = normalize_arg(arg)
1128 try:
-> 1129 minpolys = [a.minpoly() for a in elts]
1130 except (AttributeError, NotImplementedError, ValueError, TypeError):
1131 minpolys = None
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: B = C.crystalline_cohomology_basis(); aux = autom(B[1]).coordinates(basis = B)
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
coordinates of form self (1/y) dx
(1, 1)
[6nsage: aux
( + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y]), [(1/(x^2 + x))*y] + V(((x^5 + x^4 + 2*x^3 + x^2 + 2*x + 1)/(x^2 + x))*y), [((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*y]))
[6nsage: om = aux.omega8
[6nsage: om
[((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*y])
[6nsage: om - aux.f.t.teichmuller().diffn()
[((x^2 + x + 2)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^8 - x^6 + x^4 - x^3 + x - 1)/(x^7*y - x^6*y - x^5*y - x^4*y - x^3*y - x^2*y + x*y)) dx) + dV([((x^2 + x + 2)/(x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 1))*y])
[6nsage: om1 = om + aux.f.t.teichmuller().diffn()
[6nsage: om1
+ V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(2/(x^4 + 2*x^3 + 2*x^2 + x))*y])
[6nsage: om1.frobenius()
(1/(x^2*y + x*y)) dx
[6nsage: om1.frobenius().expansion_at_infty()
t^4 + 2*t^6 + t^8 + O(t^14)
[6nsage: om1.omega.is_regular_on_Uinfty()
False
[6nsage: om1.omega.is_regular_on_Uinfty()
False
[6nsage: om1.omega.cartier().is_regular_on_Uinfty()
True
[6nsage: om2 = om1.omega
[6nsage: om2 = second_patch(om1)
[6nsage: om2 = om1.omega
[6nsage: om2 = second_patch(om2)
[6nsage: om2.cartier()
((x + 1)/(x*y - y)) dx
[6nsage: om1
+ V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(2/(x^4 + 2*x^3 + 2*x^2 + x))*y])
[6nsage: load('init.sage')
[6nsage: autom(B[1]).coordinates(basis = B)
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [119], in <cell line: 1>()
----> 1 autom(B[Integer(1)]).coordinates(basis = B)
 
AttributeError: 'NoneType' object has no attribute 'coordinates'
[6nsage: load('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
coordinates of form self (1/y) dx
(1, 1)
aux 0 ( + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y]), V(((x^5 + x^4 + 2*x^3 + x^2 + 2*x + 1)/(x^2 + x))*y), + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(2/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
omega, omega_regular ((-1)/y) dx (2) dy
omega, omega_regular ((-x^3 + x)/y) dx (2*x^3 + x) dy
aux.omega0.omega ((-x^12 + x^10 + x^6 - x^4)/y) dx
aux.omega0.h2 (x^6 + 2*x^4 + x^3 + 2*x)*y
aux (V(((-x^12 + x^10 + x^6 - x^4)/y) dx), V(((2*x^8 + 2*x^7 + x^6 + x^5 + 2*x^2 + 2*x + 1)/(x^2 + x))*y), + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(2/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [120], in <cell line: 1>()
----> 1 load('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[Integer(1)]).coordinates(basis = B)
 
File <string>:100, in coordinates(self, basis)
 
File <string>:86, in div_by_p(self)
 
File <string>:168, in pth_root(self)
 
ValueError: Function is not a p-th power.
[6nsage: om2 = ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx
[6nssage: om2.expansion_at_infty()
2*t^-2 + 2 + 2*t^4 + t^6 + O(t^8)
[6nsage: om2.cartier().expansion_at_infty()
1 + 2*t^2 + t^4 + t^6 + 2*t^8 + O(t^10)
[6nsage: load('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
coordinates of form self (1/y) dx
(1, 1)
omega, omega_regular ((-1)/y) dx (2) dy
omega, omega_regular ((-x^3 + x)/y) dx (2*x^3 + x) dy
aux (V(((-x^12 + x^10 + x^6 - x^4)/y) dx), V(((2*x^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
aux_divided_by_p (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
aux_divided_by_p (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [124], in <cell line: 1>()
----> 1 load('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[Integer(1)]).coordinates(basis = B)
 
File <string>:101, in coordinates(self, basis)
 
File <string>:70, in coordinates(self)
 
File <string>:70, in coordinates(self)
 
[... skipping similar frames: coordinates at line 70 (234 times)]
 
File <string>:70, in coordinates(self)
 
File <string>:60, in coordinates(self)
 
File <string>:107, in coordinates(self, basis, basis_holo, prec)
 
File <string>:79, in serre_duality_pairing(self, fct, prec)
 
File <string>:143, in expansion_at_infty(self, place, prec)
 
File <string>:135, in expansion_at_infty(self, place, prec)
 
File <string>:18, in naive_hensel(fct, F, start, prec)
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:895, in sage.rings.polynomial.polynomial_element.Polynomial.__call__()
893 result = pol.get_unsafe(d)
894 for i in xrange(d - 1, -1, -1):
--> 895 result = result * a + pol.get_unsafe(i)
896 return result
897 pol._compiled = CompiledPolynomialFunction(pol.list())
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__()
1512 cdef int cl = classify_elements(left, right)
1513 if HAVE_SAME_PARENT(cl):
-> 1514 return (<Element>left)._mul_(right)
1515 if BOTH_ARE_ELEMENT(cl):
1516 return coercion_model.bin_op(left, right, mul)
 
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:913, in sage.rings.laurent_series_ring_element.LaurentSeries._mul_()
911 cdef LaurentSeries right = <LaurentSeries>right_r
912 return type(self)(self._parent,
--> 913 self.__u * right.__u,
914 self.__n + right.__n)
915
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__()
1512 cdef int cl = classify_elements(left, right)
1513 if HAVE_SAME_PARENT(cl):
-> 1514 return (<Element>left)._mul_(right)
1515 if BOTH_ARE_ELEMENT(cl):
1516 return coercion_model.bin_op(left, right, mul)
 
File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:540, in sage.rings.power_series_poly.PowerSeries_poly._mul_()
538 """
539 prec = self._mul_prec(right_r)
--> 540 return PowerSeries_poly(self._parent,
541 self.__f * (<PowerSeries_poly>right_r).__f,
542 prec=prec,
 
File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:44, in sage.rings.power_series_poly.PowerSeries_poly.__init__()
42 ValueError: series has negative valuation
43 """
---> 44 R = parent._poly_ring()
45 if isinstance(f, Element):
46 if (<Element>f)._parent is R:
 
File /ext/sage/9.7/src/sage/rings/power_series_ring.py:961, in PowerSeriesRing_generic._poly_ring(self)
958 pass
959 return False
--> 961 def _poly_ring(self):
962 """
963 Return the underlying polynomial ring used to represent elements of
964 this power series ring.
(...)
970 Univariate Polynomial Ring in t over Integer Ring
971 """
972 return self.__poly_ring
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: load('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
coordinates of form self (1/y) dx
(1, 1)
omega, omega_regular ((-1)/y) dx (2) dy
omega, omega_regular ((-x^3 + x)/y) dx (2*x^3 + x) dy
aux (V(((-x^12 + x^10 + x^6 - x^4)/y) dx), V(((2*x^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
aux_divided_by_p (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [125], in <cell line: 1>()
----> 1 load('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[Integer(1)]).coordinates(basis = B)
 
File <string>:100, in coordinates(self, basis)
 
File <string>:86, in div_by_p(self)
 
File <string>:26, in __sub__(self, other)
 
AttributeError: 'superelliptic_function' object has no attribute 'form'
[6n[6n[6nssage: load('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
coordinates of form self (1/y) dx
(1, 1)
omega, omega_regular ((-1)/y) dx (2) dy
omega, omega_regular ((-x^3 + x)/y) dx (2*x^3 + x) dy
aux (V(((-x^12 + x^10 + x^6 - x^4)/y) dx), V(((2*x^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
aux_divided_by_p (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True
aux_divided_by_p (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
^C---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:609, in PolynomialRing(base_ring, *args, **kwds)
608 try:
--> 609 k = Integer(arg)
610 except TypeError:
611 # Interpret arg as names
 
File /ext/sage/9.7/src/sage/rings/integer.pyx:717, in sage.rings.integer.Integer.__init__()
716
--> 717 raise TypeError("unable to coerce %s to an integer" % type(x))
718
 
TypeError: unable to coerce <class 'tuple'> to an integer
 
During handling of the above exception, another exception occurred:
 
KeyboardInterrupt Traceback (most recent call last)
Input In [126], in <cell line: 1>()
----> 1 load('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[Integer(1)]).coordinates(basis = B)
 
File <string>:102, in coordinates(self, basis)
 
File <string>:70, in coordinates(self)
 
File <string>:70, in coordinates(self)
 
[... skipping similar frames: coordinates at line 70 (133 times)]
 
File <string>:70, in coordinates(self)
 
File <string>:50, in coordinates(self)
 
File <string>:98, in de_rham_basis(self)
 
File <string>:91, in basis_de_rham_degrees(self)
 
File <string>:7, in __init__(self, C, g)
 
File <string>:259, in reduction_form(C, g)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce)
704 x0, y0 = x, y
705 try:
--> 706 x, y = resolve_fractions(x0, y0)
707 except (AttributeError, TypeError):
708 raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
709 x0, y0, self))
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:688, in FractionField_generic._element_constructor_.<locals>.resolve_fractions(x, y)
686 yd = y.denominator()
687 try:
--> 688 return (xn * yd, yn * xd)
689 except (AttributeError, TypeError, ValueError):
690 pass
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
1514 return (<Element>left)._mul_(right)
1515 if BOTH_ARE_ELEMENT(cl):
-> 1516 return coercion_model.bin_op(left, right, mul)
1517
1518 cdef long value
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1200, in sage.structure.coerce.CoercionModel.bin_op()
1198 # Now coerce to a common parent and do the operation there
1199 try:
-> 1200 xy = self.canonical_coercion(x, y)
1201 except TypeError:
1202 self._record_exception()
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1311, in sage.structure.coerce.CoercionModel.canonical_coercion()
1309 x_map, y_map = coercions
1310 if x_map is not None:
-> 1311 x_elt = (<Map>x_map)._call_(x)
1312 else:
1313 x_elt = x
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
285 raise TypeError("Cannot coerce {} to {}".format(x, C))
286 cdef Map m
--> 287 cdef Element e = method(C)
288 if e is None:
289 raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x)))
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:198, in sage.rings.polynomial.multi_polynomial.MPolynomial._polynomial_()
196 var = R.variable_name()
197 if var in self._parent.variable_names():
--> 198 return R(self.polynomial(self._parent(var)))
199 else:
200 return R([self])
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:410, in sage.rings.polynomial.multi_polynomial.MPolynomial.polynomial()
408
409 # Make polynomial ring over all variables except var.
--> 410 S = R.base_ring()[tuple(Z)]
411 ring = S[var]
412 if not self:
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:1275, in sage.structure.parent.Parent.__getitem__()
1273 except AttributeError:
1274 return self.list()[n]
-> 1275 return meth(n)
1276
1277 #########################################################################
 
File /ext/sage/9.7/src/sage/categories/rings.py:1176, in Rings.ParentMethods.__getitem__(self, arg)
1173 # 2. Otherwise, try to return a polynomial ring
1175 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-> 1176 return PolynomialRing(self, elts)
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:609, in PolynomialRing(base_ring, *args, **kwds)
607 for arg in args:
608 try:
--> 609 k = Integer(arg)
610 except TypeError:
611 # Interpret arg as names
612 if names is not None:
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: om2 = ((C.x + C.one)/(C.x*C.y - C.y))* C.dx
[6nssage: om2.expansion_at_infty()
1 + 2*t^2 + t^4 + t^6 + 2*t^8 + O(t^10)
[6nsage: om1 = ((-C.x^3 + C.x)/C.y)*C.dx
[6nsage: f1 = ((-C.x^3 + C.x)/C.y)* C.dx
[6nsage: om1 - f1.diffn() == om2
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [131], in <cell line: 1>()
----> 1 om1 - f1.diffn() == om2
 
AttributeError: 'superelliptic_form' object has no attribute 'diffn'
[6nsage: f1 = ((2*C.x^2 + C.x + 2*C.one)/(C.x + 2*C.one))*C.y
[6nsage: om1 - f1.diffn() == om2
True
[6nsage: xi = superelliptic_cech(C, om1, f1)
[6nsage: xi.omega8 == omega2
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [135], in <cell line: 1>()
----> 1 xi.omega8 == omega2
 
NameError: name 'omega2' is not defined
[6nsage: xi.omega8 == om2
True
[6nsage: xi.coordinates()
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [137], in <cell line: 1>()
----> 1 xi.coordinates()
 
File <string>:70, in coordinates(self)
 
File <string>:70, in coordinates(self)
 
[... skipping similar frames: coordinates at line 70 (516 times)]
 
File <string>:70, in coordinates(self)
 
File <string>:66, in coordinates(self)
 
File <string>:7, in decomposition_g0_g8(fct, prec)
 
File <string>:107, in coordinates(self, basis, basis_holo, prec)
 
File <string>:79, in serre_duality_pairing(self, fct, prec)
 
File <string>:143, in expansion_at_infty(self, place, prec)
 
File <string>:135, in expansion_at_infty(self, place, prec)
 
File <string>:18, in naive_hensel(fct, F, start, prec)
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:881, in sage.rings.polynomial.polynomial_element.Polynomial.__call__()
879 d = pol.degree()
880
--> 881 if d <= 0 or (isinstance(a, Element) and R.is_exact() and a.is_zero()):
882 return cst # with the right parent thanks to the above coercion
883 elif pol._parent is R and a.is_gen():
 
File /ext/sage/9.7/src/sage/rings/laurent_series_ring.py:715, in LaurentSeriesRing.is_exact(self)
703 """
704 Get the precision to which exact elements are truncated when
705 necessary (most frequently when inverting).
(...)
711 5
712 """
713 return self._power_series_ring.default_prec()
--> 715 def is_exact(self):
716 """
717 Laurent series rings are inexact.
718
(...)
723 False
724 """
725 return False
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: f1
((2*x^2 + x + 2)/(x + 2))*y
[6nsage: f1.coordinates()
[1]
[6nsage: sage: xi
(((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
[6nsage: load('init.sage')
[6nsage: f1 = ((2*C.x^2 + C.x + 2*C.one)/(C.x + 2*C.one))*C.y
[6nsage: om1 = ((-C.x^3 + C.x)/C.y)*C.dx
[6nsage: xi = superelliptic_cech(C, om1, f1)
[6nsage: xi
(((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
[6nsage: xi.coordinates()
coordinates of (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
^R
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
coordinates of (0 dx, 0, 0 dx)
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [146], in <cell line: 1>()
----> 1 xi.coordinates()
 
File <string>:72, in coordinates(self)
 
File <string>:72, in coordinates(self)
 
[... skipping similar frames: coordinates at line 72 (49 times)]
 
File <string>:72, in coordinates(self)
 
File <string>:67, in coordinates(self)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
1526 if not err:
1527 return (<Element>right)._mul_long(value)
-> 1528 return coercion_model.bin_op(left, right, mul)
1529 except TypeError:
1530 return NotImplemented
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:23, in __rmul__(self, constant)
 
File <string>:5, in __init__(self, C, omega, fct)
 
File <string>:95, in diffn(self)
 
File <string>:7, in __init__(self, C, g)
 
File <string>:245, in reduction_form(C, g)
 
File <string>:223, in reduction(C, g)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
285 raise TypeError("Cannot coerce {} to {}".format(x, C))
286 cdef Map m
--> 287 cdef Element e = method(C)
288 if e is None:
289 raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x)))
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:198, in sage.rings.polynomial.multi_polynomial.MPolynomial._polynomial_()
196 var = R.variable_name()
197 if var in self._parent.variable_names():
--> 198 return R(self.polynomial(self._parent(var)))
199 else:
200 return R([self])
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:410, in sage.rings.polynomial.multi_polynomial.MPolynomial.polynomial()
408
409 # Make polynomial ring over all variables except var.
--> 410 S = R.base_ring()[tuple(Z)]
411 ring = S[var]
412 if not self:
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:1275, in sage.structure.parent.Parent.__getitem__()
1273 except AttributeError:
1274 return self.list()[n]
-> 1275 return meth(n)
1276
1277 #########################################################################
 
File /ext/sage/9.7/src/sage/categories/rings.py:1103, in Rings.ParentMethods.__getitem__(self, arg)
1099 return (arg,)
1101 # 1. If arg is a list, try to return a power series ring.
-> 1103 if isinstance(arg, list):
1104 if not arg:
1105 raise TypeError("power series rings must have at least one variable")
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: load('init.sage')
[6nsage: f1 = ((2*C.x^2 + C.x + 2*C.one)/(C.x + 2*C.one))*C.y
[6nsage: om1 = ((-C.x^3 + C.x)/C.y)*C.dx
[6nsage: xi = superelliptic_cech(C, om1, f1)
[6nsage: xi.coordinates()
coordinates of (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
coordinates of (0 dx, 0, 0 dx)
(0, 1)
[6nsage: load('init.sage')
[6nsage: B = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
coordinates of form self (1/y) dx
(1, 1)
omega, omega_regular ((-1)/y) dx (2) dy
omega, omega_regular ((-x^3 + x)/y) dx (2*x^3 + x) dy
aux (V(((-x^12 + x^10 + x^6 - x^4)/y) dx), V(((2*x^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
aux_divided_by_p (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True
aux_divided_by_p (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
coord_aux_divided_by_p (0, 1)
[1, 4]
sage: eta2 = superelliptic_drw_cech(C.x.teichmuller()*(C.y.teichmuller()).diffn() + ((2*C.x^4 + 2*C.x^2 + 2*C.one) * C.y).verschiebung().diffn(), - (C.y/C.x).teic
....: muller())
sage: eta2.coordinates(basis = B)
(0, 1)
omega, omega_regular 0 dx (0) dy
omega, omega_regular 0 dx (0) dy
aux (0, V(((x^16 + x^10)/(x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2))*y), V(((-x^8 + x^6 - 1)/y) dx))
aux_divided_by_p (0 dx, ((x^5 + x^3)/(x^4 + x^2 + 1))*y, ((-x^3)/y) dx)
aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True
aux_divided_by_p (0 dx, ((x^5 + x^3)/(x^4 + x^2 + 1))*y, ((-x^3)/y) dx)
coordinates of form self ((-x^3)/y) dx
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [155], in <cell line: 1>()
----> 1 eta2.coordinates(basis = B)
 
File <string>:102, in coordinates(self, basis)
 
File <string>:73, in coordinates(self)
 
File <string>:59, in coordinates(self)
 
File <string>:94, in coordinates(self, basis)
 
File <string>:16, in linear_representation_polynomials(polynomial, list_of_polynomials)
 
File /ext/sage/9.7/src/sage/matrix/matrix2.pyx:903, in sage.matrix.matrix2.Matrix.solve_right()
901
902 if not self.is_square():
--> 903 X = self._solve_right_general(C, check=check)
904 else:
905 try:
 
File /ext/sage/9.7/src/sage/matrix/matrix2.pyx:1026, in sage.matrix.matrix2.Matrix._solve_right_general()
1024 # Have to check that we actually solved the equation.
1025 if self*X != B:
-> 1026 raise ValueError("matrix equation has no solutions")
1027 return X
1028
 
ValueError: matrix equation has no solutions
[6nsage: omm = (-C.x^8 + C.x^6 - C.one)/C.y)* C.dx
Input In [156]
omm = (-C.x**Integer(8) + C.x**Integer(6) - C.one)/C.y)* C.dx
^
SyntaxError: unmatched ')'
 
[6nsage: omm = (-C.x^8 + C.x^6 - C.one)/C.y* C.dx
sage: omm.expansion_at_infty()
2*t^-16 + 2*t^-8 + O(t^-6)
sage: omm.cartier().expansion_at_infty()
2*t^-6 + t^-2 + O(t^4)
sage: eta2.omega8
[(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^10 + x^8 - x^2 + 1)/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])
[6nsage: eta2.omega8.r()
((-1)/(x*y)) dx
[6nsage: omm = ((-C.x^8 + C.x^6 - C.one)/C.y) C.dx)
Input In [162]
omm = ((-C.x**Integer(8) + C.x**Integer(6) - C.one)/C.y) C.dx)
^
SyntaxError: unmatched ')'
 
[6nsage: omm = ((-C.x^8 + C.x^6 - C.one)/C.y) C.dx
Input In [163]
omm = ((-C.x**Integer(8) + C.x**Integer(6) - C.one)/C.y) C.dx
^
SyntaxError: invalid syntax
 
[6nsage: omm = ((-C.x^8 + C.x^6 - C.one)/C.y)* C.dx
[6nsage: omm.cartier().expansion_at_infty()
2*t^-6 + t^-2 + O(t^4)
[6nsage: eta2.omega8
[(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^10 + x^8 - x^2 + 1)/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])
sage: eta1 = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).verschiebung())
sage: eta1.coordinates()
coordinates of form self (1/y) dx
(1, 0)
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega, omega_regular 0 dx (0) dy
omega, omega_regular 0 dx (0) dy
aux (0, [0], V(((-x^3)/y) dx))
aux_divided_by_p (0 dx, 0, 0 dx)
aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True
aux_divided_by_p (0 dx, 0, 0 dx)
coord_aux_divided_by_p (0, 0)
[1, 0]
sage: eta2 - B[1]
( + V(((-x^8 + x^6 - 1)/y) dx) + dV([(2*x^4 + 2*x^2 + 2)*y]), V((2*x^4 + 2*x^2 + 2)*y), V(((-x^8 + x^6 - 1)/y) dx))
[6nsagsage: B[1].omega8
[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])
sage: B[1].omega8.r()
((-1)/(x*y)) dx
[6nsage: second_patch(B[1].omega8.r())
(x/y) dx
[6nsage: u = C.one/C.x
[6nsage: v = C.y/(C.x)^2
[6nsage: B[1].omega8 + u.teichmuller()*v.teichmuller().diffn()
+ V(((x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
[6nsage: aux= B[1].omega8 + u.teichmuller()*v.teichmuller().diffn()
sage: aux.h2.expansion_at_infty()
2*t + 2*t^5 + t^9 + 2*t^13 + O(t^21)
sage: aux.omega.cartier().expansion_at_infty()
2*t^6 + t^10 + O(t^16)
sage: eta2 - B[1]
( + V(((-x^8 + x^6 - 1)/y) dx) + dV([(2*x^4 + 2*x^2 + 2)*y]), V((2*x^4 + 2*x^2 + 2)*y), V(((-x^8 + x^6 - 1)/y) dx))
[6nsagsage: autom(B[1]).coordinates(basis = B)
coordinates of form self (1/y) dx
(1, 1)
omega, omega_regular ((-1)/y) dx (2) dy
omega, omega_regular ((-x^3 + x)/y) dx (2*x^3 + x) dy
aux (V(((-x^12 + x^10 + x^6 - x^4)/y) dx), V(((2*x^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
aux_divided_by_p (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True
aux_divided_by_p (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
coord_aux_divided_by_p (0, 1)
[1, 4]
[6nsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 3)
[6nsage: B = C.crystalline_cohomology_basis()
---------------------------------------------------------------------------
ZeroDivisionError Traceback (most recent call last)
Input In [182], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis()
 
File <string>:52, in crystalline_cohomology_basis(self, prec)
 
File <string>:98, in de_rham_basis(self)
 
File <string>:80, in basis_de_rham_degrees(self)
 
File <string>:5, in __init__(self, C, omega, fct)
 
File <string>:94, in diffn(self)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1739, in sage.structure.element.Element.__truediv__()
1737 return (<Element>left)._div_(right)
1738 if BOTH_ARE_ELEMENT(cl):
-> 1739 return coercion_model.bin_op(left, right, truediv)
1740
1741 try:
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
1202 self._record_exception()
1203 else:
-> 1204 return PyObject_CallObject(op, xy)
1205
1206 if op is mul:
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
1735 cdef int cl = classify_elements(left, right)
1736 if HAVE_SAME_PARENT(cl):
-> 1737 return (<Element>left)._div_(right)
1738 if BOTH_ARE_ELEMENT(cl):
1739 return coercion_model.bin_op(left, right, truediv)
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:727, in sage.rings.fraction_field_element.FractionFieldElement._div_()
725
726 if snum.is_zero():
--> 727 raise ZeroDivisionError("fraction field element division by zero")
728
729 rightinv = self.__class__(self._parent, sden, snum,
 
ZeroDivisionError: fraction field element division by zero
[6nsage: C.is_smooth()
1
[6nsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
[6nssage: B = C.crystalline_cohomology_basis()
omega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
---------------------------------------------------------------------------
IndexError Traceback (most recent call last)
Input In [185], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis()
 
File <string>:53, in crystalline_cohomology_basis(self, prec)
 
File <string>:31, in de_rham_witt_lift(cech_class, prec)
 
File <string>:7, in decomposition_g0_g8(fct, prec)
 
File <string>:107, in coordinates(self, basis, basis_holo, prec)
 
File <string>:79, in serre_duality_pairing(self, fct, prec)
 
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__()
542 return type(self)(self._parent, f, self.__n)
543
--> 544 return self.__u[i - self.__n]
545
546 def __iter__(self):
 
File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__()
451 return self.base_ring().zero()
452 else:
--> 453 raise IndexError("coefficient not known")
454 return self.__f[n]
455
 
IndexError: coefficient not known
[6nsage: B = C.crystalline_cohomology_basis(prec = 100)
omega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
---------------------------------------------------------------------------
IndexError Traceback (most recent call last)
Input In [186], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis(prec = Integer(100))
 
File <string>:53, in crystalline_cohomology_basis(self, prec)
 
File <string>:31, in de_rham_witt_lift(cech_class, prec)
 
File <string>:7, in decomposition_g0_g8(fct, prec)
 
File <string>:107, in coordinates(self, basis, basis_holo, prec)
 
File <string>:79, in serre_duality_pairing(self, fct, prec)
 
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__()
542 return type(self)(self._parent, f, self.__n)
543
--> 544 return self.__u[i - self.__n]
545
546 def __iter__(self):
 
File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__()
451 return self.base_ring().zero()
452 else:
--> 453 raise IndexError("coefficient not known")
454 return self.__f[n]
455
 
IndexError: coefficient not known
[6nsage: C.de_rham_basis()
[((1/y) dx, 0, (1/y) dx),
((x/y) dx, 0, (x/y) dx),
((x^2/y) dx, 0, (x^2/y) dx),
((x^3/y) dx, 0, (x^3/y) dx),
((x^7/y) dx, 2/x*y, ((-1)/(x*y)) dx),
(((-x^6)/y) dx, 2/x^2*y, 0 dx),
(0 dx, 2/x^3*y, (1/(x^3*y)) dx),
((x^4/y) dx, 2/x^4*y, ((-1)/(x^4*y)) dx)]
[6nsage: load('init.sage')
[6nsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
[6nsage: B = C.crystalline_cohomology_basis()
omega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
---------------------------------------------------------------------------
IndexError Traceback (most recent call last)
Input In [190], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis()
 
File <string>:53, in crystalline_cohomology_basis(self, prec)
 
File <string>:31, in de_rham_witt_lift(cech_class, prec)
 
File <string>:7, in decomposition_g0_g8(fct, prec)
 
File <string>:107, in coordinates(self, basis, basis_holo, prec)
 
File <string>:79, in serre_duality_pairing(self, fct, prec)
 
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__()
542 return type(self)(self._parent, f, self.__n)
543
--> 544 return self.__u[i - self.__n]
545
546 def __iter__(self):
 
File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__()
451 return self.base_ring().zero()
452 else:
--> 453 raise IndexError("coefficient not known")
454 return self.__f[n]
455
 
IndexError: coefficient not known
[6nsage: B = C.crystalline_cohomology_basis(prec = 200)
omega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
---------------------------------------------------------------------------
IndexError Traceback (most recent call last)
Input In [191], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis(prec = Integer(200))
 
File <string>:53, in crystalline_cohomology_basis(self, prec)
 
File <string>:34, in de_rham_witt_lift(cech_class, prec)
 
File <string>:35, in decomposition_omega0_omega8(omega, prec)
 
File /ext/sage/9.7/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds)
583 return expression.sum(*args, **kwds)
584 elif max(len(args),len(kwds)) <= 1:
--> 585 return sum(expression, *args, **kwds)
586 else:
587 from sage.symbolic.ring import SR
 
File <string>:35, in <genexpr>(.0)
 
File <string>:156, in residue(self, place, prec)
 
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__()
542 return type(self)(self._parent, f, self.__n)
543
--> 544 return self.__u[i - self.__n]
545
546 def __iter__(self):
 
File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__()
451 return self.base_ring().zero()
452 else:
--> 453 raise IndexError("coefficient not known")
454 return self.__f[n]
455
 
IndexError: coefficient not known
[6nsage: load('init.sage')
[6nsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
[6nsage: B = C.crystalline_cohomology_basis(prec = 200)
omega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(2*x^5/(x^8 + 2))*y] d[x] + V(((-x^27 - x^19)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]) 0
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift 0 [(1/(x^12 + 2*x^4))*y] d[x] + V(((x^8 + 1)/(x^24*y - x^16*y)) dx) + dV([(1/(x^32 + 2*x^24))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^3/(x^8 + 2))*y] d[x] + V(((-x^29 - x^21 + x^13)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]) [(2/(x^13 + 2*x^5))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^35*y - x^27*y)) dx) + dV([(2/(x^35 + 2*x^27))*y])
result.omega8 == compare True
result.omega8 - compare 0
[6nsage: B
[([(1/(x^9 + 2*x))*y] d[x] + V(((-x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]), V(x*y), [(1/(x^9 + 2*x))*y] d[x] + V(((-x)/(x^8*y - y)) dx) + dV([(x/(x^8 + 2))*y])),
([(1/(x^8 + 2))*y] d[x] + V(((-x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]), V(((x^8 + 1)/x^4)*y), [(1/(x^8 + 2))*y] d[x] + V(((-x^4)/(x^8*y - y)) dx) + dV([(1/(x^12 + 2*x^4))*y])),
([(x/(x^8 + 2))*y] d[x] + V(((-x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]), V(((x^8 + 1)/x)*y), [(x/(x^8 + 2))*y] d[x] + V(((-x^7)/(x^8*y - y)) dx) + dV([(1/(x^9 + 2*x))*y])),
([(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]), V((x^10 + x^2)*y), [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(x^2/(x^8 + 2))*y])),
([(x^6/(x^8 + 2))*y] d[x] + V(((x^14 + x^6)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]), [2/x*y] + V(((x^24 + x^16 + x^8 + 2)/x^2)*y), [(2/(x^10 + 2*x^2))*y] d[x] + V(((-1)/(x^10*y - x^2*y)) dx) + dV([(2/(x^10 + 2*x^2))*y])),
([(2*x^5/(x^8 + 2))*y] d[x] + V(((x^19 - x^11 + x^3)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]), [2/x^2*y] + V((2*x^19 + 2*x^11 + 2*x^3)*y), V((1/(x^5*y)) dx)),
(V(((x^8 + 1)/y) dx), [2/x^3*y], [(1/(x^12 + 2*x^4))*y] d[x] + V(((-1)/(x^16*y - x^8*y)) dx) + dV([(1/(x^8 + 2))*y])),
([(x^3/(x^8 + 2))*y] d[x] + V(((x^13 + x^5)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]), [2/x^4*y] + V(((x^16 + x^8 + 1)/x^3)*y), [(2/(x^13 + 2*x^5))*y] d[x] + V(((-1)/(x^11*y - x^3*y)) dx) + dV([(2/(x^11 + 2*x^3))*y]))]
[6nsage: autom(B[0]).coordinates(basis=B)
(1, 0, 0, 0, 0, 0, 0, 0)
aux (0, V(((2*x^11 + 2*x^10 + 2*x^8 + 2*x^7)/(x^35 + x^34 + x^32 + x^31 + x^27 + 2*x^25 + x^24 + 2*x^22 + x^19 + 2*x^16 + x^13 + 2*x^11 + x^10 + 2*x^8 + 2*x^4 + 2*x^3 + 2*x + 2))*y), V(((x^8 + x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1)/(x^16*y - x^15*y + x^14*y - x^13*y + x^12*y - x^11*y + x^10*y - x^9*y - x^8*y + x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y)) dx))
aux_divided_by_p (0 dx, ((2*x^3 + 2*x^2)/(x^14 + x^13 + 2*x^11 + 2*x^10 + x^8 + x^7 + x^6 + 2*x^4 + 2*x^3 + x + 1))*y, ((x^4 - x^3 + x^2)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx)
aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True
aux_divided_by_p (0 dx, ((2*x^3 + 2*x^2)/(x^14 + x^13 + 2*x^11 + 2*x^10 + x^8 + x^7 + x^6 + 2*x^4 + 2*x^3 + x + 1))*y, ((x^4 - x^3 + x^2)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx)
coord_aux_divided_by_p (0, 0, 0, 0, 0, 0, 0, 0)
[1, 0, 0, 0, 0, 0, 0, 0]
[6nsage: autom(B[1]).coordinates(basis=B)
(1, 1, 0, 0, 0, 0, 0, 0)
aux (0, V(((x^11 + x^10 + x^8 + x^7)/(x^32 + x^31 + 2*x^29 + 2*x^28 + 2*x^26 + 2*x^25 + x^24 + 2*x^23 + x^22 + 2*x^21 + 2*x^20 + 2*x^18 + 2*x^17 + x^16 + 2*x^15 + 2*x^14 + 2*x^12 + 2*x^11 + x^10 + 2*x^9 + x^8 + 2*x^7 + 2*x^6 + 2*x^4 + 2*x^3 + x + 1))*y), V(((x^10 + x^9 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - 1)/(x^15*y + x^14*y - x^12*y - x^11*y + x^9*y + x^8*y + x^7*y - x^5*y - x^4*y + x^2*y + x*y)) dx))
aux_divided_by_p (0 dx, ((x^3 + x^2)/(x^13 + 2*x^12 + 2*x^11 + x^10 + x^7 + 2*x^6 + 2*x^3 + x^2 + x + 2))*y, ((x^5 + x^2)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx)
aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True
aux_divided_by_p (0 dx, ((x^3 + x^2)/(x^13 + 2*x^12 + 2*x^11 + x^10 + x^7 + 2*x^6 + 2*x^3 + x^2 + x + 2))*y, ((x^5 + x^2)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx)
coord_aux_divided_by_p (0, 0, 0, 0, 0, 0, 0, 0)
[1, 1, 0, 0, 0, 0, 0, 0]
[6nsage: autom(B[2]).coordinates(basis=B)
(1, 2, 1, 0, 0, 0, 0, 0)
aux (V(((x^54 - x^46 + x^45 - x^37 - x^30 + x^22 - x^21 + x^13)/y) dx), V(((x^65 + x^64 + x^62 + x^61 + 2*x^41 + 2*x^40 + 2*x^38 + 2*x^37 + 2*x^14 + 2*x^13 + x^11 + x^10 + 2*x^8 + 2*x^7)/(x^35 + x^34 + x^32 + x^31 + x^27 + 2*x^25 + x^24 + 2*x^22 + x^19 + 2*x^16 + x^13 + 2*x^11 + x^10 + 2*x^8 + 2*x^4 + 2*x^3 + 2*x + 2))*y), V(((x^13 - x^12 + x^11 - x^10 + x^9 - x^8 - x^2 + x - 1)/(x^15*y + x^14*y - x^12*y - x^11*y + x^9*y + x^8*y + x^7*y - x^5*y - x^4*y + x^2*y + x*y)) dx))
aux_divided_by_p (((x^15 + x^12 - x^7 - x^4)/y) dx, ((x^21 + x^20 + 2*x^13 + 2*x^12 + 2*x^4 + x^3 + 2*x^2)/(x^14 + x^13 + 2*x^11 + 2*x^10 + x^8 + x^7 + x^6 + 2*x^4 + 2*x^3 + x + 1))*y, ((x^6 + x^5 + x^3 + x^2)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx)
aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True
aux_divided_by_p (((x^15 + x^12 - x^7 - x^4)/y) dx, ((x^21 + x^20 + 2*x^13 + 2*x^12 + 2*x^4 + x^3 + 2*x^2)/(x^14 + x^13 + 2*x^11 + 2*x^10 + x^8 + x^7 + x^6 + 2*x^4 + 2*x^3 + x + 1))*y, ((x^6 + x^5 + x^3 + x^2)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx)
coord_aux_divided_by_p (0, 0, 0, 0, 2, 0, 0, 2)
[1, 2, 1, 0, 6, 0, 0, 6]
[6nsage: autom(B[3]).coordinates(basis=B)
(1, 0, 0, 1, 0, 0, 0, 0)
aux (V(((x^63 - x^55 - x^39 - x^36 + x^31 + x^28 + x^12 - x^4)/y) dx), V(((x^76 + x^73 + x^70 + x^67 + x^64 + x^61 + x^58 + x^55 + 2*x^49 + 2*x^46 + 2*x^43 + 2*x^40 + 2*x^37 + 2*x^34 + 2*x^31 + 2*x^28 + x^25 + x^22 + x^19 + x^16 + 2*x^13 + 2*x^10 + 2*x^7 + 2*x^4 + 2*x)/(x^37 + x^34 + x^31 + x^29 + x^28 + x^26 + x^25 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^12 + x^11 + x^9 + x^8 + x^6 + x^3 + 1))*y), V(((-x^16 - x^14 - x^13 - x^11 - x^10 - x^8 + x^7 - x^5 - x^4 - x^3 + x - 1)/(x^15*y + x^14*y - x^12*y - x^11*y + x^9*y + x^8*y + x^7*y - x^5*y - x^4*y + x^2*y + x*y)) dx))
aux_divided_by_p (((x^18 - x^10 - x^9 + x)/y) dx, ((x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + 2*x^12 + 2*x^11 + 2*x^10 + 2*x^9 + x^8 + x^7 + x^6 + x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 2)/(x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + 2*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 2))*y, ((x^9 - x^4 + x^3 - x^2 + x + 1)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx)
aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True
aux_divided_by_p (((x^18 - x^10 - x^9 + x)/y) dx, ((x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + 2*x^12 + 2*x^11 + 2*x^10 + 2*x^9 + x^8 + x^7 + x^6 + x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 2)/(x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + 2*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 2))*y, ((x^9 - x^4 + x^3 - x^2 + x + 1)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx)
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [199], in <cell line: 1>()
----> 1 autom(B[Integer(3)]).coordinates(basis=B)
 
File <string>:102, in coordinates(self, basis)
 
File <string>:73, in coordinates(self)
 
File <string>:59, in coordinates(self)
 
File <string>:93, in coordinates(self, basis)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
786 return self._call_with_args(x, args, kwds)
787
--> 788 cpdef Element _call_(self, x):
789 """
790 Call method with a single argument, not implemented in the base class.
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
1249 return num
1250 if check and not den.is_unit():
1251 # This should probably be a ValueError.
1252 # However, too much existing code is expecting this to throw a
1253 # TypeError, so we decided to keep it for the time being.
-> 1254 raise TypeError("fraction must have unit denominator")
1255 return num * den.inverse_of_unit()
 
TypeError: fraction must have unit denominator
[6nsage: ~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
[22;0t[6n[6n[6nsage: load('init.sage')
[6nsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
[6nsage: B = C.crystalline_cohomology_basis(); autom(B[3]).coordinates(basis=B)
omega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
File <string>:60, in __mul__(self, other)
 
File <string>:14, in __init__(self, C, g)
 
File <string>:224, in reduction(C, g)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
1515 if BOTH_ARE_ELEMENT(cl):
-> 1516 return coercion_model.bin_op(left, right, mul)
1517
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1200, in sage.structure.coerce.CoercionModel.bin_op()
1199 try:
-> 1200 xy = self.canonical_coercion(x, y)
1201 except TypeError:
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1311, in sage.structure.coerce.CoercionModel.canonical_coercion()
1310 if x_map is not None:
-> 1311 x_elt = (<Map>x_map)._call_(x)
1312 else:
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
286 cdef Map m
--> 287 cdef Element e = method(C)
288 if e is None:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:198, in sage.rings.polynomial.multi_polynomial.MPolynomial._polynomial_()
197 if var in self._parent.variable_names():
--> 198 return R(self.polynomial(self._parent(var)))
199 else:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:411, in sage.rings.polynomial.multi_polynomial.MPolynomial.polynomial()
410 S = R.base_ring()[tuple(Z)]
--> 411 ring = S[var]
412 if not self:
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:1275, in sage.structure.parent.Parent.__getitem__()
1274 return self.list()[n]
-> 1275 return meth(n)
1276
 
File /ext/sage/9.7/src/sage/categories/rings.py:1176, in Rings.ParentMethods.__getitem__(self, arg)
1175 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-> 1176 return PolynomialRing(self, elts)
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:632, in PolynomialRing(base_ring, *args, **kwds)
630 raise TypeError("you must specify the names of the variables")
--> 632 names = normalize_names(n, names)
634 # At this point, we have only handled the "names" keyword if it was
635 # needed. Since we know the variable names, it would logically be
636 # an error to specify an additional "names" keyword. However,
(...)
639 # and we allow this for historical reasons. However, the names
640 # must be consistent!
 
File /ext/sage/9.7/src/sage/structure/category_object.pyx:900, in sage.structure.category_object.normalize_names()
899
--> 900 cpdef normalize_names(Py_ssize_t ngens, names):
901 r"""
 
File /ext/sage/9.7/src/sage/structure/category_object.pyx:993, in sage.structure.category_object.normalize_names()
992 # Convert names to strings and strip whitespace
--> 993 names = [str(x).strip() for x in names]
994 else:
 
File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
193 return super().__repr__()
--> 194 result = reprfunc()
195 if isinstance(result, str):
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2462, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular._repr_()
2461 cdef ring *_ring = self._parent_ring
-> 2462 s = singular_polynomial_str(self._poly, _ring)
2463 return s
 
File /ext/sage/9.7/src/sage/libs/singular/polynomial.pyx:442, in sage.libs.singular.polynomial.singular_polynomial_str()
441 s = plusminus_pattern.sub("\\1 \\2 ", s)
--> 442 s = parenthvar_pattern.sub("\\1", s)
443 return s
 
File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/re.py:324, in _subx(pattern, template)
322 return sre_parse.expand_template(template, match)
--> 324 def _subx(pattern, template):
325 # internal: Pattern.sub/subn implementation helper
326 template = _compile_repl(template, pattern)
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
 
During handling of the above exception, another exception occurred:
 
AttributeError Traceback (most recent call last)
Input In [3], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis(); autom(B[Integer(3)]).coordinates(basis=B)
 
File <string>:53, in crystalline_cohomology_basis(self, prec)
 
File <string>:24, in de_rham_witt_lift(cech_class, prec)
 
File <string>:6, in de_rham_witt_lift_form0(omega)
 
File <string>:73, in diffn(self, dy_w)
 
File <string>:177, in dy_w(C)
 
File /ext/sage/9.7/src/sage/rings/rational.pyx:2414, in sage.rings.rational.Rational.__mul__()
2412 return x
2413
-> 2414 return coercion_model.bin_op(left, right, operator.mul)
2415
2416 cpdef _mul_(self, right):
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:48, in __rmul__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
1526 if not err:
1527 return (<Element>right)._mul_long(value)
-> 1528 return coercion_model.bin_op(left, right, mul)
1529 except TypeError:
1530 return NotImplemented
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:43, in __rmul__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
1526 if not err:
1527 return (<Element>right)._mul_long(value)
-> 1528 return coercion_model.bin_op(left, right, mul)
1529 except TypeError:
1530 return NotImplemented
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:43, in __rmul__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
1526 if not err:
1527 return (<Element>right)._mul_long(value)
-> 1528 return coercion_model.bin_op(left, right, mul)
1529 except TypeError:
1530 return NotImplemented
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:43, in __rmul__(self, other)
 
File <string>:31, in __add__(self, other)
 
File <string>:63, in __mul__(self, other)
 
AttributeError: 'superelliptic_function' object has no attribute 'form'
[6nsage: B = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [4], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(3)]).coordinates(basis=B)
 
File <string>:52, in crystalline_cohomology_basis(self, prec)
 
File <string>:98, in de_rham_basis(self)
 
File <string>:80, in basis_de_rham_degrees(self)
 
File <string>:5, in __init__(self, C, omega, fct)
 
File <string>:28, in __sub__(self, other)
 
File <string>:7, in __init__(self, C, g)
 
File <string>:259, in reduction_form(C, g)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:711, in FractionField_generic._element_constructor_(self, x, y, coerce)
708 raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
709 x0, y0, self))
710 try:
--> 711 return self._element_class(self, x, y, coerce=coerce)
712 except TypeError:
713 if parent(x) is parent(x0):
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
112 FieldElement.__init__(self, parent)
113 if coerce:
--> 114 self.__numerator = parent.ring()(numerator)
115 self.__denominator = parent.ring()(denominator)
116 else:
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
1001
1002 try:
-> 1003 return self(str(element))
1004 except TypeError:
1005 pass
 
File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
192 except AttributeError:
193 return super().__repr__()
--> 194 result = reprfunc()
195 if isinstance(result, str):
196 return result
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_()
2688 NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3
2689 """
-> 2690 return self._repr()
2691
2692 def _latex_(self, name=None):
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2656, in sage.rings.polynomial.polynomial_element.Polynomial._repr()
2654 if n != m-1:
2655 s += " + "
-> 2656 x = y = repr(x)
2657 if y.find("-") == 0:
2658 y = y[1:]
 
File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
192 except AttributeError:
193 return super().__repr__()
--> 194 result = reprfunc()
195 if isinstance(result, str):
196 return result
 
File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:338, in sage.rings.fraction_field_FpT.FpTElement._repr_()
336 """
337 if nmod_poly_degree(self._denom) == 0 and nmod_poly_get_coeff_ui(self._denom, 0) == 1:
--> 338 return repr(self.numer())
339 else:
340 numer_s = repr(self.numer())
 
File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
192 except AttributeError:
193 return super().__repr__()
--> 194 result = reprfunc()
195 if isinstance(result, str):
196 return result
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_()
2688 NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3
2689 """
-> 2690 return self._repr()
2691
2692 def _latex_(self, name=None):
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2656, in sage.rings.polynomial.polynomial_element.Polynomial._repr()
2654 if n != m-1:
2655 s += " + "
-> 2656 x = y = repr(x)
2657 if y.find("-") == 0:
2658 y = y[1:]
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: B = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)
omega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(2*x^5/(x^8 + 2))*y] d[x] + V(((-x^27 - x^19)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]) 0
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift 0 [(1/(x^12 + 2*x^4))*y] d[x] + V(((x^8 + 1)/(x^24*y - x^16*y)) dx) + dV([(1/(x^32 + 2*x^24))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^3/(x^8 + 2))*y] d[x] + V(((-x^29 - x^21 + x^13)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]) [(2/(x^13 + 2*x^5))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^35*y - x^27*y)) dx) + dV([(2/(x^35 + 2*x^27))*y])
result.omega8 == compare True
result.omega8 - compare 0
(1, 0, 0, 1, 0, 0, 0, 0)
aux (V(((x^63 - x^55 - x^39 - x^36 + x^31 + x^28 + x^12 - x^4)/y) dx), V(((x^76 + x^73 + x^70 + x^67 + x^64 + x^61 + x^58 + x^55 + 2*x^49 + 2*x^46 + 2*x^43 + 2*x^40 + 2*x^37 + 2*x^34 + 2*x^31 + 2*x^28 + x^25 + x^22 + x^19 + x^16 + 2*x^13 + 2*x^10 + 2*x^7 + 2*x^4 + 2*x)/(x^37 + x^34 + x^31 + x^29 + x^28 + x^26 + x^25 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^12 + x^11 + x^9 + x^8 + x^6 + x^3 + 1))*y), V(((-x^16 - x^14 - x^13 - x^11 - x^10 - x^8 + x^7 - x^5 - x^4 - x^3 + x - 1)/(x^15*y + x^14*y - x^12*y - x^11*y + x^9*y + x^8*y + x^7*y - x^5*y - x^4*y + x^2*y + x*y)) dx))
aux_divided_by_p (((x^18 - x^10 - x^9 + x)/y) dx, ((x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + 2*x^12 + 2*x^11 + 2*x^10 + 2*x^9 + x^8 + x^7 + x^6 + x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 2)/(x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + 2*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 2))*y, ((x^9 - x^4 + x^3 - x^2 + x + 1)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx)
is regular True True
aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [5], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(3)]).coordinates(basis=B)
 
File <string>:102, in coordinates(self, basis)
 
File <string>:73, in coordinates(self)
 
File <string>:59, in coordinates(self)
 
File <string>:93, in coordinates(self, basis)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
786 return self._call_with_args(x, args, kwds)
787
--> 788 cpdef Element _call_(self, x):
789 """
790 Call method with a single argument, not implemented in the base class.
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
1249 return num
1250 if check and not den.is_unit():
1251 # This should probably be a ValueError.
1252 # However, too much existing code is expecting this to throw a
1253 # TypeError, so we decided to keep it for the time being.
-> 1254 raise TypeError("fraction must have unit denominator")
1255 return num * den.inverse_of_unit()
 
TypeError: fraction must have unit denominator
[6nsage: om1 = ((C.x^18 - C.x^10 - C.x^9 + C.x)/C.y) * C.dx
[6nsage: C
Superelliptic curve with the equation y^2 = x^9 + 2*x over Finite Field of size 3
sage: f = ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 +*2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.xx11 + C.x^10 + C.x^9 + C.x^8 + 2*C.
....: ^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2))*C.y
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [8], in <cell line: 1>()
----> 1 f = ((C.x**Integer(25) + C.x**Integer(24) + C.x**Integer(23) + C.x**Integer(22) + C.x**Integer(21) + C.x**Integer(20) + C.x**Integer(19) + C.x**Integer(18) + Integer(2)*C.x**Integer(16) + Integer(2)*C.x**Integer(15) + Integer(2)*C.x**Integer(14) + Integer(2)*C.x**Integer(13) + Integer(2)*C.x**Integer(12) + Integer(2)*C.x**Integer(11) + Integer(2)*C.x**Integer(10) + Integer(2)*C.x**Integer(9) + C.x**Integer(8) + C.x**Integer(7) + C.x**Integer(6) + C.x**Integer(5) + Integer(2)*C.x**Integer(4) + Integer(2)*C.x**Integer(3) + Integer(2)*C.x**Integer(2) + Integer(2)*C.x + Integer(2))/(C.x**Integer(15) + C.x**Integer(14) + C.x**Integer(13) + C.x**Integer(12) + C.x**Integer(11) + C.x**Integer(10) + C.x**Integer(9) + C.x**Integer(8) + Integer(2)*C.x**Integer(7) + Integer(2)*C.x**Integer(6) + Integer(2)*C.x**Integer(5) + Integer(2)*C.x**Integer(4) + Integer(2)*C.x**Integer(3) + Integer(2)*C.x**Integer(2) + Integer(2)*C.x + Integer(2)))*C.y
 
File <string>:38, in __add__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
493 """
--> 494 return self.getattr_from_category(name)
495
496 cdef getattr_from_category(self, name):
 
File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
505 else:
506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
508
509 def __dir__(self):
 
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
359 dummy_error_message.cls = type(self)
360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
362 attribute = <object>attr
363 # Check for a descriptor (__get__ in Python)
 
AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function'
sage: f = ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 +*2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.xx11 + C.x^10 + C.x^9 + C.x^8 + 2*C.
....: ^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [9], in <cell line: 1>()
----> 1 f = ((C.x**Integer(25) + C.x**Integer(24) + C.x**Integer(23) + C.x**Integer(22) + C.x**Integer(21) + C.x**Integer(20) + C.x**Integer(19) + C.x**Integer(18) + Integer(2)*C.x**Integer(16) + Integer(2)*C.x**Integer(15) + Integer(2)*C.x**Integer(14) + Integer(2)*C.x**Integer(13) + Integer(2)*C.x**Integer(12) + Integer(2)*C.x**Integer(11) + Integer(2)*C.x**Integer(10) + Integer(2)*C.x**Integer(9) + C.x**Integer(8) + C.x**Integer(7) + C.x**Integer(6) + C.x**Integer(5) + Integer(2)*C.x**Integer(4) + Integer(2)*C.x**Integer(3) + Integer(2)*C.x**Integer(2) + Integer(2)*C.x + Integer(2))/(C.x**Integer(15) + C.x**Integer(14) + C.x**Integer(13) + C.x**Integer(12) + C.x**Integer(11) + C.x**Integer(10) + C.x**Integer(9) + C.x**Integer(8) + Integer(2)*C.x**Integer(7) + Integer(2)*C.x**Integer(6) + Integer(2)*C.x**Integer(5) + Integer(2)*C.x**Integer(4) + Integer(2)*C.x**Integer(3) + Integer(2)*C.x**Integer(2) + Integer(2)*C.x + Integer(2)*C.one))*C.y
 
File <string>:38, in __add__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
493 """
--> 494 return self.getattr_from_category(name)
495
496 cdef getattr_from_category(self, name):
 
File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
505 else:
506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
508
509 def __dir__(self):
 
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
359 dummy_error_message.cls = type(self)
360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
362 attribute = <object>attr
363 # Check for a descriptor (__get__ in Python)
 
AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function'
sage: f = ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 +*2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)/(C.x^15 + C.x^14 + C.x^13 + C.x^12++ C.x^11 + C.x^10 + C.x^9 + C.x^8
....: 2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y
[6nsasage: xi = superelliptic_cech(C, om1, f)
[6nsage: xi.omega0.is_regular_on_U0()
True
[6nsage: xi.omega8.is_regular_on_Uinfty()
True
[6nsage: xi.coordinates()
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [14], in <cell line: 1>()
----> 1 xi.coordinates()
 
File <string>:73, in coordinates(self)
 
File <string>:59, in coordinates(self)
 
File <string>:93, in coordinates(self, basis)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
786 return self._call_with_args(x, args, kwds)
787
--> 788 cpdef Element _call_(self, x):
789 """
790 Call method with a single argument, not implemented in the base class.
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
1249 return num
1250 if check and not den.is_unit():
1251 # This should probably be a ValueError.
1252 # However, too much existing code is expecting this to throw a
1253 # TypeError, so we decided to keep it for the time being.
-> 1254 raise TypeError("fraction must have unit denominator")
1255 return num * den.inverse_of_unit()
 
TypeError: fraction must have unit denominator
sage: f.coordinates()
[0, 0, 0, 0]
sage: ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C^x^12 + 2*C.x^11 + 2*C.x^10 + 2*C.x
....: 9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 + 2*C.x^7
....: 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [16], in <cell line: 1>()
----> 1 ((C.x**Integer(25) + C.x**Integer(24) + C.x**Integer(23) + C.x**Integer(22) + C.x**Integer(21) + C.x**Integer(20) + C.x**Integer(19) + C.x**Integer(18) + Integer(2)*C.x**Integer(16) + Integer(2)*C.x**Integer(15) + Integer(2)*C.x**Integer(14) + Integer(2)*C.x**Integer(13) + Integer(2)*C.x**Integer(12) + Integer(2)*C.x**Integer(11) + Integer(2)*C.x**Integer(10) + Integer(2)*C.x**Integer(9) + C.x**Integer(8) + C.x**Integer(7) + C.x**Integer(6) + C.x**Integer(5) + Integer(2)*C.x**Integer(4) + Integer(2)*C.x**Integer(3) + Integer(2)*C.x**Integer(2) + Integer(2)*C.x + Integer(2))/(C.x**Integer(15) + C.x**Integer(14) + C.x**Integer(13) + C.x**Integer(12) + C.x**Integer(11) + C.x**Integer(10) + C.x**Integer(9) + C.x**Integer(8) + Integer(2)*C.x**Integer(7) + Integer(2)*C.x**Integer(6) + Integer(2)*C.x**Integer(5) + Integer(2)*C.x**Integer(4) + Integer(2)*C.x**Integer(3) + Integer(2)*C.x**Integer(2) + Integer(2)*C.x + Integer(2)*C.one))*C.y
 
File <string>:38, in __add__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
493 """
--> 494 return self.getattr_from_category(name)
495
496 cdef getattr_from_category(self, name):
 
File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
505 else:
506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
508
509 def __dir__(self):
 
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
359 dummy_error_message.cls = type(self)
360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
362 attribute = <object>attr
363 # Check for a descriptor (__get__ in Python)
 
AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function'
sage: xi.coordinates()
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [17], in <cell line: 1>()
----> 1 xi.coordinates()
 
File <string>:73, in coordinates(self)
 
File <string>:59, in coordinates(self)
 
File <string>:93, in coordinates(self, basis)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
786 return self._call_with_args(x, args, kwds)
787
--> 788 cpdef Element _call_(self, x):
789 """
790 Call method with a single argument, not implemented in the base class.
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
1249 return num
1250 if check and not den.is_unit():
1251 # This should probably be a ValueError.
1252 # However, too much existing code is expecting this to throw a
1253 # TypeError, so we decided to keep it for the time being.
-> 1254 raise TypeError("fraction must have unit denominator")
1255 return num * den.inverse_of_unit()
 
TypeError: fraction must have unit denominator
[6nsage: xi.coordinates()
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [18], in <cell line: 1>()
----> 1 xi.coordinates()
 
File <string>:73, in coordinates(self)
 
File <string>:59, in coordinates(self)
 
File <string>:93, in coordinates(self, basis)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
786 return self._call_with_args(x, args, kwds)
787
--> 788 cpdef Element _call_(self, x):
789 """
790 Call method with a single argument, not implemented in the base class.
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
1249 return num
1250 if check and not den.is_unit():
1251 # This should probably be a ValueError.
1252 # However, too much existing code is expecting this to throw a
1253 # TypeError, so we decided to keep it for the time being.
-> 1254 raise TypeError("fraction must have unit denominator")
1255 return num * den.inverse_of_unit()
 
TypeError: fraction must have unit denominator
[6nsage: sage: decomposition_g0_g8(xi.f)
(((x^24 + x^22 + x^20 + x^18 + 2*x^15 + 2*x^13 + 2*x^11)/(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2))*y,
((x^9 + 2*x^8 + x^7 + 2*x^5 + x^4 + 2*x^3 + x + 2)/(x^14 + 2*x^13 + x^11 + 2*x^10 + x^8 + 2*x^7 + x^6 + 2*x^4 + x^3 + 2*x + 1))*y,
0)
[6nsage: gg = (C.x^24 + C.x^22sage: gg = (C.x^24 + C.x^22 + C.x^20 + C.x^18 + 2*C.x^15 + 2*C.x^13 + 2*C.x^11)/(C.x^14 + C.x^12 + C.x^10 + C.x^8 + 2*C.x^6 + 2*C.x^4 + 2*C.x^2 + 2*C.one)
[6nsage: gg = (C.x^24 +sage: gg
(x^24 + x^22 + x^20 + x^18 + 2*x^15 + 2*x^13 + 2*x^11)/(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2)
[6nsage: (x^24 + x^22 + x^20 + x^18 + 2*x^15 + 2*x^13 + 2*x^11).quo_rem(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2)
(x^10 + x^2 + 2*x, x^9 + x^8 + 2*x^7 + x^6 + 2*x^5 + x^4 + 2*x^3 + x^2 + 2*x)
[6nsage: xi.f
((x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + 2*x^12 + 2*x^11 + 2*x^10 + 2*x^9 + x^8 + x^7 + x^6 + x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 2)/(x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + 2*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 2))*y
[6nsage: xi.f.coordinates()
[0, 0, 0, 0]
[6nsage: xi.f.coordinates(prec = 200)
[0, 0, 0, 0]
[6nsage: xi.f.coordinates(prec = 500)
[0, 0, 0, 0]
[6nsage: C.nb_of_pts_at_infty
1
[6nsage: gg = C.x^9 + C.x^8 + 2*C.x^7 + C.x^6 + 2*C.x^5 + C.x^4 + 2*C.x^3 + C.x^2 + 2*C.x
[6nsagesage: Fxy, Rxy, x, y=C.fct_field
[6nsage:sage: fffff = Fxy(xi.f.function)
[6nsage: fffff
(x^25*y + x^24*y + x^23*y + x^22*y + x^21*y + x^20*y + x^19*y + x^18*y - x^16*y - x^15*y - x^14*y - x^13*y - x^12*y - x^11*y - x^10*y - x^9*y + x^8*y + x^7*y + x^6*y + x^5*y - x^4*y - x^3*y - x^2*y - x*y - y)/(x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 - x^7 - x^6 - x^5 - x^4 - x^3 - x^2 - x - 1)
[6nsage: fffff.numerator().quo_rem(fffff.denominator())
(x^10*y + x^2*y - x*y,
x^9*y + x^8*y + x^7*y + x^6*y + x^5*y - x^4*y - x^3*y - x^2*y + x*y - y)
[6nsage: fffff = C.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y
[6nsage: fffff = C.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y
sage: fffff = (C.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y))/+C.x^15 + C.x^14 + C.x^13 + C.x^12
....: C.x^11 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - 1)
Input In [35]
fffff = (C.x**Integer(9)*C.y + C.x**Integer(8)*C.y + C.x**Integer(7)*C.y + C.x**Integer(6)*C.y + C.x**Integer(5)*C.y - C.x**Integer(4)*C.y - C.x**Integer(3)*C.y - C.x**Integer(2)*C.y + C.x*C.y - C.y))/(C.x**Integer(15) + C.x**Integer(14) + C.x**Integer(13) + C.x**Integer(12) + C.x**Integer(11) + C.x**Integer(10) + C.x**Integer(9) + C.x**Integer(8) - C.x**Integer(7) - C.x**Integer(6) - C.x**Integer(5) - C.x**Integer(4) - C.x**Integer(3) - C.x**Integer(2) - C.x - Integer(1))
^
SyntaxError: unmatched ')'
 
sage: fffff = (C.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 +
....: C.x^11 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - 1)
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [36], in <cell line: 1>()
----> 1 fffff = (C.x**Integer(9)*C.y + C.x**Integer(8)*C.y + C.x**Integer(7)*C.y + C.x**Integer(6)*C.y + C.x**Integer(5)*C.y - C.x**Integer(4)*C.y - C.x**Integer(3)*C.y - C.x**Integer(2)*C.y + C.x*C.y - C.y)/(C.x**Integer(15) + C.x**Integer(14) + C.x**Integer(13) + C.x**Integer(12) + C.x**Integer(11) + C.x**Integer(10) + C.x**Integer(9) + C.x**Integer(8) - C.x**Integer(7) - C.x**Integer(6) - C.x**Integer(5) - C.x**Integer(4) - C.x**Integer(3) - C.x**Integer(2) - C.x - Integer(1))
 
File <string>:50, in __sub__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
493 """
--> 494 return self.getattr_from_category(name)
495
496 cdef getattr_from_category(self, name):
 
File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
505 else:
506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
508
509 def __dir__(self):
 
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
359 dummy_error_message.cls = type(self)
360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
362 attribute = <object>attr
363 # Check for a descriptor (__get__ in Python)
 
AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function'
sage: ffff = (C.x^9*C.y + C.x^8*C.y + C.x^7*C.y + C.x^6*C.y + C.x^5*C.y - C.x^4*C.y - C.x^3*C.y - C.x^2*C.y + C.x*C.y - C.y)/(CCx^15 + C.x^14 + C.x^13 + C.x^12 +
....: .x^11 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - C.one)
sage: ffff.expansion_at_infty()
t^3 + t^13 + t^21 + O(t^23)
[6sage: load('init.sage')
sage: om1 = ((C.x^18 - C.x^10 - C.x^9 + C.x)/C.y) * C.dx
sage: f = ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 +*2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)/(C.x^15 + C.x^14 + C.x^13 + C.x^12++ C.x^11 + C.x^10 + C.x^9 + C.x^8
....: 2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y
sage: f.coordinates()
[0]
[6nsagsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
sage: om1 = ((C.x^18 - C.x^10 - C.x^9 + C.x)/C.y) * C.dx
sage: f = ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 +*2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)/(C.x^15 + C.x^14 + C.x^13 + C.x^12++ C.x^11 + C.x^10 + C.x^9 + C.x^8
....: 2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y
sage: f.coordinates()
[0, 0, 0, 0]
[6nsage: xi = superelliptic_cech(C, om1, f)
[6nsage: xi.omega8.is_regular_on_Uinfty()
True
[6nsage: xi.coordinates()
(0, 1, 1, 0, 0, 0, 0, 0)
[6nsage: sage: decomposition_g0_g8(xi.f)
((x^10 + x^2 + 2*x)*y,
((2*x^9 + 2*x^8 + 2*x^7 + 2*x^6 + 2*x^5 + x^4 + x^3 + x^2 + 2*x + 1)/(x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + 2*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 2))*y,
0)
sage: B = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)
omega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(2*x^5/(x^8 + 2))*y] d[x] + V(((-x^27 - x^19)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]) 0
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift 0 [(1/(x^12 + 2*x^4))*y] d[x] + V(((x^8 + 1)/(x^24*y - x^16*y)) dx) + dV([(1/(x^32 + 2*x^24))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^3/(x^8 + 2))*y] d[x] + V(((-x^29 - x^21 + x^13)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]) [(2/(x^13 + 2*x^5))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^35*y - x^27*y)) dx) + dV([(2/(x^35 + 2*x^27))*y])
result.omega8 == compare True
result.omega8 - compare 0
(1, 0, 0, 1, 0, 0, 0, 0)
aux (V(((x^63 - x^55 - x^39 - x^36 + x^31 + x^28 + x^12 - x^4)/y) dx), V(((x^76 + x^73 + x^70 + x^67 + x^64 + x^61 + x^58 + x^55 + 2*x^49 + 2*x^46 + 2*x^43 + 2*x^40 + 2*x^37 + 2*x^34 + 2*x^31 + 2*x^28 + x^25 + x^22 + x^19 + x^16 + 2*x^13 + 2*x^10 + 2*x^7 + 2*x^4 + 2*x)/(x^37 + x^34 + x^31 + x^29 + x^28 + x^26 + x^25 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^12 + x^11 + x^9 + x^8 + x^6 + x^3 + 1))*y), V(((-x^16 - x^14 - x^13 - x^11 - x^10 - x^8 + x^7 - x^5 - x^4 - x^3 + x - 1)/(x^15*y + x^14*y - x^12*y - x^11*y + x^9*y + x^8*y + x^7*y - x^5*y - x^4*y + x^2*y + x*y)) dx))
aux_divided_by_p (((x^18 - x^10 - x^9 + x)/y) dx, ((x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + 2*x^12 + 2*x^11 + 2*x^10 + 2*x^9 + x^8 + x^7 + x^6 + x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 2)/(x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + 2*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 2))*y, ((x^9 - x^4 + x^3 - x^2 + x + 1)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx)
is regular True True
aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True
[1, 3, 3, 1, 0, 0, 0, 0]
[6nsage: sage: autom(B[4]).coordinates(basis=B)
(1, 1, 0, 2, 1, 2, 1, 2)
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [52], in <cell line: 1>()
----> 1 autom(B[Integer(4)]).coordinates(basis=B)
 
File <string>:102, in coordinates(self, basis)
 
AttributeError: 'NoneType' object has no attribute 'coordinates'
[6nsage: raise ValueError("Test")
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [53], in <cell line: 1>()
----> 1 raise ValueError("Test")
 
ValueError: Test
[6nsage: load('init.sage')
[6nsage: B = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)
omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
---------------------------------------------------------------------------
IndexError Traceback (most recent call last)
Input In [55], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(3)]).coordinates(basis=B)
 
IndexError: list index out of range
[6nsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
[6nsage: B = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)
omega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(2*x^5/(x^8 + 2))*y] d[x] + V(((-x^27 - x^19)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]) 0
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift 0 [(1/(x^12 + 2*x^4))*y] d[x] + V(((x^8 + 1)/(x^24*y - x^16*y)) dx) + dV([(1/(x^32 + 2*x^24))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^3/(x^8 + 2))*y] d[x] + V(((-x^29 - x^21 + x^13)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]) [(2/(x^13 + 2*x^5))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^35*y - x^27*y)) dx) + dV([(2/(x^35 + 2*x^27))*y])
result.omega8 == compare True
result.omega8 - compare 0
(1, 0, 0, 1, 0, 0, 0, 0)
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [57], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(3)]).coordinates(basis=B)
 
File <string>:107, in coordinates(self, basis)
 
File <string>:94, in div_by_p(self)
 
ValueError: aux.omega0.h2.function not in Rxy
[6nsage: load('init.sage')
Traceback (most recent call last):
 
File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
exec(code_obj, self.user_global_ns, self.user_ns)
 
Input In [58] in <cell line: 1>
load('init.sage')
 
File sage/misc/persist.pyx:175 in sage.misc.persist.load
sage.repl.load.load(filename, globals())
 
File /ext/sage/9.7/src/sage/repl/load.py:272 in load
exec(preparse_file(f.read()) + "\n", globals)
 
File <string>:20 in <module>
 
File sage/misc/persist.pyx:175 in sage.misc.persist.load
sage.repl.load.load(filename, globals())
 
File /ext/sage/9.7/src/sage/repl/load.py:272 in load
exec(preparse_file(f.read()) + "\n", globals)
 
File <string>:94
raise ValueError("aux.omega0.h2.function not in Rxy":, aux.omega0.h2.function)
^
SyntaxError: invalid syntax
 
[6nsage: load('init.sage')
[6nsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
[6nsage: B = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)
omega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(2*x^5/(x^8 + 2))*y] d[x] + V(((-x^27 - x^19)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]) 0
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift 0 [(1/(x^12 + 2*x^4))*y] d[x] + V(((x^8 + 1)/(x^24*y - x^16*y)) dx) + dV([(1/(x^32 + 2*x^24))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^3/(x^8 + 2))*y] d[x] + V(((-x^29 - x^21 + x^13)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]) [(2/(x^13 + 2*x^5))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^35*y - x^27*y)) dx) + dV([(2/(x^35 + 2*x^27))*y])
result.omega8 == compare True
result.omega8 - compare 0
(1, 0, 0, 1, 0, 0, 0, 0)
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [61], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(3)]).coordinates(basis=B)
 
File <string>:107, in coordinates(self, basis)
 
File <string>:94, in div_by_p(self)
 
ValueError: ('aux.omega0.h2.function not in Rxy:', ((2*x^74 + x^73 + x^71 + 2*x^70 + 2*x^65 + x^64 + x^62 + 2*x^61 + 2*x^56 + x^55 + x^53 + 2*x^52 + x^50 + 2*x^49 + 2*x^47 + x^46 + x^44 + 2*x^43 + 2*x^38 + x^37 + x^32 + 2*x^31 + 2*x^29 + x^28 + x^26 + 2*x^25 + x^23 + 2*x^22 + 2*x^17 + x^16 + x^14 + 2*x^13 + 2*x^8 + x^7 + x^5 + 2*x^4 + 2*x^2 + x)/(x^35 + 2*x^34 + 2*x^32 + x^31 + x^27 + 2*x^25 + 2*x^24 + x^22 + x^19 + x^16 + x^13 + 2*x^11 + 2*x^10 + x^8 + x^4 + 2*x^3 + 2*x + 1))*y)
sage: om = ((2*C.x^74 + C.x^73 + C.x^71 + 2*C.x^70 + 2*C.x^65 + C.x^64 + C.x^62 + 2*C.x^61 + 2*C.x^56 + C.x^55 + C.x^53 + 2*C.x+52 + C.x^50 + 2*C.x^49 + 2*C.x^47
....: C.x^46 + C.x^44 + 2*C.x^43 + 2*C.x^38 + C.x^37 + C.x^32 + 2*C.x^31 + 2*C.x^29 + C.x^28 + C.x^26 + 2*C.x^25 + C.x^23 + 2*C.x^22 + 2*C.x^17 + C.x^16 + C.x^14
....: + 2*C.x^13 + 2*C.x^8 + C.x^7 + C.x^5 + 2*C.x^4 + 2*C.x^2 + C.x)/(C.x^35 + 2*C.x^34 + 2*C.x^32 + C.x^31 + C.x^27 + 2*C.x^2x + 2*C.x^24 + C.x^22 + C.x^19 + C.
....: ^16 + C.x^13 + 2*C.x^11 + 2*C.x^10 + C.x^8 + C.x^4 + 2*C.x^3 + 2*C.x + 1))*C.y)
Input In [62]
om = ((Integer(2)*C.x**Integer(74) + C.x**Integer(73) + C.x**Integer(71) + Integer(2)*C.x**Integer(70) + Integer(2)*C.x**Integer(65) + C.x**Integer(64) + C.x**Integer(62) + Integer(2)*C.x**Integer(61) + Integer(2)*C.x**Integer(56) + C.x**Integer(55) + C.x**Integer(53) + Integer(2)*C.x**Integer(52) + C.x**Integer(50) + Integer(2)*C.x**Integer(49) + Integer(2)*C.x**Integer(47) + C.x**Integer(46) + C.x**Integer(44) + Integer(2)*C.x**Integer(43) + Integer(2)*C.x**Integer(38) + C.x**Integer(37) + C.x**Integer(32) + Integer(2)*C.x**Integer(31) + Integer(2)*C.x**Integer(29) + C.x**Integer(28) + C.x**Integer(26) + Integer(2)*C.x**Integer(25) + C.x**Integer(23) + Integer(2)*C.x**Integer(22) + Integer(2)*C.x**Integer(17) + C.x**Integer(16) + C.x**Integer(14) + Integer(2)*C.x**Integer(13) + Integer(2)*C.x**Integer(8) + C.x**Integer(7) + C.x**Integer(5) + Integer(2)*C.x**Integer(4) + Integer(2)*C.x**Integer(2) + C.x)/(C.x**Integer(35) + Integer(2)*C.x**Integer(34) + Integer(2)*C.x**Integer(32) + C.x**Integer(31) + C.x**Integer(27) + Integer(2)*C.x**Integer(25) + Integer(2)*C.x**Integer(24) + C.x**Integer(22) + C.x**Integer(19) + C.x**Integer(16) + C.x**Integer(13) + Integer(2)*C.x**Integer(11) + Integer(2)*C.x**Integer(10) + C.x**Integer(8) + C.x**Integer(4) + Integer(2)*C.x**Integer(3) + Integer(2)*C.x + Integer(1)))*C.y)
^
SyntaxError: unmatched ')'
 
sage: om = ((2*C.x^74 + C.x^73 + C.x^71 + 2*C.x^70 + 2*C.x^65 + C.x^64 + C.x^62 + 2*C.x^61 + 2*C.x^56 + C.x^55 + C.x^53 + 2*C.x+52 + C.x^50 + 2*C.x^49 + 2*C.x^47
....: C.x^46 + C.x^44 + 2*C.x^43 + 2*C.x^38 + C.x^37 + C.x^32 + 2*C.x^31 + 2*C.x^29 + C.x^28 + C.x^26 + 2*C.x^25 + C.x^23 + 2*C.x^22 + 2*C.x^17 + C.x^16 + C.x^14
....: + 2*C.x^13 + 2*C.x^8 + C.x^7 + C.x^5 + 2*C.x^4 + 2*C.x^2 + C.x)/(C.x^35 + 2*C.x^34 + 2*C.x^32 + C.x^31 + C.x^27 + 2*C.x^2x + 2*C.x^24 + C.x^22 + C.x^19 + C.
....: ^16 + C.x^13 + 2*C.x^11 + 2*C.x^10 + C.x^8 + C.x^4 + 2*C.x^3 + 2*C.x + 1))*C.y
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [63], in <cell line: 1>()
----> 1 om = ((Integer(2)*C.x**Integer(74) + C.x**Integer(73) + C.x**Integer(71) + Integer(2)*C.x**Integer(70) + Integer(2)*C.x**Integer(65) + C.x**Integer(64) + C.x**Integer(62) + Integer(2)*C.x**Integer(61) + Integer(2)*C.x**Integer(56) + C.x**Integer(55) + C.x**Integer(53) + Integer(2)*C.x**Integer(52) + C.x**Integer(50) + Integer(2)*C.x**Integer(49) + Integer(2)*C.x**Integer(47) + C.x**Integer(46) + C.x**Integer(44) + Integer(2)*C.x**Integer(43) + Integer(2)*C.x**Integer(38) + C.x**Integer(37) + C.x**Integer(32) + Integer(2)*C.x**Integer(31) + Integer(2)*C.x**Integer(29) + C.x**Integer(28) + C.x**Integer(26) + Integer(2)*C.x**Integer(25) + C.x**Integer(23) + Integer(2)*C.x**Integer(22) + Integer(2)*C.x**Integer(17) + C.x**Integer(16) + C.x**Integer(14) + Integer(2)*C.x**Integer(13) + Integer(2)*C.x**Integer(8) + C.x**Integer(7) + C.x**Integer(5) + Integer(2)*C.x**Integer(4) + Integer(2)*C.x**Integer(2) + C.x)/(C.x**Integer(35) + Integer(2)*C.x**Integer(34) + Integer(2)*C.x**Integer(32) + C.x**Integer(31) + C.x**Integer(27) + Integer(2)*C.x**Integer(25) + Integer(2)*C.x**Integer(24) + C.x**Integer(22) + C.x**Integer(19) + C.x**Integer(16) + C.x**Integer(13) + Integer(2)*C.x**Integer(11) + Integer(2)*C.x**Integer(10) + C.x**Integer(8) + C.x**Integer(4) + Integer(2)*C.x**Integer(3) + Integer(2)*C.x + Integer(1)))*C.y
 
File <string>:38, in __add__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
493 """
--> 494 return self.getattr_from_category(name)
495
496 cdef getattr_from_category(self, name):
 
File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
505 else:
506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
508
509 def __dir__(self):
 
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
359 dummy_error_message.cls = type(self)
360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
362 attribute = <object>attr
363 # Check for a descriptor (__get__ in Python)
 
AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function'
sage: om = ((2*C.x^74 + C.x^73 + C.x^71 + 2*C.x^70 + 2*C.x^65 + C.x^64 + C.x^62 + 2*C.x^61 + 2*C.x^56 + C.x^55 + C.x^53 + 2*C.x+52 + C.x^50 + 2*C.x^49 + 2*C.x^47
....: C.x^46 + C.x^44 + 2*C.x^43 + 2*C.x^38 + C.x^37 + C.x^32 + 2*C.x^31 + 2*C.x^29 + C.x^28 + C.x^26 + 2*C.x^25 + C.x^23 + 2*C.x^22 + 2*C.x^17 + C.x^16 + C.x^14
....: + 2*C.x^13 + 2*C.x^8 + C.x^7 + C.x^5 + 2*C.x^4 + 2*C.x^2 + C.x)/(C.x^35 + 2*C.x^34 + 2*C.x^32 + C.x^31 + C.x^27 + 2*C.x^2x + 2*C.x^24 + C.x^22 + C.x^19 + C.
....: ^16 + C.x^13 + 2*C.x^11 + 2*C.x^10 + C.x^8 + C.x^4 + 2*C.x^3 + 2*C.x + C.one))*C.y
sage: om = om.diffn()
sage: om
0 dx
[6nsage:
sage: om = ((2*C.x^74 + C.x^73 + C.x^71 + 2*C.x^70 + 2*C.x^65 + C.x^64 + C.x^62 + 2*C.x^61 + 2*C.x^56 + C.x^55 + C.x^53 + 2*C.x+52 + C.x^50 + 2*C.x^49 + 2*C.x^47
....: C.x^46 + C.x^44 + 2*C.x^43 + 2*C.x^38 + C.x^37 + C.x^32 + 2*C.x^31 + 2*C.x^29 + C.x^28 + C.x^26 + 2*C.x^25 + C.x^23 + 2*C.x^22 + 2*C.x^17 + C.x^16 + C.x^14
....: + 2*C.x^13 + 2*C.x^8 + C.x^7 + C.x^5 + 2*C.x^4 + 2*C.x^2 + C.x)/(C.x^35 + 2*C.x^34 + 2*C.x^32 + C.x^31 + C.x^27 + 2*C.x^2x + 2*C.x^24 + C.x^22 + C.x^19 + C.
....: ^16 + C.x^13 + 2*C.x^11 + 2*C.x^10 + C.x^8 + C.x^4 + 2*C.x^3 + 2*C.x + C.one))*C.y
sage: om1 = om.pth_root()
sage: om1 = om1.pth_root()
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [69], in <cell line: 1>()
----> 1 om1 = om1.pth_root()
 
File <string>:168, in pth_root(self)
 
ValueError: Function is not a p-th power.
[6nsage: om1
((2*x^24 + x^23 + 2*x^21 + x^20 + 2*x^18 + x^17 + x^16 + 2*x^15 + x^14 + 2*x^12 + x^10 + 2*x^9 + x^8 + x^7 + 2*x^5 + x^4 + 2*x^2 + x + 2)/(x^14 + 2*x^13 + x^11 + 2*x^10 + x^8 + 2*x^7 + x^6 + 2*x^4 + x^3 + 2*x + 1))*y
[6nsage: om1.diffn()
((-x^18 + x^10 + x^9 + x^2 - 1)/y) dx
~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
[22;0t[6nsage: loa
^[[C---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [1], in <cell line: 1>()
----> 1 loa
 
NameError: name 'loa' is not defined
[6nsage: load('init.sage')
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y
[6nsage: g
(2*x^4 + x^2 + 2)*y + x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
[6nsage: g.diffn()
((x^18*y + x^16*y - x^12*y - x^10*y - x^6 - x^4 - x^2 - y - 1)/y) dx
[6nsage: quit()
[23;0t~/Research/2021 De Rham/DeRhamComputation/sage$ cd ..
~/Research/2021 De Rham/DeRhamComputation$ git status
On branch master
Your branch is up to date with 'origin/master'.
 
Changes not staged for commit:
(use "git add <file>..." to update what will be committed)
(use "git restore <file>..." to discard changes in working directory)
modified: sage/.run.term-0.term
modified: sage/drafty/draft.sage
modified: sage/init.sage
modified: sage/superelliptic/superelliptic_cech_class.sage
modified: sage/superelliptic/superelliptic_class.sage
modified: sage/superelliptic/superelliptic_form_class.sage
modified: sage/superelliptic_drw/automorphism.sage
modified: sage/superelliptic_drw/de_rham_witt_lift.sage
modified: sage/superelliptic_drw/decomposition_into_g0_g8.sage
modified: sage/superelliptic_drw/second_patch.sage
modified: sage/superelliptic_drw/superelliptic_drw_cech.sage
modified: sage/superelliptic_drw/superelliptic_drw_form.sage
modified: sage/tests.sage
 
Untracked files:
(use "git add <file>..." to include in what will be committed)
.crystalline_p2.ipynb.sage-jupyter2
.deRhamComputation.ipynb.sage-jupyter2
.elementary_covers_of_superelliptic_curves.ipynb.sage-jupyter2
.git.x11-0.term
.superelliptic.ipynb.sage-jupyter2
.superelliptic_alpha.ipynb.sage-jupyter2
.superelliptic_arbitrary_field.ipynb.sage-jupyter2
git.x11
sage/as_covers/tests/cartier_test.sage
sage/drafty/.2023-03-06-file-1.ipynb.sage-jupyter2
sage/drafty/2gpcovers.sage
sage/drafty/as_cartier.sage
sage/drafty/better_trace.sage
sage/drafty/cartier_image_representation.sage
sage/drafty/convert_superelliptic_into_AS.sage
sage/drafty/draft4.sage
sage/drafty/draft5.sage
sage/drafty/draft6.sage
sage/drafty/draft7.sage
sage/drafty/draft8.sage
sage/drafty/draft_klein_covers.sage
sage/drafty/lift_to_de_rham.sage
sage/drafty/pole_numbers.sage
sage/superelliptic/frobenius_kernel.sage
sage/superelliptic/tests/
sage/superelliptic_drw/regular_form.sage
sage/superelliptic_drw/tests/
superelliptic_arbitrary_field.ipynb
 
no changes added to commit (use "git add" and/or "git commit -a")
~/Research/2021 De Rham/DeRhamComputation$ git add sage/as_covers/tests/cartier_test.sage sage/superelliptic_drw/tests/ sage/superelliptic/tests/
~/Research/2021 De Rham/DeRhamComputation$ git add -u
~/Research/2021 De Rham/DeRhamComputation$ git commit -m "[1@b[1@a[1@z[1@a[1@ [1@c[1@r[1@y[1@s[1@ [1@d[1@z[1@i[1@a[1@l[1@a[1@;[1@ [1@p[1@o[1@p[1@r[1@a [1@[1@k[1@i[1@ [1@[1@ [1@c[1@o[1@o[1@r[1@d[1@i[1@n[1@a[1@t[1@e[1@s[1@ [1@d[1@r[1@[1P[1@;[1@ [1@[1@c[1@r[1@i[1@s [1@[1P ialaja"
[master 42ccc4d] baza crys dziala; poprawki w coordinates dr; wspolrzednie cris prawie dzialaja
20 files changed, 16269 insertions(+), 87 deletions(-)
create mode 100644 sage/as_covers/tests/cartier_test.sage
create mode 100644 sage/superelliptic/tests/a_number_test.sage
create mode 100644 sage/superelliptic/tests/form_coordinates_test.sage
create mode 100644 sage/superelliptic/tests/p_rank_test.sage
create mode 100644 sage/superelliptic/tests/pth_root_test.sage
create mode 100644 sage/superelliptic_drw/tests/decomposition_into_g0_g8_tests.sage
create mode 100644 sage/superelliptic_drw/tests/superelliptic_drw_tests.sage
~/Research/2021 De Rham/DeRhamComputation$ git push
Username for 'https://git.wmi.amu.edu.pl': jgarnek
Password for 'https://jgarnek@git.wmi.amu.edu.pl':
Enumerating objects: 50, done.
Counting objects: 100% (50/50), done.
Delta compression using up to 4 threads
Compressing objects: 100% (30/30), done.
Writing objects: 100% (30/30), 143.28 KiB | 1.06 MiB/s, done.
Total 30 (delta 18), reused 0 (delta 0)
remote: . Processing 1 references
remote: Processed 1 references in total
To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git
ce0ac0d..42ccc4d master -> master
~/Research/2021 De Rham/DeRhamComputation$ cd sa
bash: cd: sa: No such file or directory
~/Research/2021 De Rham/DeRhamComputation$ cd sage/
~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
[22;0t[6nsage: load('init.sage')
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y
[6nsage: g.diffn()
((x^18*y + x^16*y - x^12*y - x^10*y - x^6 - x^4 - x^2 - y - 1)/y) dx
[6nsage: g.diffn().regular_form()
(x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
[6nsage: om = g.diffn().regular_form()
[6nsage: om.dy = 0*C.x
[6nsage: om.int()
int(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx
m dx x^18
int(self) (x^16 + 2*x^12 + 2*x^10 + 2) dx
m dx x^16
int(self) (2*x^12 + 2*x^10 + 2) dx
m dx x^12
int(self) (2*x^10 + 2) dx
m dx x^10
int(self) (2) dx
m dx 1
int(self) (0) dy
x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
[6nsasage: Fxy, Rxy, x, y=C.fct_field
[6nsage: (g.function).quo_rem(y)
(2*x^4 + x^2 + 2, x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x)
[6nsage: g
(2*x^4 + x^2 + 2)*y + x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
[6nsasage: A = (g.function).quo_rem(y)[0]
[6nssage: A = Rx(A)
[6nsage: A.monomial_coefficient(x^3)
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [13], in <cell line: 1>()
----> 1 A.monomial_coefficient(x**Integer(3))
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:6094, in sage.rings.polynomial.polynomial_element.Polynomial.monomial_coefficient()
6092 """
6093 if not m.parent() is self._parent:
-> 6094 raise TypeError("monomial must have same parent as self.")
6095
6096 d = m.degree()
 
TypeError: monomial must have same parent as self.
[6nsage: A.monomial_coefficient(Rx(x^3))
0
sage: A.leading_coefficient()
2
sage: A
2*x^4 + x^2 + 2
sage: load('init.sage')
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y
[6nsage: om = g.diffn().regular_form()
[6nsage: om
(x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
[6nsage: om.int()
int(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
((x^20 + x^18 + 2*x^14 + 2*x^12 + 2*x^6 + 2*x^4 + x^2 + 2)/x^2)*y
[6nsage: om.int().diffn()
int(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
((-x^18 + x^12 - x^6 + x^4 + x^2)/y) dx
[6nsage: om.int().diffn() == om.form()
int(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
False
[6nsage: load('init.sage')
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)
int(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
result przed (x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y
((x^20 + x^18 + 2*x^14 + 2*x^12 + 2*x^6 + 2*x^4 + x^2 + 2)/x^2)*y
[6nsage: load('init.sage')
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)
int(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [27], in <cell line: 1>()
----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om)
 
File <string>:48, in int(self)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
1514 return (<Element>left)._mul_(right)
1515 if BOTH_ARE_ELEMENT(cl):
-> 1516 return coercion_model.bin_op(left, right, mul)
1517
1518 cdef long value
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op()
1246 # We should really include the underlying error.
1247 # This causes so much headache.
-> 1248 raise bin_op_exception(op, x, y)
1249
1250 cpdef canonical_coercion(self, x, y):
 
TypeError: unsupported operand parent(s) for *: 'Finite Field of size 3' and 'Rational Field'
[6nsage: load('init.sage')
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)
int(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
W 0
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [29], in <cell line: 1>()
----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om)
 
File <string>:49, in int(self)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
1514 return (<Element>left)._mul_(right)
1515 if BOTH_ARE_ELEMENT(cl):
-> 1516 return coercion_model.bin_op(left, right, mul)
1517
1518 cdef long value
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op()
1246 # We should really include the underlying error.
1247 # This causes so much headache.
-> 1248 raise bin_op_exception(op, x, y)
1249
1250 cpdef canonical_coercion(self, x, y):
 
TypeError: unsupported operand parent(s) for *: 'Finite Field of size 3' and 'Rational Field'
[6nsage: load('init.sage')
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)
int(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
W 0
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [31], in <cell line: 1>()
----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om)
 
File <string>:49, in int(self)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
1514 return (<Element>left)._mul_(right)
1515 if BOTH_ARE_ELEMENT(cl):
-> 1516 return coercion_model.bin_op(left, right, mul)
1517
1518 cdef long value
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op()
1246 # We should really include the underlying error.
1247 # This causes so much headache.
-> 1248 raise bin_op_exception(op, x, y)
1249
1250 cpdef canonical_coercion(self, x, y):
 
TypeError: unsupported operand parent(s) for *: 'Finite Field of size 3' and 'Rational Field'
[6nsage: load('init.sage')
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)
int(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
W 0
n_lead, f_lead, (2*a + r) 1 1 11
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [33], in <cell line: 1>()
----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om)
 
File <string>:50, in int(self)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
1514 return (<Element>left)._mul_(right)
1515 if BOTH_ARE_ELEMENT(cl):
-> 1516 return coercion_model.bin_op(left, right, mul)
1517
1518 cdef long value
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op()
1246 # We should really include the underlying error.
1247 # This causes so much headache.
-> 1248 raise bin_op_exception(op, x, y)
1249
1250 cpdef canonical_coercion(self, x, y):
 
TypeError: unsupported operand parent(s) for *: 'Finite Field of size 3' and 'Rational Field'
[6nsage: load('init.sage')
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)
int(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
W 0
n_lead, f_lead, (2*a + r) 1 1 11
W_coeff 2
W 2*x^4
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [35], in <cell line: 1>()
----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om)
 
File <string>:46, in int(self)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
493 """
--> 494 return self.getattr_from_category(name)
495
496 cdef getattr_from_category(self, name):
 
File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
505 else:
506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
508
509 def __dir__(self):
 
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
359 dummy_error_message.cls = type(self)
360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
362 attribute = <object>attr
363 # Check for a descriptor (__get__ in Python)
 
AttributeError: 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular' object has no attribute 'leading_coefficient'
[6nsage: load('init.sage')
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)
int(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
W 0
n_lead, f_lead, (2*a + r) 1 1 11
W_coeff 2
W 2*x^4
n_lead, f_lead, (2*a + r) 1 1 7
W_coeff 1
W 2*x^4 + x^2
n_lead, f_lead, (2*a + r) 1 1 3
---------------------------------------------------------------------------
ZeroDivisionError Traceback (most recent call last)
Input In [37], in <cell line: 1>()
----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om)
 
File <string>:50, in int(self)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
159 print(type(C), C)
160 print(type(C._element_constructor), C._element_constructor)
--> 161 raise
162
163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x)
1143 """
1144 TESTS::
1145
(...)
1182 True
1183 """
1184 try:
-> 1185 return integer_mod.IntegerMod(self, x)
1186 except (NotImplementedError, PariError):
1187 raise TypeError("error coercing to finite field")
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod()
199 return a
200 t = modulus.element_class()
--> 201 return t(parent, value)
202
203
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:374, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
372 z = <Integer>value
373 elif isinstance(value, rational.Rational):
--> 374 z = value % self.__modulus.sageInteger
375 elif integer_check_long_py(value, &longval, &err) and not err:
376 self.set_from_long(longval)
 
File /ext/sage/9.7/src/sage/rings/rational.pyx:2825, in sage.rings.rational.Rational.__mod__()
2823 n = rat.numer() % other
2824 d = rat.denom() % other
-> 2825 d = d.inverse_mod(other)
2826 return (n * d) % other
2827
 
File /ext/sage/9.7/src/sage/rings/integer.pyx:6774, in sage.rings.integer.Integer.inverse_mod()
6772 sig_off()
6773 if r == 0:
-> 6774 raise ZeroDivisionError(f"inverse of Mod({self}, {m}) does not exist")
6775 return ans
6776
 
ZeroDivisionError: inverse of Mod(0, 3) does not exist
[6nsage: load('init.sage')
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)
int(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
W 0
numerator x^6 + x^4 + x^2 + 1
W 2*x^4
numerator x^4 + x^2 + 1
W 2*x^4 + x^2
numerator x^2 + 1
---------------------------------------------------------------------------
ZeroDivisionError Traceback (most recent call last)
Input In [39], in <cell line: 1>()
----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om)
 
File <string>:50, in int(self)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
159 print(type(C), C)
160 print(type(C._element_constructor), C._element_constructor)
--> 161 raise
162
163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x)
1143 """
1144 TESTS::
1145
(...)
1182 True
1183 """
1184 try:
-> 1185 return integer_mod.IntegerMod(self, x)
1186 except (NotImplementedError, PariError):
1187 raise TypeError("error coercing to finite field")
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod()
199 return a
200 t = modulus.element_class()
--> 201 return t(parent, value)
202
203
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:374, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
372 z = <Integer>value
373 elif isinstance(value, rational.Rational):
--> 374 z = value % self.__modulus.sageInteger
375 elif integer_check_long_py(value, &longval, &err) and not err:
376 self.set_from_long(longval)
 
File /ext/sage/9.7/src/sage/rings/rational.pyx:2825, in sage.rings.rational.Rational.__mod__()
2823 n = rat.numer() % other
2824 d = rat.denom() % other
-> 2825 d = d.inverse_mod(other)
2826 return (n * d) % other
2827
 
File /ext/sage/9.7/src/sage/rings/integer.pyx:6774, in sage.rings.integer.Integer.inverse_mod()
6772 sig_off()
6773 if r == 0:
-> 6774 raise ZeroDivisionError(f"inverse of Mod({self}, {m}) does not exist")
6775 return ans
6776
 
ZeroDivisionError: inverse of Mod(0, 3) does not exist
[6nsage:
sage: om = (C.x^2 + C.one)/C.y * C.dx
sage: om.cartier()
(x/y) dx
[6nsage: load('init.sage')
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)
int(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
(superelliptic_function(C, numerator)*C.dx).cartier() 1 dx
W 0
numerator x^6 + x^4 + x^2 + 1
(superelliptic_function(C, numerator)*C.dx).cartier() 1 dx
W 2*x^4
numerator x^4 + x^2 + 1
(superelliptic_function(C, numerator)*C.dx).cartier() 1 dx
W 2*x^4 + x^2
numerator x^2 + 1
---------------------------------------------------------------------------
ZeroDivisionError Traceback (most recent call last)
Input In [43], in <cell line: 1>()
----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om)
 
File <string>:51, in int(self)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
159 print(type(C), C)
160 print(type(C._element_constructor), C._element_constructor)
--> 161 raise
162
163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x)
1143 """
1144 TESTS::
1145
(...)
1182 True
1183 """
1184 try:
-> 1185 return integer_mod.IntegerMod(self, x)
1186 except (NotImplementedError, PariError):
1187 raise TypeError("error coercing to finite field")
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod()
199 return a
200 t = modulus.element_class()
--> 201 return t(parent, value)
202
203
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:374, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
372 z = <Integer>value
373 elif isinstance(value, rational.Rational):
--> 374 z = value % self.__modulus.sageInteger
375 elif integer_check_long_py(value, &longval, &err) and not err:
376 self.set_from_long(longval)
 
File /ext/sage/9.7/src/sage/rings/rational.pyx:2825, in sage.rings.rational.Rational.__mod__()
2823 n = rat.numer() % other
2824 d = rat.denom() % other
-> 2825 d = d.inverse_mod(other)
2826 return (n * d) % other
2827
 
File /ext/sage/9.7/src/sage/rings/integer.pyx:6774, in sage.rings.integer.Integer.inverse_mod()
6772 sig_off()
6773 if r == 0:
-> 6774 raise ZeroDivisionError(f"inverse of Mod({self}, {m}) does not exist")
6775 return ans
6776
 
ZeroDivisionError: inverse of Mod(0, 3) does not exist
[6nsage: load('init.sage')
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)
int(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 0
numerator x^6 + x^4 + x^2 + 1
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 2*x^4
numerator x^4 + x^2 + 1
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() (x/y) dx
W 2*x^4 + x^2
numerator x^2 + 1
---------------------------------------------------------------------------
ZeroDivisionError Traceback (most recent call last)
Input In [45], in <cell line: 1>()
----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om)
 
File <string>:51, in int(self)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
159 print(type(C), C)
160 print(type(C._element_constructor), C._element_constructor)
--> 161 raise
162
163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x)
1143 """
1144 TESTS::
1145
(...)
1182 True
1183 """
1184 try:
-> 1185 return integer_mod.IntegerMod(self, x)
1186 except (NotImplementedError, PariError):
1187 raise TypeError("error coercing to finite field")
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod()
199 return a
200 t = modulus.element_class()
--> 201 return t(parent, value)
202
203
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:374, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
372 z = <Integer>value
373 elif isinstance(value, rational.Rational):
--> 374 z = value % self.__modulus.sageInteger
375 elif integer_check_long_py(value, &longval, &err) and not err:
376 self.set_from_long(longval)
 
File /ext/sage/9.7/src/sage/rings/rational.pyx:2825, in sage.rings.rational.Rational.__mod__()
2823 n = rat.numer() % other
2824 d = rat.denom() % other
-> 2825 d = d.inverse_mod(other)
2826 return (n * d) % other
2827
 
File /ext/sage/9.7/src/sage/rings/integer.pyx:6774, in sage.rings.integer.Integer.inverse_mod()
6772 sig_off()
6773 if r == 0:
-> 6774 raise ZeroDivisionError(f"inverse of Mod({self}, {m}) does not exist")
6775 return ans
6776
 
ZeroDivisionError: inverse of Mod(0, 3) does not exist
[6nsage: load('init.sage')
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)
int(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 0
numerator x^6 + x^4 + x^2 + 1
2*f*W.derivative() + W*f.derivative(), numerator x^6 x^6 + x^4 + x^2 + 1
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 2*x^4
numerator x^4 + x^2 + 1
2*f*W.derivative() + W*f.derivative(), numerator x^6 + x^4 + x^2 x^4 + x^2 + 1
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() (x/y) dx
W 2*x^4 + x^2
numerator x^2 + 1
---------------------------------------------------------------------------
ZeroDivisionError Traceback (most recent call last)
Input In [47], in <cell line: 1>()
----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om)
 
File <string>:51, in int(self)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
159 print(type(C), C)
160 print(type(C._element_constructor), C._element_constructor)
--> 161 raise
162
163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x)
1143 """
1144 TESTS::
1145
(...)
1182 True
1183 """
1184 try:
-> 1185 return integer_mod.IntegerMod(self, x)
1186 except (NotImplementedError, PariError):
1187 raise TypeError("error coercing to finite field")
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod()
199 return a
200 t = modulus.element_class()
--> 201 return t(parent, value)
202
203
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:374, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
372 z = <Integer>value
373 elif isinstance(value, rational.Rational):
--> 374 z = value % self.__modulus.sageInteger
375 elif integer_check_long_py(value, &longval, &err) and not err:
376 self.set_from_long(longval)
 
File /ext/sage/9.7/src/sage/rings/rational.pyx:2825, in sage.rings.rational.Rational.__mod__()
2823 n = rat.numer() % other
2824 d = rat.denom() % other
-> 2825 d = d.inverse_mod(other)
2826 return (n * d) % other
2827
 
File /ext/sage/9.7/src/sage/rings/integer.pyx:6774, in sage.rings.integer.Integer.inverse_mod()
6772 sig_off()
6773 if r == 0:
-> 6774 raise ZeroDivisionError(f"inverse of Mod({self}, {m}) does not exist")
6775 return ans
6776
 
ZeroDivisionError: inverse of Mod(0, 3) does not exist
[6nsage: load('init.sage')
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)
int(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 0
numerator x^6 + x^4 + x^2 + 1
2*f*W.derivative() + W*f.derivative(), numerator x^6 x^6 + x^4 + x^2 + 1
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 2*x^4
numerator x^4 + x^2 + 1
2*f*W.derivative() + W*f.derivative(), numerator x^6 + x^4 + x^2 x^4 + x^2 + 1
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 2*x^4 + x^2
numerator 1
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [49], in <cell line: 1>()
----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om)
 
File <string>:52, in int(self)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
159 print(type(C), C)
160 print(type(C._element_constructor), C._element_constructor)
--> 161 raise
162
163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:456, in PolynomialRing_general._element_constructor_(self, x, check, is_gen, construct, **kwds)
454 x = x.numerator() * x.denominator().inverse_of_unit()
455 else:
--> 456 raise TypeError("denominator must be a unit")
457 elif isinstance(x, pari_gen):
458 if x.type() == 't_RFRAC':
 
TypeError: denominator must be a unit
[6nsage: load('init.sage')
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)
int(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 0
numerator x^6 + x^4 + x^2 + 1
W_coeff 2
2*f*W.derivative() + W*f.derivative(), numerator x^6 x^6 + x^4 + x^2 + 1
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 2*x^4
numerator x^4 + x^2 + 1
W_coeff 1
2*f*W.derivative() + W*f.derivative(), numerator x^6 + x^4 + x^2 x^4 + x^2 + 1
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 2*x^4 + x^2
numerator 1
W_coeff 2
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [51], in <cell line: 1>()
----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om)
 
File <string>:53, in int(self)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
159 print(type(C), C)
160 print(type(C._element_constructor), C._element_constructor)
--> 161 raise
162
163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:456, in PolynomialRing_general._element_constructor_(self, x, check, is_gen, construct, **kwds)
454 x = x.numerator() * x.denominator().inverse_of_unit()
455 else:
--> 456 raise TypeError("denominator must be a unit")
457 elif isinstance(x, pari_gen):
458 if x.type() == 't_RFRAC':
 
TypeError: denominator must be a unit
[6nsage: load('init.sage')
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)
int(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 0
numerator x^6 + x^4 + x^2 + 1
a 4
2*f*W.derivative() + W*f.derivative(), numerator x^6 x^6 + x^4 + x^2 + 1
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 2*x^4
numerator x^4 + x^2 + 1
a 2
2*f*W.derivative() + W*f.derivative(), numerator x^6 + x^4 + x^2 x^4 + x^2 + 1
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 2*x^4 + x^2
numerator 1
a -2
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [53], in <cell line: 1>()
----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om)
 
File <string>:53, in int(self)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
159 print(type(C), C)
160 print(type(C._element_constructor), C._element_constructor)
--> 161 raise
162
163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:456, in PolynomialRing_general._element_constructor_(self, x, check, is_gen, construct, **kwds)
454 x = x.numerator() * x.denominator().inverse_of_unit()
455 else:
--> 456 raise TypeError("denominator must be a unit")
457 elif isinstance(x, pari_gen):
458 if x.type() == 't_RFRAC':
 
TypeError: denominator must be a unit
[6nsage: load('init.sage')
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)
int(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 0
numerator x^6 + x^4 + x^2 + 1
a 4
2*f*W.derivative() + W*f.derivative(), numerator x^6 x^6 + x^4 + x^2 + 1
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 2*x^4
numerator x^4 + x^2 + 1
a 2
2*f*W.derivative() + W*f.derivative(), numerator x^6 + x^4 + x^2 x^4 + x^2 + 1
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 2*x^4 + x^2
numerator 1
(2*x^4 + x^2 + 2)*y + x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
[6nsage: om
(2*x^4 + x^2 + 2)*y + x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
[6nsage: om.regular_form().int()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [57], in <cell line: 1>()
----> 1 om.regular_form().int()
 
AttributeError: 'superelliptic_function' object has no attribute 'regular_form'
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form()
[6nsage: om.int().diffn() == om.form()
int(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 0
numerator x^6 + x^4 + x^2 + 1
a 4
2*f*W.derivative() + W*f.derivative(), numerator x^6 x^6 + x^4 + x^2 + 1
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 2*x^4
numerator x^4 + x^2 + 1
a 2
2*f*W.derivative() + W*f.derivative(), numerator x^6 + x^4 + x^2 x^4 + x^2 + 1
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 2*x^4 + x^2
numerator 1
True
[6nsage: om.int()
int(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 0
numerator x^6 + x^4 + x^2 + 1
a 4
2*f*W.derivative() + W*f.derivative(), numerator x^6 x^6 + x^4 + x^2 + 1
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 2*x^4
numerator x^4 + x^2 + 1
a 2
2*f*W.derivative() + W*f.derivative(), numerator x^6 + x^4 + x^2 x^4 + x^2 + 1
(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx
W 2*x^4 + x^2
numerator 1
(2*x^4 + x^2 + 2)*y + x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
[6nsage: load('init.sage')
[6nsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form()
[6nsage: om.int()
(2*x^4 + x^2 + 2)*y + x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x
[6nsage: om.int().diffn() == om.form()
True
[6nsage: g - om.int()
0
sage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
....: B = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)
omega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(2*x^5/(x^8 + 2))*y] d[x] + V(((-x^27 - x^19)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]) 0
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift 0 [(1/(x^12 + 2*x^4))*y] d[x] + V(((x^8 + 1)/(x^24*y - x^16*y)) dx) + dV([(1/(x^32 + 2*x^24))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^3/(x^8 + 2))*y] d[x] + V(((-x^29 - x^21 + x^13)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]) [(2/(x^13 + 2*x^5))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^35*y - x^27*y)) dx) + dV([(2/(x^35 + 2*x^27))*y])
result.omega8 == compare True
result.omega8 - compare 0
(1, 0, 0, 1, 0, 0, 0, 0)
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [66], in <cell line: 2>()
1 C = superelliptic((x**Integer(3) - x)**Integer(3) + x**Integer(3) - x, Integer(2))
----> 2 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(3)]).coordinates(basis=B)
 
File <string>:107, in coordinates(self, basis)
 
File <string>:94, in div_by_p(self)
 
ValueError: ('aux.omega0.h2.function not in Rxy:', ((2*x^74 + x^73 + x^71 + 2*x^70 + 2*x^65 + x^64 + x^62 + 2*x^61 + 2*x^56 + x^55 + x^53 + 2*x^52 + x^50 + 2*x^49 + 2*x^47 + x^46 + x^44 + 2*x^43 + 2*x^38 + x^37 + x^32 + 2*x^31 + 2*x^29 + x^28 + x^26 + 2*x^25 + x^23 + 2*x^22 + 2*x^17 + x^16 + x^14 + 2*x^13 + 2*x^8 + x^7 + x^5 + 2*x^4 + 2*x^2 + x)/(x^35 + 2*x^34 + 2*x^32 + x^31 + x^27 + 2*x^25 + 2*x^24 + x^22 + x^19 + x^16 + x^13 + 2*x^11 + 2*x^10 + x^8 + x^4 + 2*x^3 + 2*x + 1))*y)
sage: ff = ((2*C.x^74 + C.x^73 + C.x^71 + 2*C.x^70 + 2*C.x^65 + C.x^64 + C.x^62 + 2*C.x^61 + 2*C.x^56 + C.x^55 + C.x^53 + 2*C.x+52 + C.x^50 + 2*C.x^49 + 2*C.x^47
....: C.x^46 + C.x^44 + 2*C.x^43 + 2*C.x^38 + C.x^37 + C.x^32 + 2*C.x^31 + 2*C.x^29 + C.x^28 + C.x^26 + 2*C.x^25 + C.x^23 + 2*C.x^22 + 2*C.x^17 + C.x^16 + C.x^14
....: + 2*C.x^13 + 2*C.x^8 + C.x^7 + C.x^5 + 2*C.x^4 + 2*C.x^2 + C.x)/(C.x^35 + 2*C.x^34 + 2*C.x^32 + C.x^31 + C.x^27 + 2*C.x^2x + 2*C.x^24 + C.x^22 + C.x^19 + C.
....: ^16 + C.x^13 + 2*C.x^11 + 2*C.x^10 + C.x^8 + C.x^4 + 2*C.x^3 + 2*C.x + C.one))*C.y
sage: ff.diffn()
0 dx
sage: ff.pth_root()
((2*x^24 + x^23 + 2*x^21 + x^20 + 2*x^18 + x^17 + x^16 + 2*x^15 + x^14 + 2*x^12 + x^10 + 2*x^9 + x^8 + x^7 + 2*x^5 + x^4 + 2*x^2 + x + 2)/(x^14 + 2*x^13 + x^11 + 2*x^10 + x^8 + 2*x^7 + x^6 + 2*x^4 + x^3 + 2*x + 1))*y
[6nsagsage: load('init.sage')
sage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
....: B = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)
omega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(2*x^5/(x^8 + 2))*y] d[x] + V(((-x^27 - x^19)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]) 0
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift 0 [(1/(x^12 + 2*x^4))*y] d[x] + V(((x^8 + 1)/(x^24*y - x^16*y)) dx) + dV([(1/(x^32 + 2*x^24))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^3/(x^8 + 2))*y] d[x] + V(((-x^29 - x^21 + x^13)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]) [(2/(x^13 + 2*x^5))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^35*y - x^27*y)) dx) + dV([(2/(x^35 + 2*x^27))*y])
result.omega8 == compare True
result.omega8 - compare 0
(1, 0, 0, 1, 0, 0, 0, 0)
h2 ((2*x^74 + x^73 + x^71 + 2*x^70 + 2*x^65 + x^64 + x^62 + 2*x^61 + 2*x^56 + x^55 + x^53 + 2*x^52 + x^50 + 2*x^49 + 2*x^47 + x^46 + x^44 + 2*x^43 + 2*x^38 + x^37 + x^32 + 2*x^31 + 2*x^29 + x^28 + x^26 + 2*x^25 + x^23 + 2*x^22 + 2*x^17 + x^16 + x^14 + 2*x^13 + 2*x^8 + x^7 + x^5 + 2*x^4 + 2*x^2 + x)/(x^35 + 2*x^34 + 2*x^32 + x^31 + x^27 + 2*x^25 + 2*x^24 + x^22 + x^19 + x^16 + x^13 + 2*x^11 + 2*x^10 + x^8 + x^4 + 2*x^3 + 2*x + 1))*y
aux (V(((x^63 - x^55 - x^39 - x^36 + x^31 + x^28 + x^12 - x^4)/y) dx), V(((x^53 + x^52 + 2*x^50 + 2*x^49 + x^47 + x^46 + 2*x^44 + 2*x^43 + x^41 + x^40 + 2*x^38 + 2*x^37 + x^35 + x^34 + 2*x^32 + 2*x^31 + x^29 + x^28 + x^26 + x^25 + x^23 + x^22 + 2*x^20 + 2*x^19 + x^17 + x^16 + x^14 + x^13 + 2*x^11 + 2*x^10 + x^8 + x^7 + 2*x^5 + 2*x^4 + 2*x^2 + 2*x)/(x^14 + x^13 + 2*x^11 + 2*x^10 + x^8 + x^7 + x^6 + 2*x^4 + 2*x^3 + x + 1))*y), V(((-x^16 - x^14 - x^13 - x^11 - x^10 - x^8 + x^7 - x^5 - x^4 - x^3 + x - 1)/(x^15*y + x^14*y - x^12*y - x^11*y + x^9*y + x^8*y + x^7*y - x^5*y - x^4*y + x^2*y + x*y)) dx))
aux_divided_by_p (((x^18 - x^10 - x^9 + x)/y) dx, ((x^17 + 2*x^16 + x^15 + 2*x^14 + x^13 + 2*x^12 + x^11 + 2*x^10 + x^9 + x^8 + x^7 + 2*x^6 + x^5 + x^4 + 2*x^3 + x^2 + 2*x + 2)/(x^7 + 2*x^6 + x^5 + 2*x^4 + x^3 + 2*x^2 + x + 2))*y, ((x^9 - x^4 + x^3 - x^2 + x + 1)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx)
is regular True True
aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True
[4, 3, 3, 1, 0, 0, 3, 0]
[6nsagsage: autom(B[4]).coordinates(basis=B)
(1, 1, 0, 2, 1, 2, 1, 2)
h2 ((2*x^69 + x^67 + x^63 + 2*x^61 + x^48 + 2*x^46 + x^45 + 2*x^43 + 2*x^42 + x^40 + 2*x^39 + x^37 + x^33 + 2*x^31 + x^30 + 2*x^28 + x^27 + 2*x^25 + 2*x^21 + x^19 + 2*x^18 + x^16 + x^15 + 2*x^13 + x^12 + 2*x^10 + x^9 + 2*x^7 + x^3 + 2*x)/(x^30 + 2*x^28 + 2*x^24 + 2*x^22 + 2*x^20 + 2*x^16 + 2*x^14 + 2*x^10 + 2*x^8 + 2*x^6 + 2*x^2 + 1))*y
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [72], in <cell line: 1>()
----> 1 autom(B[Integer(4)]).coordinates(basis=B)
 
File <string>:114, in coordinates(self, basis)
 
File <string>:99, in div_by_p(self)
 
ValueError: ('aux.omega8.h2.expansion_at_infty().valuation() < 0:', 2*t^-15 + t^-3 + 2*t + 2*t^3 + O(t^5))
[6nsage: load('init.sage')
sage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
....: B = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)
omega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(2*x^5/(x^8 + 2))*y] d[x] + V(((-x^27 - x^19)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]) 0
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift 0 [(1/(x^12 + 2*x^4))*y] d[x] + V(((x^8 + 1)/(x^24*y - x^16*y)) dx) + dV([(1/(x^32 + 2*x^24))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^3/(x^8 + 2))*y] d[x] + V(((-x^29 - x^21 + x^13)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]) [(2/(x^13 + 2*x^5))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^35*y - x^27*y)) dx) + dV([(2/(x^35 + 2*x^27))*y])
result.omega8 == compare True
result.omega8 - compare 0
(1, 1, 0, 2, 1, 2, 1, 2)
h2 ((2*x^69 + x^67 + x^63 + 2*x^61 + x^48 + 2*x^46 + x^45 + 2*x^43 + 2*x^42 + x^40 + 2*x^39 + x^37 + x^33 + 2*x^31 + x^30 + 2*x^28 + x^27 + 2*x^25 + 2*x^21 + x^19 + 2*x^18 + x^16 + x^15 + 2*x^13 + x^12 + 2*x^10 + x^9 + 2*x^7 + x^3 + 2*x)/(x^30 + 2*x^28 + 2*x^24 + 2*x^22 + 2*x^20 + 2*x^16 + 2*x^14 + 2*x^10 + 2*x^8 + 2*x^6 + 2*x^2 + 1))*y
aux.omega8.h2 ((2*x^30 + x^24 + 2*x^21 + 2*x^18 + x^17 + x^16 + x^15 + x^14 + 2*x^12 + 2*x^11 + x^10 + 2*x^9 + 2*x^8 + x^7 + x^6 + 2*x^5 + 2*x^4 + 2*x^2 + 2*x + 1)/(x^27 + x^19 + x^11))*y
second_patch(aux.omega8.h2.diffn()).is_regular_on_U0() False
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [74], in <cell line: 2>()
1 C = superelliptic((x**Integer(3) - x)**Integer(3) + x**Integer(3) - x, Integer(2))
----> 2 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(4)]).coordinates(basis=B)
 
File <string>:116, in coordinates(self, basis)
 
File <string>:101, in div_by_p(self)
 
ValueError: ('aux.omega8.h2.expansion_at_infty().valuation() < 0:', 2*t^-15 + t^-3 + 2*t + 2*t^3 + O(t^5))
[6nsage: C.x.expansion_at_infty()
t^-2 + t^14 + O(t^18)
[6nsage: C.y.expansion_at_infty()
t^-9 + 2*t^7 + O(t^11)
[6nsage: u = C.one/C.x
[6nsage: g = C.genus()
[6nsage: v = C.y/(C.x)^(g+1)
[6nsage: u.expansion_at_infty()
t^2 + 2*t^18 + O(t^22)
[6nsage: v.expansion_at_infty()
t + O(t^21)
sage: gg = ((2*C.x^30 + C.x^24 + 2*C.x^21 + 2*C.x^18 + C.x^17 + C.x^16 + C.x^15 + C.x^14 + 2*C.x^12 + 2*C.x^11 + C.x^10 + 2*C.xx9 + 2*C.x^8 + C.x^7 + C.x^6 + 2*C.
....: ^5 + 2*C.x^4 + 2*C.x^2 + 2*C.x + 1)/(C.x^27 + C.x^19 + C.x^11))*C.y
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [82], in <cell line: 1>()
----> 1 gg = ((Integer(2)*C.x**Integer(30) + C.x**Integer(24) + Integer(2)*C.x**Integer(21) + Integer(2)*C.x**Integer(18) + C.x**Integer(17) + C.x**Integer(16) + C.x**Integer(15) + C.x**Integer(14) + Integer(2)*C.x**Integer(12) + Integer(2)*C.x**Integer(11) + C.x**Integer(10) + Integer(2)*C.x**Integer(9) + Integer(2)*C.x**Integer(8) + C.x**Integer(7) + C.x**Integer(6) + Integer(2)*C.x**Integer(5) + Integer(2)*C.x**Integer(4) + Integer(2)*C.x**Integer(2) + Integer(2)*C.x + Integer(1))/(C.x**Integer(27) + C.x**Integer(19) + C.x**Integer(11)))*C.y
 
File <string>:38, in __add__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
493 """
--> 494 return self.getattr_from_category(name)
495
496 cdef getattr_from_category(self, name):
 
File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
505 else:
506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
508
509 def __dir__(self):
 
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
359 dummy_error_message.cls = type(self)
360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
362 attribute = <object>attr
363 # Check for a descriptor (__get__ in Python)
 
AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function'
sage: gg = ((2*C.x^30 + C.x^24 + 2*C.x^21 + 2*C.x^18 + C.x^17 + C.x^16 + C.x^15 + C.x^14 + 2*C.x^12 + 2*C.x^11 + C.x^10 + 2*C.xx9 + 2*C.x^8 + C.x^7 + C.x^6 + 2*C.
....: ^5 + 2*C.x^4 + 2*C.x^2 + 2*C.x + C.one)/(C.x^27 + C.x^19 + C.x^11))*C.y
sage: gg.expansion_at_infty()
2*t^-15 + t^-3 + 2*t + 2*t^3 + O(t^5)
[6nsage: gg.diffn().expansion_at_infty()
2*t^10 + t^12 + 2*t^16 + O(t^20)
[6nsage: load('init.sage')
sage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
....: B = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)
omega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(2*x^5/(x^8 + 2))*y] d[x] + V(((-x^27 - x^19)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]) 0
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift 0 [(1/(x^12 + 2*x^4))*y] d[x] + V(((x^8 + 1)/(x^24*y - x^16*y)) dx) + dV([(1/(x^32 + 2*x^24))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^3/(x^8 + 2))*y] d[x] + V(((-x^29 - x^21 + x^13)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]) [(2/(x^13 + 2*x^5))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^35*y - x^27*y)) dx) + dV([(2/(x^35 + 2*x^27))*y])
result.omega8 == compare True
result.omega8 - compare 0
(1, 1, 0, 2, 1, 2, 1, 2)
h2 ((2*x^69 + x^67 + x^63 + 2*x^61 + x^48 + 2*x^46 + x^45 + 2*x^43 + 2*x^42 + x^40 + 2*x^39 + x^37 + x^33 + 2*x^31 + x^30 + 2*x^28 + x^27 + 2*x^25 + 2*x^21 + x^19 + 2*x^18 + x^16 + x^15 + 2*x^13 + x^12 + 2*x^10 + x^9 + 2*x^7 + x^3 + 2*x)/(x^30 + 2*x^28 + 2*x^24 + 2*x^22 + 2*x^20 + 2*x^16 + 2*x^14 + 2*x^10 + 2*x^8 + 2*x^6 + 2*x^2 + 1))*y
aux.omega8.omega ((x^28 - x^26 + x^25 - x^24 + x^23 - x^22 - x^21 + x^20 + x^19 + x^18 + x^17 + x^15 - x^14 + x^13 + x^12 + x^11 - x^10 - x^8 - x^7 + x^6 - x^5 + x^4 + x^2 + x - 1)/(x^16*y - x^15*y + x^14*y - x^13*y + x^12*y - x^11*y + x^10*y - x^9*y - x^8*y + x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y)) dx
aux.omega8.h2 ((2*x^30 + x^24 + 2*x^21 + 2*x^18 + x^17 + x^16 + x^15 + x^14 + 2*x^12 + 2*x^11 + x^10 + 2*x^9 + 2*x^8 + x^7 + x^6 + 2*x^5 + 2*x^4 + 2*x^2 + 2*x + 1)/(x^27 + x^19 + x^11))*y
second_patch(aux.omega8.h2.diffn()).is_regular_on_U0() False
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [87], in <cell line: 2>()
1 C = superelliptic((x**Integer(3) - x)**Integer(3) + x**Integer(3) - x, Integer(2))
----> 2 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(4)]).coordinates(basis=B)
 
File <string>:117, in coordinates(self, basis)
 
File <string>:102, in div_by_p(self)
 
ValueError: ('aux.omega8.h2.expansion_at_infty().valuation() < 0:', 2*t^-15 + t^-3 + 2*t + 2*t^3 + O(t^5))
sage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^140+ C.x^13 + C.x^12 + C.x^11 - C.x^1
....: - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - 1)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C9y - C.x^11*C.y + C.x^10*C.y - C.x^
....: *C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [88], in <cell line: 1>()
----> 1 om = ((C.x**Integer(28) - C.x**Integer(26) + C.x**Integer(25) - C.x**Integer(24) + C.x**Integer(23) - C.x**Integer(22) - C.x**Integer(21) + C.x**Integer(20) + C.x**Integer(19) + C.x**Integer(18) + C.x**Integer(17) + C.x**Integer(15) - C.x**Integer(14) + C.x**Integer(13) + C.x**Integer(12) + C.x**Integer(11) - C.x**Integer(10) - C.x**Integer(8) - C.x**Integer(7) + C.x**Integer(6) - C.x**Integer(5) + C.x**Integer(4) + C.x**Integer(2) + C.x - Integer(1))/(C.x**Integer(16)*C.y - C.x**Integer(15)*C.y + C.x**Integer(14)*C.y - C.x**Integer(13)*C.y + C.x**Integer(12)*C.y - C.x**Integer(11)*C.y + C.x**Integer(10)*C.y - C.x**Integer(9)*C.y - C.x**Integer(8)*C.y + C.x**Integer(7)*C.y - C.x**Integer(6)*C.y + C.x**Integer(5)*C.y - C.x**Integer(4)*C.y + C.x**Integer(3)*C.y - C.x**Integer(2)*C.y + C.x*C.y))*C.dx
 
File <string>:50, in __sub__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
493 """
--> 494 return self.getattr_from_category(name)
495
496 cdef getattr_from_category(self, name):
 
File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
505 else:
506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
508
509 def __dir__(self):
 
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
359 dummy_error_message.cls = type(self)
360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
362 attribute = <object>attr
363 # Check for a descriptor (__get__ in Python)
 
AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function'
sage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^140+ C.x^13 + C.x^12 + C.x^11 - C.x^1
....: - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^C2*C.y - C.x^11*C.y + C.x^10*C.y -
....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx
sage: om.expansion_at_infty()
t^-18 + t^-16 + 2*t^-14 + O(t^-8)
sage: om.cartier()
((x^13 - x^12 - x^11 - x^10 - x^9 + x^8 - x^5 + x^4 - x^3 - x^2 + x - 1)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx
sage: om.cartier().expansion_at_infty()
t^-6 + t^-2 + 1 + t^2 + O(t^4)
[6nsage: lau = om.cartier().expansion_at_infty()
sage: lau.truncate_neg()
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [94], in <cell line: 1>()
----> 1 lau.truncate_neg()
 
TypeError: LaurentSeries.truncate_neg() takes exactly one argument (0 given)
[6nsage: lau.truncate_neg(3)
O(t^4)
[6nsage: lau
t^-6 + t^-2 + 1 + t^2 + O(t^4)
[6nsage: lau.laurent_polynomial()
t^-6 + t^-2 + 1 + t^2
sage: lau.integral()
---------------------------------------------------------------------------
ZeroDivisionError Traceback (most recent call last)
Input In [98], in <cell line: 1>()
----> 1 lau.integral()
 
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1654, in sage.rings.laurent_series_ring_element.LaurentSeries.integral()
1652
1653 if n < 0:
-> 1654 v = [a[i]/(n+i+1) for i in range(min(-1-n,len(a)))] + [0]
1655 else:
1656 v = []
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__()
1740
1741 try:
-> 1742 return coercion_model.bin_op(left, right, truediv)
1743 except TypeError:
1744 return NotImplemented
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
1202 self._record_exception()
1203 else:
-> 1204 return PyObject_CallObject(op, xy)
1205
1206 if op is mul:
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
1735 cdef int cl = classify_elements(left, right)
1736 if HAVE_SAME_PARENT(cl):
-> 1737 return (<Element>left)._div_(right)
1738 if BOTH_ARE_ELEMENT(cl):
1739 return coercion_model.bin_op(left, right, truediv)
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
2622 if right_inverse is None:
-> 2623 raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
2624 else:
2625 return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)
 
ZeroDivisionError: inverse of Mod(0, 3) does not exist
sage: lau.lift_to_precision(0)
t^-6 + t^-2 + 1 + t^2 + O(t^4)
sage: for i in lau.exponents():
....: print(lau.coefficient(t^i))
....:
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [100], in <cell line: 1>()
1 for i in lau.exponents():
----> 2 print(lau.coefficient(t**i))
 
File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
493 """
--> 494 return self.getattr_from_category(name)
495
496 cdef getattr_from_category(self, name):
 
File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
505 else:
506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
508
509 def __dir__(self):
 
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
359 dummy_error_message.cls = type(self)
360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
362 attribute = <object>attr
363 # Check for a descriptor (__get__ in Python)
 
AttributeError: 'sage.rings.laurent_series_ring_element.LaurentSeries' object has no attribute 'coefficient'
sage: for i in lau.exponents():
....: print(lau.coefficient()[i])
....:
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [101], in <cell line: 1>()
1 for i in lau.exponents():
----> 2 print(lau.coefficient()[i])
 
File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
493 """
--> 494 return self.getattr_from_category(name)
495
496 cdef getattr_from_category(self, name):
 
File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
505 else:
506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
508
509 def __dir__(self):
 
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
359 dummy_error_message.cls = type(self)
360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
362 attribute = <object>attr
363 # Check for a descriptor (__get__ in Python)
 
AttributeError: 'sage.rings.laurent_series_ring_element.LaurentSeries' object has no attribute 'coefficient'
sage: for i in lau.exponents():
....: print(lau[i])
....:
1
1
1
1
sage: for i in lau.exponents():
....: print(i, lau[i])
....:
-6 1
-2 1
0 1
2 1
[6nsage: om
((x^28 - x^26 + x^25 - x^24 + x^23 - x^22 - x^21 + x^20 + x^19 + x^18 + x^17 + x^15 - x^14 + x^13 + x^12 + x^11 - x^10 - x^8 - x^7 + x^6 - x^5 + x^4 + x^2 + x - 1)/(x^16*y - x^15*y + x^14*y - x^13*y + x^12*y - x^11*y + x^10*y - x^9*y - x^8*y + x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y)) dx
[6nsage: om.cartier().cartier()
(x^3/y) dx
[6nsage: om.cartier().cartier().expansion_at_infty()
1 + O(t^10)
[6nsage: om.cartier().cartier().expansion_at_infty(prec = 100)
1 + 2*t^16 + 2*t^48 + t^64 + O(t^100)
[6nsage: om1 = om.cartier().cartier()
[6nsage: om1.inv_cartier()
((x^18 - x^10)/y) dx
[6nsage: om1.inv_cartier().inv_cartier()
((x^63 - x^55 - x^39 + x^31)/y) dx
[6nsage: om2 = om1.inv_cartier().inv_cartier()
[6nsage: sage: om1 = second_patch(om)
[6nsage: om1.cartier().cartier()
((-1)/y) dx
[6nsage: om1.cartier().cartier().inv_cartier().inv_cartier()
((-x^36 + x^28 + x^12 - x^4)/y) dx
[6nsage: parent(lau)
Laurent Series Ring in t over Finite Field of size 3
[6nsage: parent(parent(lau))
<class 'sage.rings.laurent_series_ring.LaurentSeriesRing_with_category'>
[6nssage: base_ring(parent(lau))
Finite Field of size 3
sage: load('auxilliaries/laurent_analytic_part.sage')
sage: laurent_analytic_part(lau)
t^-6 + t^-2
sage: lau
t^-6 + t^-2 + 1 + t^2 + O(t^4)
[6nsage: laurent_analytic_part(lau).integral()
---------------------------------------------------------------------------
ZeroDivisionError Traceback (most recent call last)
Input In [121], in <cell line: 1>()
----> 1 laurent_analytic_part(lau).integral()
 
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1654, in sage.rings.laurent_series_ring_element.LaurentSeries.integral()
1652
1653 if n < 0:
-> 1654 v = [a[i]/(n+i+1) for i in range(min(-1-n,len(a)))] + [0]
1655 else:
1656 v = []
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__()
1740
1741 try:
-> 1742 return coercion_model.bin_op(left, right, truediv)
1743 except TypeError:
1744 return NotImplemented
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
1202 self._record_exception()
1203 else:
-> 1204 return PyObject_CallObject(op, xy)
1205
1206 if op is mul:
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
1735 cdef int cl = classify_elements(left, right)
1736 if HAVE_SAME_PARENT(cl):
-> 1737 return (<Element>left)._div_(right)
1738 if BOTH_ARE_ELEMENT(cl):
1739 return coercion_model.bin_op(left, right, truediv)
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
2622 if right_inverse is None:
-> 2623 raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
2624 else:
2625 return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)
 
ZeroDivisionError: inverse of Mod(0, 3) does not exist
[6nsage: om
((x^28 - x^26 + x^25 - x^24 + x^23 - x^22 - x^21 + x^20 + x^19 + x^18 + x^17 + x^15 - x^14 + x^13 + x^12 + x^11 - x^10 - x^8 - x^7 + x^6 - x^5 + x^4 + x^2 + x - 1)/(x^16*y - x^15*y + x^14*y - x^13*y + x^12*y - x^11*y + x^10*y - x^9*y - x^8*y + x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y)) dx
[6nsage: om1 = om.cartier()
sage: lau = om1.expansion_at_infty()
sage: lau.analytic_part().integral()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [125], in <cell line: 1>()
----> 1 lau.analytic_part().integral()
 
File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
493 """
--> 494 return self.getattr_from_category(name)
495
496 cdef getattr_from_category(self, name):
 
File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
505 else:
506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
508
509 def __dir__(self):
 
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
359 dummy_error_message.cls = type(self)
360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
362 attribute = <object>attr
363 # Check for a descriptor (__get__ in Python)
 
AttributeError: 'sage.rings.laurent_series_ring_element.LaurentSeries' object has no attribute 'analytic_part'
[6nsage: laurent_analytic_part(lau).integral()
---------------------------------------------------------------------------
ZeroDivisionError Traceback (most recent call last)
Input In [126], in <cell line: 1>()
----> 1 laurent_analytic_part(lau).integral()
 
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1654, in sage.rings.laurent_series_ring_element.LaurentSeries.integral()
1652
1653 if n < 0:
-> 1654 v = [a[i]/(n+i+1) for i in range(min(-1-n,len(a)))] + [0]
1655 else:
1656 v = []
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__()
1740
1741 try:
-> 1742 return coercion_model.bin_op(left, right, truediv)
1743 except TypeError:
1744 return NotImplemented
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
1202 self._record_exception()
1203 else:
-> 1204 return PyObject_CallObject(op, xy)
1205
1206 if op is mul:
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
1735 cdef int cl = classify_elements(left, right)
1736 if HAVE_SAME_PARENT(cl):
-> 1737 return (<Element>left)._div_(right)
1738 if BOTH_ARE_ELEMENT(cl):
1739 return coercion_model.bin_op(left, right, truediv)
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
2622 if right_inverse is None:
-> 2623 raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
2624 else:
2625 return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)
 
ZeroDivisionError: inverse of Mod(0, 3) does not exist
[6nsage: lau.analytic_part()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [127], in <cell line: 1>()
----> 1 lau.analytic_part()
 
File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
493 """
--> 494 return self.getattr_from_category(name)
495
496 cdef getattr_from_category(self, name):
 
File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
505 else:
506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
508
509 def __dir__(self):
 
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
359 dummy_error_message.cls = type(self)
360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
362 attribute = <object>attr
363 # Check for a descriptor (__get__ in Python)
 
AttributeError: 'sage.rings.laurent_series_ring_element.LaurentSeries' object has no attribute 'analytic_part'
[6nsage: laurent_analytic_part(lau)
t^-6 + t^-2
~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
[22;0t[6nsage: load('init.sage')
lo[6nsage: load('auxilliaries/laurent_analytic_part.sage')
[sage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
sage: ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C..^13 + C.x^12 + C.x^11 - C.x^10 - C
....: x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.* - C.x^11*C.y + C.x^10*C.y - C.x^9
....: C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx
((x^28 - x^26 + x^25 - x^24 + x^23 - x^22 - x^21 + x^20 + x^19 + x^18 + x^17 + x^15 - x^14 + x^13 + x^12 + x^11 - x^10 - x^8 - x^7 + x^6 - x^5 + x^4 + x^2 + x - 1)/(x^16*y - x^15*y + x^14*y - x^13*y + x^12*y - x^11*y + x^10*y - x^9*y - x^8*y + x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y)) dx
sage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^140+ C.x^13 + C.x^12 + C.x^11 - C.x^1
....: - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^C2*C.y - C.x^11*C.y + C.x^10*C.y -
....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx
sage: om.cartier().cartier().expansion_at_infty(prec = 100)
1 + 2*t^16 + 2*t^48 + t^64 + O(t^100)
[6nsage: om.cartier()
((x^13 - x^12 - x^11 - x^10 - x^9 + x^8 - x^5 + x^4 - x^3 - x^2 + x - 1)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx
[6nsage: om.cartier().expansion_at_infty()
t^-6 + t^-2 + 1 + t^2 + O(t^4)
[6nsage: lau = om.cartier().expansion_at_infty()
[6nssage: laurent_analytic_part(lau)
t^-6 + t^-2
[6nsage: laurent_analytic_part(lau).integral()
---------------------------------------------------------------------------
ZeroDivisionError Traceback (most recent call last)
Input In [11], in <cell line: 1>()
----> 1 laurent_analytic_part(lau).integral()
 
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1654, in sage.rings.laurent_series_ring_element.LaurentSeries.integral()
1652
1653 if n < 0:
-> 1654 v = [a[i]/(n+i+1) for i in range(min(-1-n,len(a)))] + [0]
1655 else:
1656 v = []
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__()
1740
1741 try:
-> 1742 return coercion_model.bin_op(left, right, truediv)
1743 except TypeError:
1744 return NotImplemented
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
1202 self._record_exception()
1203 else:
-> 1204 return PyObject_CallObject(op, xy)
1205
1206 if op is mul:
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
1735 cdef int cl = classify_elements(left, right)
1736 if HAVE_SAME_PARENT(cl):
-> 1737 return (<Element>left)._div_(right)
1738 if BOTH_ARE_ELEMENT(cl):
1739 return coercion_model.bin_op(left, right, truediv)
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
2622 if right_inverse is None:
-> 2623 raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
2624 else:
2625 return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)
 
ZeroDivisionError: inverse of Mod(0, 3) does not exist
~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
[22;0t[6nsage: load('init.sage')
[6nsage: load('auxilliaries/laurent_analytic_part.sage')
sage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^140+ C.x^13 + C.x^12 + C.x^11 - C.x^1
....: - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^C2*C.y - C.x^11*C.y + C.x^10*C.y -
....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx
sage: lau = om.cartier().expansion_at_infty()
sage: lau
t^-8 + t^-6 + t^-4 + 1 + O(t^2)
[6nsage: lau.integral()
---------------------------------------------------------------------------
ZeroDivisionError Traceback (most recent call last)
Input In [6], in <cell line: 1>()
----> 1 lau.integral()
 
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1654, in sage.rings.laurent_series_ring_element.LaurentSeries.integral()
1652
1653 if n < 0:
-> 1654 v = [a[i]/(n+i+1) for i in range(min(-1-n,len(a)))] + [0]
1655 else:
1656 v = []
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__()
1740
1741 try:
-> 1742 return coercion_model.bin_op(left, right, truediv)
1743 except TypeError:
1744 return NotImplemented
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
1202 self._record_exception()
1203 else:
-> 1204 return PyObject_CallObject(op, xy)
1205
1206 if op is mul:
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
1735 cdef int cl = classify_elements(left, right)
1736 if HAVE_SAME_PARENT(cl):
-> 1737 return (<Element>left)._div_(right)
1738 if BOTH_ARE_ELEMENT(cl):
1739 return coercion_model.bin_op(left, right, truediv)
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
2622 if right_inverse is None:
-> 2623 raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
2624 else:
2625 return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)
 
ZeroDivisionError: inverse of Mod(0, 3) does not exist
[6nssage: F
Finite Field of size 3
sage: Rt.<t> = LaurentSeriesRing(F)
sage: t.integral()
2*t^2
sage: lau
t^-8 + t^-6 + t^-4 + 1 + O(t^2)
[6nsage: t^(-8).integral()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [11], in <cell line: 1>()
----> 1 t**(-Integer(8)).integral()
 
File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
493 """
--> 494 return self.getattr_from_category(name)
495
496 cdef getattr_from_category(self, name):
 
File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
505 else:
506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
508
509 def __dir__(self):
 
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
359 dummy_error_message.cls = type(self)
360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
362 attribute = <object>attr
363 # Check for a descriptor (__get__ in Python)
 
AttributeError: 'sage.rings.integer.Integer' object has no attribute 'integral'
[6nsage: (t^(-8)).integral()
2*t^-7
[6nsage: (t^(-6)).integral()
t^-5
[6nsage: lau
t^-8 + t^-6 + t^-4 + 1 + O(t^2)
[6nsage: (t^(-4)).integral()
---------------------------------------------------------------------------
ZeroDivisionError Traceback (most recent call last)
Input In [15], in <cell line: 1>()
----> 1 (t**(-Integer(4))).integral()
 
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1654, in sage.rings.laurent_series_ring_element.LaurentSeries.integral()
1652
1653 if n < 0:
-> 1654 v = [a[i]/(n+i+1) for i in range(min(-1-n,len(a)))] + [0]
1655 else:
1656 v = []
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__()
1740
1741 try:
-> 1742 return coercion_model.bin_op(left, right, truediv)
1743 except TypeError:
1744 return NotImplemented
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
1202 self._record_exception()
1203 else:
-> 1204 return PyObject_CallObject(op, xy)
1205
1206 if op is mul:
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
1735 cdef int cl = classify_elements(left, right)
1736 if HAVE_SAME_PARENT(cl):
-> 1737 return (<Element>left)._div_(right)
1738 if BOTH_ARE_ELEMENT(cl):
1739 return coercion_model.bin_op(left, right, truediv)
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
2622 if right_inverse is None:
-> 2623 raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
2624 else:
2625 return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)
 
ZeroDivisionError: inverse of Mod(0, 3) does not exist
sage: om.cartier().cartier()
((x^6 + x^3 - x^2 - 1)/(x^6*y + x^4*y + x^2*y + y)) dx
[6nsage: om.cartier().cartier().expansion_at_infty(prec = 100)
1 + t^4 + t^6 + 2*t^8 + t^10 + 2*t^20 + t^22 + 2*t^26 + 2*t^28 + t^30 + 2*t^34 + t^36 + t^38 + t^40 + t^42 + 2*t^46 + t^52 + t^54 + 2*t^56 + t^58 + t^60 + 2*t^64 + t^66 + t^68 + 2*t^72 + t^74 + t^76 + 2*t^80 + t^82 + t^84 + 2*t^88 + t^90 + t^92 + 2*t^96 + t^98 + O(t^100)
[6nsage: om.cartier().expansion_at_infty()
t^-8 + t^-6 + t^-4 + 1 + O(t^2)
[6nsage: sage: g = C.genus()
[6nsage: v = C.y/(C.x)^(g+1)
[6nsage: v.expansion_at_infty()
t + O(t^21)
[6nsage: om = v^(-4)*v.diffn()
[6nsage: om.expansion_at_infty()
t^-4 + t^4 + O(t^6)
[6nsage: om.cartier()
(x^3/(x^2*y - y)) dx
[6nsage: om.cartier().expansion_at_infty()
t^-2 + t^2 + O(t^8)
[6nsage: om.cartier().expansion_at_infty()
t^-2 + t^2 + O(t^8)
[6nsage: om.cartier().cartier().expansion_at_infty(prec = 100)
0
[6nsage: om.cartier().cartier()
0 dx
[6nsage: om
(x^6/(x^4*y + x^2*y + y)) dx
[6nsage: om.cartier()
(x^3/(x^2*y - y)) dx
sage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^140+ C.x^13 + C.x^12 + C.x^11 - C.x^1
....: - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^C2*C.y - C.x^11*C.y + C.x^10*C.y -
....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx
sage: om.cartier()
((x^11 + x^9 - x^7 - x^4 - x)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx
[6nsage: om.cartier().expansion_at_infty()
t^-8 + t^-6 + t^-4 + 1 + O(t^2)
[6nsage: om.cartier().cartier().expansion_at_infty(prec = 100)
1 + t^4 + t^6 + 2*t^8 + t^10 + 2*t^20 + t^22 + 2*t^26 + 2*t^28 + t^30 + 2*t^34 + t^36 + t^38 + t^40 + t^42 + 2*t^46 + t^52 + t^54 + 2*t^56 + t^58 + t^60 + 2*t^64 + t^66 + t^68 + 2*t^72 + t^74 + t^76 + 2*t^80 + t^82 + t^84 + 2*t^88 + t^90 + t^92 + 2*t^96 + t^98 + O(t^100)
[6nsage: quit()
~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
[22;0t[6nsage: load('auxilliaries/laurent_analytic_part.sage')
[6nsage: load('init.sage')
[6nsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
sage: ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C..^13 + C.x^12 + C.x^11 - C.x^10 - C
....: x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.* - C.x^11*C.y + C.x^10*C.y - C.x^9
....: C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx
((x^28 - x^26 + x^25 - x^24 + x^23 - x^22 - x^21 + x^20 + x^19 + x^18 + x^17 + x^15 - x^14 + x^13 + x^12 + x^11 - x^10 - x^8 - x^7 + x^6 - x^5 + x^4 + x^2 + x - 1)/(x^16*y - x^15*y + x^14*y - x^13*y + x^12*y - x^11*y + x^10*y - x^9*y - x^8*y + x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y)) dx
sage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^140+ C.x^13 + C.x^12 + C.x^11 - C.x^1
....: - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^C2*C.y - C.x^11*C.y + C.x^10*C.y -
....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx
sage: om.expansion_at_infty()
t^-18 + t^-16 + 2*t^-14 + O(t^-8)
[6nsage: om.expansion_at_infty(prec = 50)
t^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2 + 2 + 2*t^4 + t^6 + t^8 + 2*t^14 + 2*t^16 + t^24 + t^28 + 2*t^30 + O(t^32)
[6nsage: om.cartier().expansion_at_infty()
t^-6 + t^-2 + 1 + t^2 + O(t^4)
[6nsage: om
((x^28 - x^26 + x^25 - x^24 + x^23 - x^22 - x^21 + x^20 + x^19 + x^18 + x^17 + x^15 - x^14 + x^13 + x^12 + x^11 - x^10 - x^8 - x^7 + x^6 - x^5 + x^4 + x^2 + x - 1)/(x^16*y - x^15*y + x^14*y - x^13*y + x^12*y - x^11*y + x^10*y - x^9*y - x^8*y + x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y)) dx
sage: om == ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^11 + C.x^13 + C.x^12 + C.x^11 - C.x^
....: 0 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y -
....: C.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx
True
sage: om.cartier().expansion_at_infty()
t^-6 + t^-2 + 1 + t^2 + O(t^4)
[6nsage: lau = om.cartier().expansion_at_infty(prec = 30)
[6nsage: laux
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [13], in <cell line: 1>()
----> 1 laux
 
NameError: name 'laux' is not defined
[6nsage: lau
t^-6 + t^-2 + 1 + t^2 + t^6 + 2*t^10 + t^14 + t^16 + 2*t^18 + 2*t^22 + O(t^24)
[6nssage: laurent_analytic_part(lau).integral()
---------------------------------------------------------------------------
ZeroDivisionError Traceback (most recent call last)
Input In [15], in <cell line: 1>()
----> 1 laurent_analytic_part(lau).integral()
 
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1654, in sage.rings.laurent_series_ring_element.LaurentSeries.integral()
1652
1653 if n < 0:
-> 1654 v = [a[i]/(n+i+1) for i in range(min(-1-n,len(a)))] + [0]
1655 else:
1656 v = []
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__()
1740
1741 try:
-> 1742 return coercion_model.bin_op(left, right, truediv)
1743 except TypeError:
1744 return NotImplemented
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
1202 self._record_exception()
1203 else:
-> 1204 return PyObject_CallObject(op, xy)
1205
1206 if op is mul:
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
1735 cdef int cl = classify_elements(left, right)
1736 if HAVE_SAME_PARENT(cl):
-> 1737 return (<Element>left)._div_(right)
1738 if BOTH_ARE_ELEMENT(cl):
1739 return coercion_model.bin_op(left, right, truediv)
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
2622 if right_inverse is None:
-> 2623 raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
2624 else:
2625 return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)
 
ZeroDivisionError: inverse of Mod(0, 3) does not exist
[6nsage: lau
t^-6 + t^-2 + 1 + t^2 + t^6 + 2*t^10 + t^14 + t^16 + 2*t^18 + 2*t^22 + O(t^24)
[6nsage: laurent_analytic_part(lau)
t^-6 + t^-2
[6nsage: Rt.<t> = LaurentSeriesRing(F)
sage: (t^(-6)).integral()
t^-5
[6nsage: (t^(-2)).integral()
2*t^-1
[6nsage: laurent_analytic_part(lau)
t^-6 + t^-2
[6nsage: laurent_analytic_part(lau).integral()
---------------------------------------------------------------------------
ZeroDivisionError Traceback (most recent call last)
Input In [22], in <cell line: 1>()
----> 1 laurent_analytic_part(lau).integral()
 
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1654, in sage.rings.laurent_series_ring_element.LaurentSeries.integral()
1652
1653 if n < 0:
-> 1654 v = [a[i]/(n+i+1) for i in range(min(-1-n,len(a)))] + [0]
1655 else:
1656 v = []
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__()
1740
1741 try:
-> 1742 return coercion_model.bin_op(left, right, truediv)
1743 except TypeError:
1744 return NotImplemented
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
1202 self._record_exception()
1203 else:
-> 1204 return PyObject_CallObject(op, xy)
1205
1206 if op is mul:
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
1735 cdef int cl = classify_elements(left, right)
1736 if HAVE_SAME_PARENT(cl):
-> 1737 return (<Element>left)._div_(right)
1738 if BOTH_ARE_ELEMENT(cl):
1739 return coercion_model.bin_op(left, right, truediv)
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
2622 if right_inverse is None:
-> 2623 raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
2624 else:
2625 return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)
 
ZeroDivisionError: inverse of Mod(0, 3) does not exist
[6nsage: laurent_analytic_part(lau).int()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [23], in <cell line: 1>()
----> 1 laurent_analytic_part(lau).int()
 
File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
493 """
--> 494 return self.getattr_from_category(name)
495
496 cdef getattr_from_category(self, name):
 
File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
505 else:
506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
508
509 def __dir__(self):
 
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
359 dummy_error_message.cls = type(self)
360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
362 attribute = <object>attr
363 # Check for a descriptor (__get__ in Python)
 
AttributeError: 'sage.rings.laurent_series_ring_element.LaurentSeries' object has no attribute 'int'
[6nsage: laurent_analytic_part(lau).integral()
---------------------------------------------------------------------------
ZeroDivisionError Traceback (most recent call last)
Input In [24], in <cell line: 1>()
----> 1 laurent_analytic_part(lau).integral()
 
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1654, in sage.rings.laurent_series_ring_element.LaurentSeries.integral()
1652
1653 if n < 0:
-> 1654 v = [a[i]/(n+i+1) for i in range(min(-1-n,len(a)))] + [0]
1655 else:
1656 v = []
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__()
1740
1741 try:
-> 1742 return coercion_model.bin_op(left, right, truediv)
1743 except TypeError:
1744 return NotImplemented
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
1202 self._record_exception()
1203 else:
-> 1204 return PyObject_CallObject(op, xy)
1205
1206 if op is mul:
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
1735 cdef int cl = classify_elements(left, right)
1736 if HAVE_SAME_PARENT(cl):
-> 1737 return (<Element>left)._div_(right)
1738 if BOTH_ARE_ELEMENT(cl):
1739 return coercion_model.bin_op(left, right, truediv)
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
2622 if right_inverse is None:
-> 2623 raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
2624 else:
2625 return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)
 
ZeroDivisionError: inverse of Mod(0, 3) does not exist
[6nsage: (t^(-2) + t^(-6)).integral()
---------------------------------------------------------------------------
ZeroDivisionError Traceback (most recent call last)
Input In [25], in <cell line: 1>()
----> 1 (t**(-Integer(2)) + t**(-Integer(6))).integral()
 
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1654, in sage.rings.laurent_series_ring_element.LaurentSeries.integral()
1652
1653 if n < 0:
-> 1654 v = [a[i]/(n+i+1) for i in range(min(-1-n,len(a)))] + [0]
1655 else:
1656 v = []
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__()
1740
1741 try:
-> 1742 return coercion_model.bin_op(left, right, truediv)
1743 except TypeError:
1744 return NotImplemented
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
1202 self._record_exception()
1203 else:
-> 1204 return PyObject_CallObject(op, xy)
1205
1206 if op is mul:
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
1735 cdef int cl = classify_elements(left, right)
1736 if HAVE_SAME_PARENT(cl):
-> 1737 return (<Element>left)._div_(right)
1738 if BOTH_ARE_ELEMENT(cl):
1739 return coercion_model.bin_op(left, right, truediv)
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
2622 if right_inverse is None:
-> 2623 raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
2624 else:
2625 return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)
 
ZeroDivisionError: inverse of Mod(0, 3) does not exist
[6nsage: (t^(-2)).integral() + (t^(-6)).integral()
t^-5 + 2*t^-1
[6nsage: load('auxilliaries/laurent_analytic_part.sage')
[6nsage: laurent_integral(laurent_analytic_part(lau))
t^-5 + 2*t^-1
[6nsage: quit()
~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
[22;0t[6nsasage: load('init.sage')
---------------------------------------------------------------------------
OSError Traceback (most recent call last)
Input In [1], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:21, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:244, in load(filename, globals, attach)
242 break
243 else:
--> 244 raise IOError('did not find file %r to load or attach' % filename)
246 ext = os.path.splitext(fpath)[1].lower()
247 if ext == '.py':
 
OSError: did not find file 'sage/superelliptic_drw/superelliptic_drw_auxilliaries.sage' to load or attach
[6nsage: load('init.sage')
[6nsage: Rx
Univariate Polynomial Ring in x over Finite Field of size 3
[6nssage: g = x^3 - x
[6nsage: g(x = C.x/C.y)
sage/rings/polynomial/polynomial_zmod_flint.pyx:7: DeprecationWarning: invalid escape sequence '\Z'
"""
sage/rings/polynomial/polynomial_zmod_flint.pyx:7: DeprecationWarning: invalid escape sequence '\Z'
"""
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [5], in <cell line: 1>()
----> 1 g(x = C.x/C.y)
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zmod_flint.pyx:332, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint.__call__()
330 nmod_poly_compose(&t.x, &self.x, &y.x)
331 return t
--> 332 return Polynomial.__call__(self, *x, **kwds)
333
334 @coerce_binop
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:870, in sage.rings.polynomial.polynomial_element.Polynomial.__call__()
868 # This can save lots of coercions when the common parent is the
869 # polynomial's base ring (e.g., for evaluations at integers).
--> 870 cst, aa = coercion_model.canonical_coercion(cst, a)
871 # Use fast multiplication actions like matrix × scalar.
872 # If there is no action, replace a by an element of the
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1393, in sage.structure.coerce.CoercionModel.canonical_coercion()
1391 self._record_exception()
1392
-> 1393 raise TypeError("no common canonical parent for objects with parents: '%s' and '%s'"%(xp, yp))
1394
1395
 
TypeError: no common canonical parent for objects with parents: 'Finite Field of size 3' and '<class '__main__.superelliptic_function'>'
[6nsage: load('init.sage')
[6nsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
sage: ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1
....: ....: 0 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y*+ C.x^12*C.y - C.x^11*C.y + C.x^10
....: C.y -
....: ....: C.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx
Input In [8]
((C.x**Integer(28) - C.x**Integer(26) + C.x**Integer(25) - C.x**Integer(24) + C.x**Integer(23) - C.x**Integer(22) - C.x**Integer(21) + C.x**Integer(20) + C.x**Integer(19) + C.x**Integer(18) + C.x**Integer(17) + C.x**Integer(15) - C.x**Integer(14) + C.x**Integer(13) + C.x**Integer(12) + C.x**Integer(11) - C.x**Integer(1)
^
SyntaxError: invalid syntax. Perhaps you forgot a comma?
 
sage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^140+ C.x^13 + C.x^12 + C.x^11 - C.x^1
....: - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^C2*C.y - C.x^11*C.y + C.x^10*C.y -
....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx
sage: decomposition_omega8_hpdh(om)
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [10], in <cell line: 1>()
----> 1 decomposition_omega8_hpdh(om)
 
File <string>:32, in decomposition_omega8_hpdh(omega, prec)
 
NameError: name 'laurent_analytic_part' is not defined
[6nsage: load('init.sage')
[6nsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
sage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^140+ C.x^13 + C.x^12 + C.x^11 - C.x^1
....: - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^C2*C.y - C.x^11*C.y + C.x^10*C.y -
....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx
sage: decomposition_omega8_hpdh(om)
(((x^37 + x^36 - x^35 - x^31 + x^30 + x^29 + x^28 - x^26 + x^25 + x^24 - x^22 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^25*y - x*y)) dx,
0)
sage: om.expansion_at_infty(prec = 50)
t^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2 + 2 + 2*t^4 + t^6 + t^8 + 2*t^14 + 2*t^16 + t^24 + t^28 + 2*t^30 + O(t^32)
[6nsage: load('init.sage')
[6nsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
sage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^140+ C.x^13 + C.x^12 + C.x^11 - C.x^1
....: - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^C2*C.y - C.x^11*C.y + C.x^10*C.y -
....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx
[6nsage: decomposition_omega8_hpdh(om)
omega_analytic t^-6 + t^-2
omega_analytic (x^30 + x^10*y^4)/y^6
omega_analytic ((x^30 + x^28 + x^20 + x^12)/(x^24*y - y)) dx
omega8 ((x^37 + x^36 - x^35 - x^31 + x^30 + x^29 + x^28 - x^26 + x^25 + x^24 - x^22 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^25*y - x*y)) dx
dh 0 dx
(((x^37 + x^36 - x^35 - x^31 + x^30 + x^29 + x^28 - x^26 + x^25 + x^24 - x^22 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^25*y - x*y)) dx,
0)
[6nsage: load('init.sage')
[6nsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
sage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^140+ C.x^13 + C.x^12 + C.x^11 - C.x^1
....: - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^C2*C.y - C.x^11*C.y + C.x^10*C.y -
....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx
[6nsage: decomposition_omega8_hpdh(om)
omega_analytic t^-6 + t^-2
omega_analytic, superelliptic_function(C, omega_analytic), Cv.diffn() (x^30 + x^10*y^4)/y^6 (x^27 + x^25 + x^17 + x^9)/(x^24 + 2) (x^3/y) dx
omega_analytic ((x^30 + x^28 + x^20 + x^12)/(x^24*y - y)) dx
omega8 ((x^37 + x^36 - x^35 - x^31 + x^30 + x^29 + x^28 - x^26 + x^25 + x^24 - x^22 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^25*y - x*y)) dx
dh 0 dx
(((x^37 + x^36 - x^35 - x^31 + x^30 + x^29 + x^28 - x^26 + x^25 + x^24 - x^22 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^25*y - x*y)) dx,
0)
[6nsage: load('init.sage')
[6nsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
sage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^140+ C.x^13 + C.x^12 + C.x^11 - C.x^1
....: - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^C2*C.y - C.x^11*C.y + C.x^10*C.y -
....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx
[6nsage: decomposition_omega8_hpdh(om)
omega_analytic t^-6 + t^-2
omega_analytic, superelliptic_function(C, omega_analytic), Cv.diffn() (x^30 + x^10*y^4)/y^6 (x^27 + x^25 + x^17 + x^9)/(x^24 + 2) (x^3/y) dx
omega_analytic ((x^30 + x^28 + x^20 + x^12)/(x^24*y - y)) dx
omega8 ((x^37 + x^36 - x^35 - x^31 + x^30 + x^29 + x^28 - x^26 + x^25 + x^24 - x^22 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^25*y - x*y)) dx
dh 0 dx
omega8.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + O(t^-8)
(((x^37 + x^36 - x^35 - x^31 + x^30 + x^29 + x^28 - x^26 + x^25 + x^24 - x^22 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^25*y - x*y)) dx,
0)
sage: om.expansion_at_infty(prec = 50)
t^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2 + 2 + 2*t^4 + t^6 + t^8 + 2*t^14 + 2*t^16 + t^24 + t^28 + 2*t^30 + O(t^32)
[6nsage: laurent_analytic_part(om.expansion_at_infty(prec = 50))
t^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2
[6nsage: load('init.sage')
[6nsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
sage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^140+ C.x^13 + C.x^12 + C.x^11 - C.x^1
....: - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^C2*C.y - C.x^11*C.y + C.x^10*C.y -
....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx
[6nsage: decomposition_omega8_hpdh(om)
omega_analytic t^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2
omega_analytic, superelliptic_function(C, omega_analytic), Cv.diffn() (x^90 + x^80*y^2 - x^70*y^4 + x^20*y^14 + x^10*y^16)/y^18 (x^81 + x^80 + 2*x^79 + x^74 + x^73 + 2*x^72 + 2*x^71 + 2*x^66 + x^65 + 2*x^63 + x^57 + x^50 + x^49 + 2*x^42 + x^41 + x^33 + x^26 + x^25 + 2*x^18 + x^17 + x^9)/(x^72 + 2) (x^3/y) dx
omega_analytic ((x^84 + x^83 - x^82 + x^77 + x^76 - x^75 - x^74 - x^69 + x^68 - x^66 + x^60 + x^53 + x^52 - x^45 + x^44 + x^36 + x^29 + x^28 - x^21 + x^20 + x^12)/(x^72*y - y)) dx
omega8 ((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx
dh ((x^30 + x^28 + x^20 + x^12)/(x^24*y - y)) dx
omega8.expansion_at_infty() t^-2 + 2 + t^2 + 2*t^4 + t^6 + O(t^8)
(((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx,
((x^38 + 2*x^36 + x^30 + x^12)/(x^40 + x^32 + x^24 + 2*x^16 + 2*x^8 + 2))*y)
[6nsage: sage: g = C.genus()
[6nsage: v = C.y/(C.x)^(g+1)
[6nsage: v.expansion_at_infty()
t + O(t^21)
[6nsage: v.diffn().expansion_at_infty()
1 + O(t^10)
[6nsage: load('init.sage')
[6nsage: sage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
sage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^140+ C.x^13 + C.x^12 + C.x^11 - C.x^1
....: - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^C2*C.y - C.x^11*C.y + C.x^10*C.y -
....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx
[6nsage: decomposition_omega8_hpdh(om)
omega_analytic t^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2
omega_analytic, superelliptic_function(C, omega_analytic), Cv.diffn() (x^90 + x^80*y^2 - x^70*y^4 + x^20*y^14 + x^10*y^16)/y^18 (x^81 + x^80 + 2*x^79 + x^74 + x^73 + 2*x^72 + 2*x^71 + 2*x^66 + x^65 + 2*x^63 + x^57 + x^50 + x^49 + 2*x^42 + x^41 + x^33 + x^26 + x^25 + 2*x^18 + x^17 + x^9)/(x^72 + 2) (x^3/y) dx
omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + O(t^-8)
omega_analytic ((x^84 + x^83 - x^82 + x^77 + x^76 - x^75 - x^74 - x^69 + x^68 - x^66 + x^60 + x^53 + x^52 - x^45 + x^44 + x^36 + x^29 + x^28 - x^21 + x^20 + x^12)/(x^72*y - y)) dx
omega8 ((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx
dh ((x^30 + x^28 + x^20 + x^12)/(x^24*y - y)) dx
omega8.expansion_at_infty() t^-2 + 2 + t^2 + 2*t^4 + t^6 + O(t^8)
(((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx,
((x^38 + 2*x^36 + x^30 + x^12)/(x^40 + x^32 + x^24 + 2*x^16 + 2*x^8 + 2))*y)
[6nsage: load('init.sage')
[6nsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
sage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^140+ C.x^13 + C.x^12 + C.x^11 - C.x^1
....: - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^C2*C.y - C.x^11*C.y + C.x^10*C.y -
....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx
[6nsage: decomposition_omega8_hpdh(om)
omega_analytic t^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2
omega_analytic, superelliptic_function(C, omega_analytic), Cv.diffn() (x^90 + x^80*y^2 - x^70*y^4 + x^20*y^14 + x^10*y^16)/y^18 (x^81 + x^80 + 2*x^79 + x^74 + x^73 + 2*x^72 + 2*x^71 + 2*x^66 + x^65 + 2*x^63 + x^57 + x^50 + x^49 + 2*x^42 + x^41 + x^33 + x^26 + x^25 + 2*x^18 + x^17 + x^9)/(x^72 + 2) (x^3/y) dx
omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + 2*t^2 + t^14 + t^16 + t^28 + 2*t^30 + O(t^32)
omega_analytic ((x^84 + x^83 - x^82 + x^77 + x^76 - x^75 - x^74 - x^69 + x^68 - x^66 + x^60 + x^53 + x^52 - x^45 + x^44 + x^36 + x^29 + x^28 - x^21 + x^20 + x^12)/(x^72*y - y)) dx
omega8 ((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx
dh ((x^30 + x^28 + x^20 + x^12)/(x^24*y - y)) dx
omega8.expansion_at_infty() t^-2 + 2 + t^2 + 2*t^4 + t^6 + t^8 + t^14 + t^16 + t^24 + t^34 + 2*t^36 + t^38 + t^40 + 2*t^46 + O(t^48)
(((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx,
((x^38 + 2*x^36 + x^30 + x^12)/(x^40 + x^32 + x^24 + 2*x^16 + 2*x^8 + 2))*y)
[6nsage: load('init.sage')
[6nsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
sage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^140+ C.x^13 + C.x^12 + C.x^11 - C.x^1
....: - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^C2*C.y - C.x^11*C.y + C.x^10*C.y -
....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx
[6nsage: decomposition_omega8_hpdh(om)
---------------------------------------------------------------------------
KeyError Traceback (most recent call last)
File /ext/sage/9.7/src/sage/structure/category_object.pyx:839, in sage.structure.category_object.CategoryObject.getattr_from_category()
838 try:
--> 839 return self.__cached_methods[name]
840 except KeyError:
 
KeyError: 'integer_ring'
 
During handling of the above exception, another exception occurred:
 
AttributeError Traceback (most recent call last)
File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce)
705 try:
--> 706 x, y = resolve_fractions(x0, y0)
707 except (AttributeError, TypeError):
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:683, in FractionField_generic._element_constructor_.<locals>.resolve_fractions(x, y)
682 def resolve_fractions(x, y):
--> 683 xn = x.numerator()
684 xd = x.denominator()
 
File /ext/sage/9.7/src/sage/categories/complete_discrete_valuation.py:281, in CompleteDiscreteValuationFields.ElementMethods.numerator(self)
252 """
253 Return the numerator of this element, normalized in such a
254 way that `x = x.numerator() / x.denominator()` always holds
(...)
279 7^5 + O(7^10)
280 """
--> 281 R = self.parent().integer_ring()
282 return R(self * self.denominator())
 
File /ext/sage/9.7/src/sage/structure/category_object.pyx:833, in sage.structure.category_object.CategoryObject.__getattr__()
832 """
--> 833 return self.getattr_from_category(name)
834
 
File /ext/sage/9.7/src/sage/structure/category_object.pyx:848, in sage.structure.category_object.CategoryObject.getattr_from_category()
847
--> 848 attr = getattr_from_other_class(self, cls, name)
849 self.__cached_methods[name] = attr
 
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:356, in sage.cpython.getattr.getattr_from_other_class()
355 dummy_error_message.name = name
--> 356 raise AttributeError(dummy_error_message)
357 cdef PyObject* attr = instance_getattr(cls, name)
 
AttributeError: 'PolynomialRing_dense_mod_p_with_category' object has no attribute '_cached_repr'
 
During handling of the above exception, another exception occurred:
 
TypeError Traceback (most recent call last)
Input In [49], in <cell line: 1>()
----> 1 decomposition_omega8_hpdh(om)
 
File <string>:34, in decomposition_omega8_hpdh(omega, prec)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
159 print(type(C), C)
160 print(type(C._element_constructor), C._element_constructor)
--> 161 raise
162
163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:708, in FractionField_generic._element_constructor_(self, x, y, coerce)
706 x, y = resolve_fractions(x0, y0)
707 except (AttributeError, TypeError):
--> 708 raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
709 x0, y0, self))
710 try:
711 return self._element_class(self, x, y, coerce=coerce)
 
TypeError: cannot convert t^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2/1 to an element of Fraction Field of Univariate Polynomial Ring in T over Finite Field of size 3
[6nsage: load('init.sage')
[6nsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
sage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^140+ C.x^13 + C.x^12 + C.x^11 - C.x^1
....: - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^C2*C.y - C.x^11*C.y + C.x^10*C.y -
....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx
[6nsasage: decomposition_omega8_hpdh(om)
omega_analytic (T^16 + T^14 + 2*T^4 + T^2 + 1)/T^18
omega_analytic, superelliptic_function(C, omega_analytic), Cv.diffn() (x^90 + x^80*y^2 - x^70*y^4 + x^20*y^14 + x^10*y^16)/y^18 (x^81 + x^80 + 2*x^79 + x^74 + x^73 + 2*x^72 + 2*x^71 + 2*x^66 + x^65 + 2*x^63 + x^57 + x^50 + x^49 + 2*x^42 + x^41 + x^33 + x^26 + x^25 + 2*x^18 + x^17 + x^9)/(x^72 + 2) (x^3/y) dx
omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + 2*t^2 + t^14 + t^16 + t^28 + 2*t^30 + O(t^32)
omega_analytic ((x^84 + x^83 - x^82 + x^77 + x^76 - x^75 - x^74 - x^69 + x^68 - x^66 + x^60 + x^53 + x^52 - x^45 + x^44 + x^36 + x^29 + x^28 - x^21 + x^20 + x^12)/(x^72*y - y)) dx
omega8 ((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx
dh ((x^30 + x^28 + x^20 + x^12)/(x^24*y - y)) dx
omega8.expansion_at_infty() t^-2 + 2 + t^2 + 2*t^4 + t^6 + t^8 + t^14 + t^16 + t^24 + t^34 + 2*t^36 + t^38 + t^40 + 2*t^46 + O(t^48)
(((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx,
((x^38 + 2*x^36 + x^30 + x^12)/(x^40 + x^32 + x^24 + 2*x^16 + 2*x^8 + 2))*y)
[6nsage: load('init.sage')
[6nsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
sage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^140+ C.x^13 + C.x^12 + C.x^11 - C.x^1
....: - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^C2*C.y - C.x^11*C.y + C.x^10*C.y -
....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx
[6nsage: decomposition_omega8_hpdh(om)
omega_analytic (T^16 + T^14 + 2*T^4 + T^2 + 1)/T^18
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [57], in <cell line: 1>()
----> 1 decomposition_omega8_hpdh(om)
 
File <string>:39, in decomposition_omega8_hpdh(omega, prec)
 
AttributeError: 'superelliptic_function' object has no attribute 'expanstion_at_infty'
[6nsage: load('init.sage')
[6nsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
sage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^140+ C.x^13 + C.x^12 + C.x^11 - C.x^1
....: - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^C2*C.y - C.x^11*C.y + C.x^10*C.y -
....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx
[6nsage: decomposition_omega8_hpdh(om)
omega_analytic (T^16 + T^14 + 2*T^4 + T^2 + 1)/T^18
omega_analytic, superelliptic_function(C, omega_analytic), Cv.diffn() (x^90 + x^80*y^2 - x^70*y^4 + x^20*y^14 + x^10*y^16)/y^18 (x^81 + x^80 + 2*x^79 + x^74 + x^73 + 2*x^72 + 2*x^71 + 2*x^66 + x^65 + 2*x^63 + x^57 + x^50 + x^49 + 2*x^42 + x^41 + x^33 + x^26 + x^25 + 2*x^18 + x^17 + x^9)/(x^72 + 2) (x^3/y) dx t^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2 + 1 + t^2 + t^12 + 2*t^14 + 2*t^16 + t^18 + 2*t^28 + 2*t^30 + O(t^32)
omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + 2*t^2 + t^14 + t^16 + t^28 + 2*t^30 + O(t^32)
omega_analytic ((x^84 + x^83 - x^82 + x^77 + x^76 - x^75 - x^74 - x^69 + x^68 - x^66 + x^60 + x^53 + x^52 - x^45 + x^44 + x^36 + x^29 + x^28 - x^21 + x^20 + x^12)/(x^72*y - y)) dx
omega8 ((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx
dh ((x^30 + x^28 + x^20 + x^12)/(x^24*y - y)) dx
omega8.expansion_at_infty() t^-2 + 2 + t^2 + 2*t^4 + t^6 + t^8 + t^14 + t^16 + t^24 + t^34 + 2*t^36 + t^38 + t^40 + 2*t^46 + O(t^48)
(((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx,
((x^38 + 2*x^36 + x^30 + x^12)/(x^40 + x^32 + x^24 + 2*x^16 + 2*x^8 + 2))*y)
[6nsage: load('init.sage')
[6nsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
sage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^140+ C.x^13 + C.x^12 + C.x^11 - C.x^1
....: - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^C2*C.y - C.x^11*C.y + C.x^10*C.y -
....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx
[6nsage: decomposition_omega8_hpdh(om)
omega_analytic (T^16 + T^14 + 2*T^4 + T^2 + 1)/T^18
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [65], in <cell line: 1>()
----> 1 decomposition_omega8_hpdh(om)
 
File <string>:39, in decomposition_omega8_hpdh(omega, prec)
 
TypeError: superelliptic_function.diffn() got an unexpected keyword argument 'prec'
[6nsage: load('init.sage')
[6nsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
sage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^140+ C.x^13 + C.x^12 + C.x^11 - C.x^1
....: - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^C2*C.y - C.x^11*C.y + C.x^10*C.y -
....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx
[6nsage: decomposition_omega8_hpdh(om)
omega_analytic (T^16 + T^14 + 2*T^4 + T^2 + 1)/T^18
expansions t^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2 + 1 + t^2 + t^12 + 2*t^14 + 2*t^16 + t^18 + 2*t^28 + 2*t^30 + O(t^32)
1 + 2*t^16 + 2*t^48 + O(t^50)
t^-18 + t^-16 + 2*t^-14 + t^-4 + 2*t^2 + t^14 + t^16 + t^28 + 2*t^30 + O(t^32)
omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + 2*t^2 + t^14 + t^16 + t^28 + 2*t^30 + O(t^32)
omega_analytic ((x^84 + x^83 - x^82 + x^77 + x^76 - x^75 - x^74 - x^69 + x^68 - x^66 + x^60 + x^53 + x^52 - x^45 + x^44 + x^36 + x^29 + x^28 - x^21 + x^20 + x^12)/(x^72*y - y)) dx
omega8 ((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx
dh ((x^30 + x^28 + x^20 + x^12)/(x^24*y - y)) dx
omega8.expansion_at_infty() t^-2 + 2 + t^2 + 2*t^4 + t^6 + t^8 + t^14 + t^16 + t^24 + t^34 + 2*t^36 + t^38 + t^40 + 2*t^46 + O(t^48)
(((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx,
((x^38 + 2*x^36 + x^30 + x^12)/(x^40 + x^32 + x^24 + 2*x^16 + 2*x^8 + 2))*y)
sage: load('init.sage')
<string>:218: DeprecationWarning: invalid escape sequence '\s'
sage: load('init.sage')
<string>:218: DeprecationWarning: invalid escape sequence '\s'
sage: load('init.sage')
<string>:218: DeprecationWarning: invalid escape sequence '\s'
sage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
sage: C.uniformizer()
(x^4/(x^8 + 2))*y
[6nsage: C.uniformizer().expansion_at_infty()
t^-1 + 2*t^15 + O(t^19)
[6nsage: C.uniformizer()
(x^4/(x^8 + 2))*y
[6nsage: C.uniformizer().expansion_at_infty()
t^-1 + 2*t^15 + O(t^19)
[6nsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
[6nsage: C.uniformizer().expansion_at_infty()
t^-1 + 2*t^15 + O(t^19)
[6nsage: load('init.sage')
<string>:218: DeprecationWarning: invalid escape sequence '\s'
[6nsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
[6nsage: C.uniformizer().expansion_at_infty()
t^-1 + 2*t^15 + O(t^19)
[6nsage: C.uniformizer().expansion_at_infty(prec = 200)
t^-1 + 2*t^15 + 2*t^31 + 2*t^47 + 2*t^111 + 2*t^127 + 2*t^143 + 2*t^159 + t^191 + O(t^199)
[6nsage: load('init.sage')
<string>:219: DeprecationWarning: invalid escape sequence '\s'
[6nsage: sage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
[6nsage: C.uniformizer().expansion_at_infty(prec = 200)
a, b, delta, M, R 5 1 1 2 9
t^-1 + 2*t^15 + 2*t^31 + 2*t^47 + 2*t^111 + 2*t^127 + 2*t^143 + 2*t^159 + t^191 + O(t^199)
[6nsage: C.x.expansion_at_infty()
t^-2 + t^14 + O(t^18)
[6nsage: load('init.sage')
<string>:219: DeprecationWarning: invalid escape sequence '\s'
[6nsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
[6nsage: C.uniformizer().expansion_at_infty(prec = 200)
a, b, delta, M, R 5 1 1 2 9
t + O(t^201)
[6nsage: C.uniformizer().expansion_at_infty(prec = 200)
a, b, delta, M, R 5 1 1 2 9
t + O(t^201)
[6nsage: C.uniformizer().expansion_at_infty(prec = 220)
a, b, delta, M, R 5 1 1 2 9
t + O(t^221)
[6nsage: ((C.uniformizer())^(-1)).expansion_at_infty(prec = 220)
a, b, delta, M, R 5 1 1 2 9
t^-1 + 2*t^15 + 2*t^31 + 2*t^47 + 2*t^111 + 2*t^127 + 2*t^143 + 2*t^159 + t^191 + O(t^219)
[6nsage: ((C.uniformizer())^(-1)).expansion_at_infty(prec = 320)
a, b, delta, M, R 5 1 1 2 9
t^-1 + 2*t^15 + 2*t^31 + 2*t^47 + 2*t^111 + 2*t^127 + 2*t^143 + 2*t^159 + t^191 + t^255 + 2*t^271 + O(t^319)
[6nsage: ((C.uniformizer())^(-1)).expansion_at_infty(prec = 1000)
a, b, delta, M, R 5 1 1 2 9
t^-1 + 2*t^15 + 2*t^31 + 2*t^47 + 2*t^111 + 2*t^127 + 2*t^143 + 2*t^159 + t^191 + t^255 + 2*t^271 + 2*t^319 + 2*t^431 + 2*t^447 + 2*t^463 + 2*t^479 + t^559 + t^575 + t^591 + t^623 + t^751 + 2*t^975 + O(t^999)
[6nsage: C.x.expansion_at_infty(prec = 20)
t^-2 + t^14 + O(t^18)
[6nsage: C.x.expansion_at_infty(prec = 100)
t^-2 + t^14 + 2*t^30 + 2*t^46 + 2*t^62 + O(t^98)
[6nsage: C.uniformizer()
a, b, delta, M, R 5 1 1 2 9
1/x^5*y
[6nsage: C.uniformizer().expansion_at_infty(prec = 220)
a, b, delta, M, R 5 1 1 2 9
t + O(t^221)
[6nsage: a = C.uniformizer()
a, b, delta, M, R 5 1 1 2 9
[6nsage: (a^(-1)).expansion_at_infty(prec = 100)
t^-1 + 2*t^15 + 2*t^31 + 2*t^47 + O(t^99)
[6nsage: a^(-1)
(x^4/(x^8 + 2))*y
[6nssage: C.y^2
x^9 + 2*x
[6nsage: C.x.expansion_at_infty(prec = 100)
t^-2 + t^14 + 2*t^30 + 2*t^46 + 2*t^62 + O(t^98)
[6nsage: Rt.<t> = LaurentSeriesRing(F)
[6nsage: C.y.expansion_at_infty()
t^-9 + 2*t^7 + O(t^11)
[6nsage: C.y.expansion_at_infty(prec = 100)
t^-9 + 2*t^7 + 2*t^23 + 2*t^55 + 2*t^71 + t^87 + O(t^91)
[6nsage: sage: xx = t^(-2) + t^(14) + 2*t^(30)
[6nsage: yy = t^(-9) + 2*t^7 + 2*t^23
[6nsage: xx^4*yy/(xx^8 - 1)
t^-1 + 2*t^15 + O(t^19)
[6nssage: (C.x - a^(-2)).expansion_at_infty()
2*t^14 + O(t^34)
[6nsage: (C.x - a^(-2)).expansion_at_infty(prec = 100)
2*t^14 + 2*t^62 + t^110 + O(t^114)
[6nsage: C.x.expansion_at_infty(prec = 100)
t^-2 + t^14 + 2*t^30 + 2*t^46 + 2*t^62 + O(t^98)
[6nsagsage: xx^8 - 1
t^-16 + 1 + 2*t^16 + 2*t^48 + t^64 + t^80 + t^112 + t^144 + 2*t^160 + 2*t^176 + 2*t^208 + t^224 + t^240
[6nsasage: yy/xx^5
t + O(t^21)
[6nsage: Rt.<t> = LaurentSeriesRing(F, prec = 100)
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [116], in <cell line: 1>()
----> 1 Rt = LaurentSeriesRing(F, prec = Integer(100), names=('t',)); (t,) = Rt._first_ngens(1)
 
File /ext/sage/9.7/src/sage/misc/classcall_metaclass.pyx:320, in sage.misc.classcall_metaclass.ClasscallMetaclass.__call__()
318 """
319 if cls.classcall is not None:
--> 320 return cls.classcall(cls, *args, **kwds)
321 else:
322 # Fast version of type.__call__(cls, *args, **kwds)
 
File /ext/sage/9.7/src/sage/rings/laurent_series_ring.py:201, in LaurentSeriesRing.__classcall__(cls, *args, **kwds)
199 power_series = args[0]
200 else:
--> 201 power_series = PowerSeriesRing(*args, **kwds)
203 return UniqueRepresentation.__classcall__(cls, power_series)
 
TypeError: PowerSeriesRing() got an unexpected keyword argument 'prec'
[6nsage: Rt.<t> = LaurentSeriesRing(F, default_precision = 100)
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [117], in <cell line: 1>()
----> 1 Rt = LaurentSeriesRing(F, default_precision = Integer(100), names=('t',)); (t,) = Rt._first_ngens(1)
 
File /ext/sage/9.7/src/sage/misc/classcall_metaclass.pyx:320, in sage.misc.classcall_metaclass.ClasscallMetaclass.__call__()
318 """
319 if cls.classcall is not None:
--> 320 return cls.classcall(cls, *args, **kwds)
321 else:
322 # Fast version of type.__call__(cls, *args, **kwds)
 
File /ext/sage/9.7/src/sage/rings/laurent_series_ring.py:201, in LaurentSeriesRing.__classcall__(cls, *args, **kwds)
199 power_series = args[0]
200 else:
--> 201 power_series = PowerSeriesRing(*args, **kwds)
203 return UniqueRepresentation.__classcall__(cls, power_series)
 
TypeError: PowerSeriesRing() got an unexpected keyword argument 'default_precision'
[6nsage: Rt.<t> = LaurentSeriesRing(F, default_prec = 100)
[6nsage: xx = t^(-2) + t^(14) + 2*t^(30)
[6nsage: yy = t^(-9) + 2*t^7 + 2*t^23
[6nsasage: yy/xx^5
t + t^49 + t^65 + 2*t^97 + O(t^101)
[6nsage: xx^5/yy
t^-1 + 2*t^47 + 2*t^63 + 2*t^95 + O(t^99)
[6nsage: xx^4*yy/(xx^8 - 1)
t^-1 + 2*t^15 + 2*t^31 + t^47 + 2*t^79 + 2*t^95 + O(t^99)
[6nsage: sage: (xx^8 - 1)/(xx^4 * yy)
t + t^17 + 2*t^33 + 2*t^49 + t^81 + t^97 + O(t^101)
[6nsage: C.y^2
x^9 + 2*x
[6nsage: yy^2 - xx^9 + xx
2*t^-2 + t^30 + t^46 + 2*t^126 + t^270
[6nsage: C.y^2
x^9 + 2*x
[6nsage: yy^2 - (xx^9 +2*xx)
2*t^-2 + t^30 + t^46 + 2*t^126 + t^270
[6nsage: yy
t^-9 + 2*t^7 + 2*t^23
[6nsage: xx
t^-2 + t^14 + 2*t^30
[6nsage: yy^2
t^-18 + t^-2 + 2*t^14 + 2*t^30 + t^46
[6nsage: xx^9 + 2*xx
t^-18 + 2*t^-2 + 2*t^14 + t^30 + t^126 + 2*t^270
[6nsage: C = superelliptic(x^3 - x, 2)
[6nsage: xx = C.x.expansion_at_infty(prec = 100)
[6nsage: yy = C.y.expanstion_at_infty(prec = 100)
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [135], in <cell line: 1>()
----> 1 yy = C.y.expanstion_at_infty(prec = Integer(100))
 
AttributeError: 'superelliptic_function' object has no attribute 'expanstion_at_infty'
[6nsage: yy = C.y.expansion_at_infty(prec = 100)
[6nsage: yy^2 - (xx^3 - xx)
2*t^-2 + t^6 + t^10 + 2*t^14 + t^18 + t^34 + 2*t^38 + t^42 + t^46 + 2*t^50 + t^54 + O(t^94)
[6nsage: yy
t^-3 + 2*t + 2*t^5 + 2*t^9 + t^13 + 2*t^17 + 2*t^33 + t^37 + 2*t^41 + 2*t^45 + t^49 + 2*t^53 + O(t^97)
[6nsage: xx
t^-2 + t^2 + 2*t^6 + 2*t^10 + t^14 + 2*t^18 + 2*t^34 + t^38 + 2*t^42 + 2*t^46 + t^50 + 2*t^54 + O(t^98)
[6nsage: C = superelliptic(x^3 - x + 1, 2)
[6nsage: sage: (C.y^2).expansion_at_infty()
t^-6 + 2*t^-2 + 1 + 2*t^2 + t^4 + 2*t^6 + O(t^14)
[6nsage: sage: yy = C.y.expansion_at_infty(prec = 100)
[6nsage: xx = C.x.expansion_at_infty(prec = 100)
[6nsage: yy^2 - (xx^3 - xx + 1)
2*t^-2 + 1 + 2*t^4 + 2*t^6 + 2*t^8 + 2*t^10 + 2*t^12 + 2*t^14 + t^28 + t^30 + t^32 + 2*t^40 + 2*t^42 + 2*t^44 + 2*t^46 + 2*t^48 + 2*t^50 + t^52 + t^54 + t^56 + t^82 + t^84 + t^86 + 2*t^88 + 2*t^90 + 2*t^92 + O(t^94)
[6nsage: C = superelliptic(x^3 - x, 2)
[6nsage: xx = C.x.expansion_at_infty(prec = 100)
[6nsage: yy = C.y.expansion_at_infty(prec = 100)
[6nsage: xx
t^-2 + t^2 + 2*t^6 + 2*t^10 + t^14 + 2*t^18 + 2*t^34 + t^38 + 2*t^42 + 2*t^46 + t^50 + 2*t^54 + O(t^98)
[6nsage: yy
t^-3 + 2*t + 2*t^5 + 2*t^9 + t^13 + 2*t^17 + 2*t^33 + t^37 + 2*t^41 + 2*t^45 + t^49 + 2*t^53 + O(t^97)
[6nsage: 1/xx
t^2 + 2*t^6 + 2*t^10 + t^14 + 2*t^18 + 2*t^34 + t^38 + 2*t^42 + 2*t^46 + t^50 + 2*t^54 + O(t^102)
[6nsagesage: b = F(2)
[6nsage: b.nth_root(2)
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [152], in <cell line: 1>()
----> 1 b.nth_root(Integer(2))
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:1572, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.nth_root()
1570 else:
1571 return sign[0] * K(R.teichmuller(modp) * (plog // n).exp())
-> 1572 return self._nth_root_common(n, all, algorithm, cunningham)
1573
1574 def _nth_root_naive(self, n):
 
File /ext/sage/9.7/src/sage/rings/finite_rings/element_base.pyx:74, in sage.rings.finite_rings.element_base.FiniteRingElement._nth_root_common()
72 if n == 0:
73 if all: return []
---> 74 else: raise ValueError("no nth root")
75 gcd, alpha, beta = n.xgcd(q-1) # gcd = alpha*n + beta*(q-1), so 1/n = alpha/gcd (mod q-1)
76 if gcd == 1:
 
ValueError: no nth root
[6nsage: b.nth_root(3)
2
[6nsage: load('init.sage')
<string>:219: DeprecationWarning: invalid escape sequence '\s'
[6nsage: C = superelliptic(x^3 - x, 2)
[6nsasage: C.x.expansion_at_infty(prec = 100)
ww 1 + 2*t^4 + 2*t^8 + t^12 + 2*t^16 + 2*t^32 + t^36 + 2*t^40 + 2*t^44 + t^48 + 2*t^52 + O(t^100)
t^-2 + t^2 + 2*t^6 + 2*t^10 + t^14 + 2*t^18 + 2*t^34 + t^38 + 2*t^42 + 2*t^46 + t^50 + 2*t^54 + O(t^98)
[6nsage: C.uniformizer().expansion_at_infty(prec = 220)
a, b, delta, M, R 2 1 1 2 3
ww 1 + 2*t^4 + 2*t^8 + t^12 + 2*t^16 + 2*t^32 + t^36 + 2*t^40 + 2*t^44 + t^48 + 2*t^52 + 2*t^104 + t^108 + 2*t^112 + 2*t^116 + t^120 + 2*t^124 + 2*t^140 + t^144 + 2*t^148 + 2*t^152 + t^156 + 2*t^160 + O(t^220)
t + O(t^221)
[6nsage: load('init.sage')
<string>:219: DeprecationWarning: invalid escape sequence '\s'
[6nsage: C.x.expansion_at_infty(prec = 100)
ww 1 + 2*t^4 + 2*t^8 + t^12 + 2*t^16 + 2*t^32 + t^36 + 2*t^40 + 2*t^44 + t^48 + 2*t^52 + O(t^100)
t^-2 + t^2 + 2*t^6 + 2*t^10 + t^14 + 2*t^18 + 2*t^34 + t^38 + 2*t^42 + 2*t^46 + t^50 + 2*t^54 + O(t^98)
[6nsasage: load('init.sage')
<string>:219: DeprecationWarning: invalid escape sequence '\s'
[6nsage: C.uniformizer().expansion_at_infty(prec = 220)
a, b, delta, M, R 1 1 1 2 3
ww 1 + 2*t^4 + 2*t^8 + t^12 + 2*t^16 + 2*t^32 + t^36 + 2*t^40 + 2*t^44 + t^48 + 2*t^52 + 2*t^104 + t^108 + 2*t^112 + 2*t^116 + t^120 + 2*t^124 + 2*t^140 + t^144 + 2*t^148 + 2*t^152 + t^156 + 2*t^160 + O(t^220)
t + O(t^221)
[6nsage: ((C.uniformizer())^(-1)).expansion_at_infty(prec = 220)
a, b, delta, M, R 1 1 1 2 3
ww 1 + 2*t^4 + 2*t^8 + t^12 + 2*t^16 + 2*t^32 + t^36 + 2*t^40 + 2*t^44 + t^48 + 2*t^52 + 2*t^104 + t^108 + 2*t^112 + 2*t^116 + t^120 + 2*t^124 + 2*t^140 + t^144 + 2*t^148 + 2*t^152 + t^156 + 2*t^160 + O(t^220)
t^-1 + O(t^219)
[6nsage: load('init.sage')
<string>:218: DeprecationWarning: invalid escape sequence '\s'
[sage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
sage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^140+ C.x^13 + C.x^12 + C.x^11 - C.x^1
....: - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^C2*C.y - C.x^11*C.y + C.x^10*C.y -
....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx
[6nsage: decomposition_omega8_hpdh(om)
omega_analytic (T^14 + 2*T^4 + T^2 + 1)/T^18
expansions t^-18 + t^-16 + 2*t^-14 + t^-4 + 1 + t^2 + t^12 + 2*t^16 + t^18 + 2*t^28 + O(t^32)
1 + t^16 + t^48 + O(t^50)
t^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2 + 2 + 2*t^12 + 2*t^18 + t^30 + O(t^32)
omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2 + 2 + 2*t^12 + 2*t^18 + t^30 + O(t^32)
omega_analytic ((x^84 + x^83 - x^82 + x^77 - x^75 - x^74 - x^69 - x^66 + x^53 - x^45 + x^29 - x^21)/(x^72*y - y)) dx
omega8 ((-x^77 - x^76 + x^75 - x^74 + x^73 + x^72 - x^69 - x^67 + x^65 - x^61 + x^57 + x^56 - x^53 - x^51 + x^49 - x^48 - x^45 + x^43 + x^41 - x^37 + x^33 + x^32 - x^29 - x^27 + x^25 - x^24 - x^21 + x^19 + x^17 + x^13 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx
dh ((x^30 + x^28 + x^20 + x^12)/(x^24*y - y)) dx
omega8.expansion_at_infty() 2*t^-2 + 2 + t^2 + 2*t^4 + t^6 + t^8 + 2*t^16 + 2*t^18 + t^20 + 2*t^22 + 2*t^30 + 2*t^40 + t^46 + O(t^48)
(((-x^77 - x^76 + x^75 - x^74 + x^73 + x^72 - x^69 - x^67 + x^65 - x^61 + x^57 + x^56 - x^53 - x^51 + x^49 - x^48 - x^45 + x^43 + x^41 - x^37 + x^33 + x^32 - x^29 - x^27 + x^25 - x^24 - x^21 + x^19 + x^17 + x^13 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx,
((x^38 + 2*x^36 + x^30 + x^12)/(x^40 + x^32 + x^24 + 2*x^16 + 2*x^8 + 2))*y)
[6nsage: C.uniformizer().expansion_at_infty(prec = 220)
t + O(t^221)
[6nsage: ((C.uniformizer())^(-1)).expansion_at_infty(prec = 220)
t^-1 + O(t^219)
sage: om.expansion_at_infty(prec = 50)
t^-18 + t^-16 + 2*t^-14 + t^-4 + 1 + t^2 + 2*t^4 + t^6 + t^8 + 2*t^12 + 2*t^16 + t^18 + t^20 + 2*t^22 + O(t^32)
[6nsage: C.uniformizer().diffn().expansion_at_infty(prec = 220)
1 + O(t^220)
[6nsage: load('init.sage')
<string>:218: DeprecationWarning: invalid escape sequence '\s'
[6nsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
sage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^140+ C.x^13 + C.x^12 + C.x^11 - C.x^1
....: - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^C2*C.y - C.x^11*C.y + C.x^10*C.y -
....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx
[6nsage: decomposition_omega8_hpdh(om)
omega_analytic (T^14 + 2*T^4 + T^2 + 1)/T^18
expansions t^-18 + t^-16 + 2*t^-14 + t^-4 + O(t^32)
1 + O(t^50)
t^-18 + t^-16 + 2*t^-14 + t^-4 + O(t^32)
omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + O(t^32)
omega_analytic ((x^72 + x^71 - x^70 + x^65 - x^64 - x^62 - x^56 - x^55 - x^49 - x^48 + x^47 - x^46 - x^40 - x^38 - x^32 - x^31 - x^24 + x^23 - x^22 - x^16 - x^14 - x^8 - x^7 + 1)/(x^60*y)) dx
omega8 ((x^78 - x^76 - x^75 - x^74 + x^73 + x^72 - x^71 - x^69 - x^67 - x^66 + x^65 - x^64 + x^63 - x^60 + x^59 + x^58 - x^57 - x^56 + x^55 - x^54 + x^48 - x^47 + x^46 + x^45 - x^44 + x^43 - x^42 + x^41 - x^40 + x^39 - x^38 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 + x^21 - x^20 + x^19 - x^18 + x^17 - x^16 - x^15 - x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1)/(x^75*y - x^74*y + x^73*y - x^72*y + x^71*y - x^70*y + x^69*y - x^68*y - x^67*y + x^66*y - x^65*y + x^64*y - x^63*y + x^62*y - x^61*y + x^60*y)) dx
dh ((x^24 + x^22 - x^16 + x^14 - x^8 + 1)/(x^18*y)) dx
omega8.expansion_at_infty() 1 + t^2 + 2*t^4 + t^6 + t^8 + 2*t^12 + 2*t^16 + t^18 + t^20 + 2*t^22 + t^32 + 2*t^40 + t^48 + O(t^50)
(((x^78 - x^76 - x^75 - x^74 + x^73 + x^72 - x^71 - x^69 - x^67 - x^66 + x^65 - x^64 + x^63 - x^60 + x^59 + x^58 - x^57 - x^56 + x^55 - x^54 + x^48 - x^47 + x^46 + x^45 - x^44 + x^43 - x^42 + x^41 - x^40 + x^39 - x^38 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 + x^21 - x^20 + x^19 - x^18 + x^17 - x^16 - x^15 - x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1)/(x^75*y - x^74*y + x^73*y - x^72*y + x^71*y - x^70*y + x^69*y - x^68*y - x^67*y + x^66*y - x^65*y + x^64*y - x^63*y + x^62*y - x^61*y + x^60*y)) dx,
((x^32 + 2*x^30 + 2*x^24 + 2*x^14 + 2*x^8 + 1)/(x^34 + x^26 + x^18))*y)
[6nsage: om8, A = decomposition_omega8_hpdh(om)
omega_analytic (T^14 + 2*T^4 + T^2 + 1)/T^18
expansions t^-18 + t^-16 + 2*t^-14 + t^-4 + O(t^32)
1 + O(t^50)
t^-18 + t^-16 + 2*t^-14 + t^-4 + O(t^32)
omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + O(t^32)
omega_analytic ((x^72 + x^71 - x^70 + x^65 - x^64 - x^62 - x^56 - x^55 - x^49 - x^48 + x^47 - x^46 - x^40 - x^38 - x^32 - x^31 - x^24 + x^23 - x^22 - x^16 - x^14 - x^8 - x^7 + 1)/(x^60*y)) dx
omega8 ((x^78 - x^76 - x^75 - x^74 + x^73 + x^72 - x^71 - x^69 - x^67 - x^66 + x^65 - x^64 + x^63 - x^60 + x^59 + x^58 - x^57 - x^56 + x^55 - x^54 + x^48 - x^47 + x^46 + x^45 - x^44 + x^43 - x^42 + x^41 - x^40 + x^39 - x^38 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 + x^21 - x^20 + x^19 - x^18 + x^17 - x^16 - x^15 - x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1)/(x^75*y - x^74*y + x^73*y - x^72*y + x^71*y - x^70*y + x^69*y - x^68*y - x^67*y + x^66*y - x^65*y + x^64*y - x^63*y + x^62*y - x^61*y + x^60*y)) dx
dh ((x^24 + x^22 - x^16 + x^14 - x^8 + 1)/(x^18*y)) dx
omega8.expansion_at_infty() 1 + t^2 + 2*t^4 + t^6 + t^8 + 2*t^12 + 2*t^16 + t^18 + t^20 + 2*t^22 + t^32 + 2*t^40 + t^48 + O(t^50)
sage: om.cartier() == om8.cartier() + A.diffn()
True
sage: om8.is_regular_on_Uinfty()
True
sage: quit()
[23;0t~/Research/2021 De Rham/DeRhamComputation/sage$ cd ..
~/Research/2021 De Rham/DeRhamComputation$ git add asage/superelliptic_drw/superelliptic_drw_auxilliaries.sage
~/Research/2021 De Rham/DeRhamComputation$ git add -u
~/Research/2021 De Rham/DeRhamComputation$ git commit -[1Pm "naprawiony problem z uniformizatorem w superelliptic; decomposition_omega8_hpdh dziala"
[master 995d5f0] naprawiony problem z uniformizatorem w superelliptic; decomposition_omega8_hpdh dziala
7 files changed, 3618 insertions(+), 35 deletions(-)
create mode 100644 sage/superelliptic_drw/superelliptic_drw_auxilliaries.sage
~/Research/2021 De Rham/DeRhamComputation$ git push
Username for 'https://git.wmi.amu.edu.pl': jgarnek
Password for 'https://jgarnek@git.wmi.amu.edu.pl':
Enumerating objects: 22, done.
Counting objects: 100% (22/22), done.
Delta compression using up to 4 threads
Compressing objects: 100% (12/12), done.
Writing objects: 100% (12/12), 40.37 KiB | 359.00 KiB/s, done.
Total 12 (delta 10), reused 0 (delta 0)
remote: . Processing 1 references
remote: Processed 1 references in total
To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git
42ccc4d..995d5f0 master -> master
~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
[22;0t[6nsage: load('init.sage')
<string>:218: DeprecationWarning: invalid escape sequence '\s'
[6nsage: load('init.sage')
<string>:218: DeprecationWarning: invalid escape sequence '\s'
[6nsage: load('init.sage')
sage: load('superelliptic/tests/expansion_at_infty.sage')
True
sage: load('superelliptic/tests/expansion_at_infty.sage')
True
True True
[6nsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
sage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^140+ C.x^13 + C.x^12 + C.x^11 - C.x^1
....: - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^C2*C.y - C.x^11*C.y + C.x^10*C.y -
....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx
[6nsage: decomposition_omega8_hpdh(om)
omega_analytic (T^14 + 2*T^4 + T^2 + 1)/T^18
omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + O(t^32)
omega_analytic ((x^72 + x^71 - x^70 + x^65 - x^64 - x^62 - x^56 - x^55 - x^49 - x^48 + x^47 - x^46 - x^40 - x^38 - x^32 - x^31 - x^24 + x^23 - x^22 - x^16 - x^14 - x^8 - x^7 + 1)/(x^60*y)) dx
omega8 ((x^78 - x^76 - x^75 - x^74 + x^73 + x^72 - x^71 - x^69 - x^67 - x^66 + x^65 - x^64 + x^63 - x^60 + x^59 + x^58 - x^57 - x^56 + x^55 - x^54 + x^48 - x^47 + x^46 + x^45 - x^44 + x^43 - x^42 + x^41 - x^40 + x^39 - x^38 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 + x^21 - x^20 + x^19 - x^18 + x^17 - x^16 - x^15 - x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1)/(x^75*y - x^74*y + x^73*y - x^72*y + x^71*y - x^70*y + x^69*y - x^68*y - x^67*y + x^66*y - x^65*y + x^64*y - x^63*y + x^62*y - x^61*y + x^60*y)) dx
dh ((x^24 + x^22 - x^16 + x^14 - x^8 + 1)/(x^18*y)) dx
omega8.expansion_at_infty() 1 + t^2 + 2*t^4 + t^6 + t^8 + 2*t^12 + 2*t^16 + t^18 + t^20 + 2*t^22 + t^32 + 2*t^40 + t^48 + O(t^50)
(((x^78 - x^76 - x^75 - x^74 + x^73 + x^72 - x^71 - x^69 - x^67 - x^66 + x^65 - x^64 + x^63 - x^60 + x^59 + x^58 - x^57 - x^56 + x^55 - x^54 + x^48 - x^47 + x^46 + x^45 - x^44 + x^43 - x^42 + x^41 - x^40 + x^39 - x^38 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 + x^21 - x^20 + x^19 - x^18 + x^17 - x^16 - x^15 - x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1)/(x^75*y - x^74*y + x^73*y - x^72*y + x^71*y - x^70*y + x^69*y - x^68*y - x^67*y + x^66*y - x^65*y + x^64*y - x^63*y + x^62*y - x^61*y + x^60*y)) dx,
((x^32 + 2*x^30 + 2*x^24 + 2*x^14 + 2*x^8 + 1)/(x^34 + x^26 + x^18))*y)
sage: load('superelliptic_drw/tests/auxilliary_decompositions_test.sage')
omega_analytic (T^14 + 2*T^4 + T^2 + 1)/T^18
omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + O(t^32)
omega_analytic ((x^72 + x^71 - x^70 + x^65 - x^64 - x^62 - x^56 - x^55 - x^49 - x^48 + x^47 - x^46 - x^40 - x^38 - x^32 - x^31 - x^24 + x^23 - x^22 - x^16 - x^14 - x^8 - x^7 + 1)/(x^60*y)) dx
omega8 ((x^78 - x^76 - x^75 - x^74 + x^73 + x^72 - x^71 - x^69 - x^67 - x^66 + x^65 - x^64 + x^63 - x^60 + x^59 + x^58 - x^57 - x^56 + x^55 - x^54 + x^48 - x^47 + x^46 + x^45 - x^44 + x^43 - x^42 + x^41 - x^40 + x^39 - x^38 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 + x^21 - x^20 + x^19 - x^18 + x^17 - x^16 - x^15 - x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1)/(x^75*y - x^74*y + x^73*y - x^72*y + x^71*y - x^70*y + x^69*y - x^68*y - x^67*y + x^66*y - x^65*y + x^64*y - x^63*y + x^62*y - x^61*y + x^60*y)) dx
dh ((x^24 + x^22 - x^16 + x^14 - x^8 + 1)/(x^18*y)) dx
omega8.expansion_at_infty() 1 + t^2 + 2*t^4 + t^6 + t^8 + 2*t^12 + 2*t^16 + t^18 + t^20 + 2*t^22 + t^32 + 2*t^40 + t^48 + O(t^50)
True
True True
[6nsage: load('superelliptic_drw/tests/auxilliary_decompositions_test.sage')
omega_analytic (T^14 + 2*T^4 + T^2 + 1)/T^18
omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + O(t^32)
omega_analytic ((x^72 + x^71 - x^70 + x^65 - x^64 - x^62 - x^56 - x^55 - x^49 - x^48 + x^47 - x^46 - x^40 - x^38 - x^32 - x^31 - x^24 + x^23 - x^22 - x^16 - x^14 - x^8 - x^7 + 1)/(x^60*y)) dx
omega8 ((x^78 - x^76 - x^75 - x^74 + x^73 + x^72 - x^71 - x^69 - x^67 - x^66 + x^65 - x^64 + x^63 - x^60 + x^59 + x^58 - x^57 - x^56 + x^55 - x^54 + x^48 - x^47 + x^46 + x^45 - x^44 + x^43 - x^42 + x^41 - x^40 + x^39 - x^38 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 + x^21 - x^20 + x^19 - x^18 + x^17 - x^16 - x^15 - x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1)/(x^75*y - x^74*y + x^73*y - x^72*y + x^71*y - x^70*y + x^69*y - x^68*y - x^67*y + x^66*y - x^65*y + x^64*y - x^63*y + x^62*y - x^61*y + x^60*y)) dx
dh ((x^24 + x^22 - x^16 + x^14 - x^8 + 1)/(x^18*y)) dx
omega8.expansion_at_infty() 1 + t^2 + 2*t^4 + t^6 + t^8 + 2*t^12 + 2*t^16 + t^18 + t^20 + 2*t^22 + t^32 + 2*t^40 + t^48 + O(t^50)
True
True True
True True
~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
[22;0t[6nsage: load('init.sage')
[6nsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
[6nsage: B = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)
omega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(2*x^5/(x^8 + 2))*y] d[x] + V(((-x^27 - x^19)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]) 0
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift 0 [(1/(x^12 + 2*x^4))*y] d[x] + V(((x^8 + 1)/(x^24*y - x^16*y)) dx) + dV([(1/(x^32 + 2*x^24))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^3/(x^8 + 2))*y] d[x] + V(((-x^29 - x^21 + x^13)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]) [(2/(x^13 + 2*x^5))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^35*y - x^27*y)) dx) + dV([(2/(x^35 + 2*x^27))*y])
result.omega8 == compare True
result.omega8 - compare 0
(1, 1, 0, 2, 1, 2, 1, 2)
omega_analytic (T^14 + 2*T^4 + T^2 + 1)/T^18
omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + O(t^32)
omega_analytic ((x^72 + x^71 - x^70 + x^65 - x^64 - x^62 - x^56 - x^55 - x^49 - x^48 + x^47 - x^46 - x^40 - x^38 - x^32 - x^31 - x^24 + x^23 - x^22 - x^16 - x^14 - x^8 - x^7 + 1)/(x^60*y)) dx
omega8 ((x^78 - x^76 - x^75 - x^74 + x^73 + x^72 - x^71 - x^69 - x^67 - x^66 + x^65 - x^64 + x^63 - x^60 + x^59 + x^58 - x^57 - x^56 + x^55 - x^54 + x^48 - x^47 + x^46 + x^45 - x^44 + x^43 - x^42 + x^41 - x^40 + x^39 - x^38 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 + x^21 - x^20 + x^19 - x^18 + x^17 - x^16 - x^15 - x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1)/(x^75*y - x^74*y + x^73*y - x^72*y + x^71*y - x^70*y + x^69*y - x^68*y - x^67*y + x^66*y - x^65*y + x^64*y - x^63*y + x^62*y - x^61*y + x^60*y)) dx
dh ((x^24 + x^22 - x^16 + x^14 - x^8 + 1)/(x^18*y)) dx
omega8.expansion_at_infty() 1 + t^2 + 2*t^4 + t^6 + t^8 + 2*t^12 + 2*t^16 + t^18 + t^20 + 2*t^22 + t^32 + 2*t^40 + t^48 + O(t^50)
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [3], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(4)]).coordinates(basis=B)
 
File <string>:103, in coordinates(self, basis)
 
File <string>:85, in div_by_p(self)
 
NameError: name 'decomposition_g8_p2th_power' is not defined
[6nsage: load('init.sage')
[6nsage: B = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)
^Csage/rings/polynomial/polynomial_zmod_flint.pyx:7: DeprecationWarning: invalid escape sequence '\Z'
"""
sage/rings/polynomial/polynomial_zmod_flint.pyx:7: DeprecationWarning: invalid escape sequence '\Z'
"""
---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
File <string>:59, in __mul__(self, other)
 
File <string>:235, in reduction(C, g)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
286 cdef Map m
--> 287 cdef Element e = method(C)
288 if e is None:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:198, in sage.rings.polynomial.multi_polynomial.MPolynomial._polynomial_()
197 if var in self._parent.variable_names():
--> 198 return R(self.polynomial(self._parent(var)))
199 else:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:419, in sage.rings.polynomial.multi_polynomial.MPolynomial.polynomial()
418 for e, val in self.dict().iteritems() if not e[ind]}
--> 419 v = [B(w)] # coefficients that don't involve var
420 z = var
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:469, in PolynomialRing_general._element_constructor_(self, x, check, is_gen, construct, **kwds)
468 x = x.truncate()
--> 469 return C(self, x, check, is_gen, construct=construct, **kwds)
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zmod_flint.pyx:129, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint.__init__()
128 pass
--> 129 Polynomial_template.__init__(self, parent, x, check, is_gen, construct)
130
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_template.pxi:157, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_template.__init__()
156 for deg, coef in x.iteritems():
--> 157 celement_pow(monomial, gen, deg, NULL, (<Polynomial_template>self)._cparent)
158 celement_mul(monomial, &(<Polynomial_template>self.__class__(parent, coef)).x, monomial, (<Polynomial_template>self)._cparent)
 
File /ext/sage/9.7/src/sage/libs/flint/nmod_poly_linkage.pxi:547, in sage.rings.polynomial.polynomial_zmod_flint.celement_pow()
546 else:
--> 547 sig_on()
548 nmod_poly_pow(res, x, e)
 
KeyboardInterrupt:
 
During handling of the above exception, another exception occurred:
 
AttributeError Traceback (most recent call last)
Input In [5], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(4)]).coordinates(basis=B)
 
File <string>:53, in crystalline_cohomology_basis(self, prec)
 
File <string>:25, in de_rham_witt_lift(cech_class, prec)
 
File <string>:15, in de_rham_witt_lift_form8(omega)
 
File <string>:73, in diffn(self, dy_w)
 
File <string>:177, in dy_w(C)
 
File <string>:149, in auxilliary_derivative(P)
 
File <string>:55, in __rmul__(self, other)
 
File <string>:84, in __add__(self, other)
 
File <string>:31, in __add__(self, other)
 
File <string>:63, in __mul__(self, other)
 
AttributeError: 'superelliptic_function' object has no attribute 'form'
[6nsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
[6nsage: B = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [7], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(4)]).coordinates(basis=B)
 
File <string>:52, in crystalline_cohomology_basis(self, prec)
 
File <string>:98, in de_rham_basis(self)
 
File <string>:80, in basis_de_rham_degrees(self)
 
File <string>:5, in __init__(self, C, omega, fct)
 
File <string>:95, in diffn(self)
 
File <string>:7, in __init__(self, C, g)
 
File <string>:257, in reduction_form(C, g)
 
File <string>:236, in reduction(C, g)
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2321, in sage.rings.polynomial.polynomial_element.Polynomial.__truediv__()
2319 # Same parents => bypass coercion
2320 if have_same_parent(left, right):
-> 2321 return (<Element>left)._div_(right)
2322
2323 # Try division of polynomial by a scalar
 
File /ext/sage/9.7/src/sage/structure/element.pyx:2739, in sage.structure.element.RingElement._div_()
2737 except AttributeError:
2738 raise bin_op_exception('/', self, other)
-> 2739 return frac(self, other)
2740
2741 def __divmod__(self, other):
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:899, in sage.structure.parent.Parent.__call__()
897 return mor._call_(x)
898 else:
--> 899 return mor._call_with_args(x, args, kwds)
900
901 raise TypeError(_LazyString("No conversion defined from %s to %s", (R, self), {}))
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:173, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args()
171 else:
172 if len(kwds) == 0:
--> 173 return C._element_constructor(x, *args)
174 else:
175 return C._element_constructor(x, *args, **kwds)
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:648, in FractionField_generic._element_constructor_(self, x, y, coerce)
646 x, y = x.numerator() * y.denominator(), y.numerator() * x.denominator()
647 try:
--> 648 return self._element_class(self, x, y, coerce=coerce)
649 except (TypeError, ValueError):
650 pass
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:1167, in sage.rings.fraction_field_element.FractionFieldElement_1poly_field.__init__()
1165 1/2/x
1166 """
-> 1167 FractionFieldElement.__init__(self, parent, numerator, denominator,
1168 coerce, reduce)
1169 if not reduce:
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:121, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
119 if reduce and parent.is_exact():
120 try:
--> 121 self.reduce()
122 except ArithmeticError:
123 pass
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:1239, in sage.rings.fraction_field_element.FractionFieldElement_1poly_field.reduce()
1237 if self._is_reduced:
1238 return
-> 1239 super(self.__class__, self).reduce()
1240 self.normalize_leading_coefficients()
1241
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:164, in sage.rings.fraction_field_element.FractionFieldElement.reduce()
162 return codomain.coerce(nnum/nden)
163
--> 164 cpdef reduce(self):
165 """
166 Reduce this fraction.
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:198, in sage.rings.fraction_field_element.FractionFieldElement.reduce()
196 try:
197 g = self.__numerator.gcd(self.__denominator)
--> 198 if not g.is_unit():
199 self.__numerator //= g
200 self.__denominator //= g
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element_generic.py:1021, in Polynomial_generic_domain.is_unit(self)
1019 if self.degree() > 0:
1020 return False
-> 1021 return self[0].is_unit()
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
[6nsage: B = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)
omega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(2*x^5/(x^8 + 2))*y] d[x] + V(((-x^27 - x^19)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]) 0
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift 0 [(1/(x^12 + 2*x^4))*y] d[x] + V(((x^8 + 1)/(x^24*y - x^16*y)) dx) + dV([(1/(x^32 + 2*x^24))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^3/(x^8 + 2))*y] d[x] + V(((-x^29 - x^21 + x^13)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]) [(2/(x^13 + 2*x^5))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^35*y - x^27*y)) dx) + dV([(2/(x^35 + 2*x^27))*y])
result.omega8 == compare True
result.omega8 - compare 0
(1, 1, 0, 2, 1, 2, 1, 2)
omega_analytic (T^14 + 2*T^4 + T^2 + 1)/T^18
omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + O(t^32)
omega_analytic ((x^72 + x^71 - x^70 + x^65 - x^64 - x^62 - x^56 - x^55 - x^49 - x^48 + x^47 - x^46 - x^40 - x^38 - x^32 - x^31 - x^24 + x^23 - x^22 - x^16 - x^14 - x^8 - x^7 + 1)/(x^60*y)) dx
omega8 ((x^78 - x^76 - x^75 - x^74 + x^73 + x^72 - x^71 - x^69 - x^67 - x^66 + x^65 - x^64 + x^63 - x^60 + x^59 + x^58 - x^57 - x^56 + x^55 - x^54 + x^48 - x^47 + x^46 + x^45 - x^44 + x^43 - x^42 + x^41 - x^40 + x^39 - x^38 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 + x^21 - x^20 + x^19 - x^18 + x^17 - x^16 - x^15 - x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1)/(x^75*y - x^74*y + x^73*y - x^72*y + x^71*y - x^70*y + x^69*y - x^68*y - x^67*y + x^66*y - x^65*y + x^64*y - x^63*y + x^62*y - x^61*y + x^60*y)) dx
dh ((x^24 + x^22 - x^16 + x^14 - x^8 + 1)/(x^18*y)) dx
omega8.expansion_at_infty() 1 + t^2 + 2*t^4 + t^6 + t^8 + 2*t^12 + 2*t^16 + t^18 + t^20 + 2*t^22 + t^32 + 2*t^40 + t^48 + O(t^50)
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [9], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(4)]).coordinates(basis=B)
 
File <string>:103, in coordinates(self, basis)
 
File <string>:85, in div_by_p(self)
 
File <string>:52, in decomposition_g8_p2th_power(fct)
 
NameError: name 'decomposition_g8_pth_power' is not defined
[6nsage: load('init.sage')
[6nsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
[6nsage: B = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)
omega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(2*x^5/(x^8 + 2))*y] d[x] + V(((-x^27 - x^19)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]) 0
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift 0 [(1/(x^12 + 2*x^4))*y] d[x] + V(((x^8 + 1)/(x^24*y - x^16*y)) dx) + dV([(1/(x^32 + 2*x^24))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^3/(x^8 + 2))*y] d[x] + V(((-x^29 - x^21 + x^13)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]) [(2/(x^13 + 2*x^5))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^35*y - x^27*y)) dx) + dV([(2/(x^35 + 2*x^27))*y])
result.omega8 == compare True
result.omega8 - compare 0
(1, 1, 0, 2, 1, 2, 1, 2)
omega_analytic (T^14 + 2*T^4 + T^2 + 1)/T^18
omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + O(t^32)
omega_analytic ((x^72 + x^71 - x^70 + x^65 - x^64 - x^62 - x^56 - x^55 - x^49 - x^48 + x^47 - x^46 - x^40 - x^38 - x^32 - x^31 - x^24 + x^23 - x^22 - x^16 - x^14 - x^8 - x^7 + 1)/(x^60*y)) dx
omega8 ((x^78 - x^76 - x^75 - x^74 + x^73 + x^72 - x^71 - x^69 - x^67 - x^66 + x^65 - x^64 + x^63 - x^60 + x^59 + x^58 - x^57 - x^56 + x^55 - x^54 + x^48 - x^47 + x^46 + x^45 - x^44 + x^43 - x^42 + x^41 - x^40 + x^39 - x^38 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 + x^21 - x^20 + x^19 - x^18 + x^17 - x^16 - x^15 - x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1)/(x^75*y - x^74*y + x^73*y - x^72*y + x^71*y - x^70*y + x^69*y - x^68*y - x^67*y + x^66*y - x^65*y + x^64*y - x^63*y + x^62*y - x^61*y + x^60*y)) dx
dh ((x^24 + x^22 - x^16 + x^14 - x^8 + 1)/(x^18*y)) dx
omega8.expansion_at_infty() 1 + t^2 + 2*t^4 + t^6 + t^8 + 2*t^12 + 2*t^16 + t^18 + t^20 + 2*t^22 + t^32 + 2*t^40 + t^48 + O(t^50)
---------------------------------------------------------------------------
ArithmeticError Traceback (most recent call last)
Input In [12], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(4)]).coordinates(basis=B)
 
File <string>:103, in coordinates(self, basis)
 
File <string>:85, in div_by_p(self)
 
File <string>:67, in decomposition_g8_p2th_power(fct)
 
File <string>:60, in decomposition_g8_pth_power(fct, prec)
 
File <string>:14, in __init__(self, C, g)
 
File <string>:228, in reduction(C, g)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
159 print(type(C), C)
160 print(type(C._element_constructor), C._element_constructor)
--> 161 raise
162
163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
636 ring_one = self.ring().one()
637 try:
--> 638 return self._element_class(self, x, ring_one, coerce=coerce)
639 except (TypeError, ValueError):
640 pass
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
112 FieldElement.__init__(self, parent)
113 if coerce:
--> 114 self.__numerator = parent.ring()(numerator)
115 self.__denominator = parent.ring()(denominator)
116 else:
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
159 print(type(C), C)
160 print(type(C._element_constructor), C._element_constructor)
--> 161 raise
162
163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
1001
1002 try:
-> 1003 return self(str(element))
1004 except TypeError:
1005 pass
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
159 print(type(C), C)
160 print(type(C._element_constructor), C._element_constructor)
--> 161 raise
162
163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:988, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
986 try:
987 if '/' in element:
--> 988 element = sage_eval(element,d)
989 else:
990 element = element.replace("^","**")
 
File /ext/sage/9.7/src/sage/misc/sage_eval.py:198, in sage_eval(source, locals, cmds, preparse)
196 return locals['_sage_eval_returnval_']
197 else:
--> 198 return eval(source, sage.all.__dict__, locals)
 
File <string>:1, in <module>
 
File /ext/sage/9.7/src/sage/rings/big_oh.py:166, in O(*x, **kwds)
164 elif hasattr(x, 'O'):
165 return x.O(**kwds)
--> 166 raise ArithmeticError("O(%s) not defined" % (x,))
 
ArithmeticError: O(y^53) not defined
[6nsage: load('init.sage')
[6nsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
[6nsage: B = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)
omega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(2*x^5/(x^8 + 2))*y] d[x] + V(((-x^27 - x^19)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]) 0
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift 0 [(1/(x^12 + 2*x^4))*y] d[x] + V(((x^8 + 1)/(x^24*y - x^16*y)) dx) + dV([(1/(x^32 + 2*x^24))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^3/(x^8 + 2))*y] d[x] + V(((-x^29 - x^21 + x^13)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]) [(2/(x^13 + 2*x^5))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^35*y - x^27*y)) dx) + dV([(2/(x^35 + 2*x^27))*y])
result.omega8 == compare True
result.omega8 - compare 0
(1, 1, 0, 2, 1, 2, 1, 2)
decomposition_omega8_hpdh ((x^28 - x^26 + x^25 - x^24 + x^23 - x^22 - x^21 + x^20 + x^19 + x^18 + x^17 + x^15 - x^14 + x^13 + x^12 + x^11 - x^10 - x^8 - x^7 + x^6 - x^5 + x^4 + x^2 + x - 1)/(x^16*y - x^15*y + x^14*y - x^13*y + x^12*y - x^11*y + x^10*y - x^9*y - x^8*y + x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y)) dx
omega_analytic (T^14 + 2*T^4 + T^2 + 1)/T^18
omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + O(t^32)
omega_analytic ((x^72 + x^71 - x^70 + x^65 - x^64 - x^62 - x^56 - x^55 - x^49 - x^48 + x^47 - x^46 - x^40 - x^38 - x^32 - x^31 - x^24 + x^23 - x^22 - x^16 - x^14 - x^8 - x^7 + 1)/(x^60*y)) dx
omega8 ((x^78 - x^76 - x^75 - x^74 + x^73 + x^72 - x^71 - x^69 - x^67 - x^66 + x^65 - x^64 + x^63 - x^60 + x^59 + x^58 - x^57 - x^56 + x^55 - x^54 + x^48 - x^47 + x^46 + x^45 - x^44 + x^43 - x^42 + x^41 - x^40 + x^39 - x^38 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 + x^21 - x^20 + x^19 - x^18 + x^17 - x^16 - x^15 - x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1)/(x^75*y - x^74*y + x^73*y - x^72*y + x^71*y - x^70*y + x^69*y - x^68*y - x^67*y + x^66*y - x^65*y + x^64*y - x^63*y + x^62*y - x^61*y + x^60*y)) dx
dh ((x^24 + x^22 - x^16 + x^14 - x^8 + 1)/(x^18*y)) dx
omega8.expansion_at_infty() 1 + t^2 + 2*t^4 + t^6 + t^8 + 2*t^12 + 2*t^16 + t^18 + t^20 + 2*t^22 + t^32 + 2*t^40 + t^48 + O(t^50)
decomposition_g8_p2th_power ((2*x^87 + 2*x^84 + x^83 + x^82 + x^81 + x^80 + 2*x^78 + 2*x^77 + x^76 + 2*x^75 + 2*x^74 + x^73 + x^72 + 2*x^71 + 2*x^70 + 2*x^68 + 2*x^67 + x^63 + x^60 + 2*x^59 + 2*x^58 + 2*x^57 + 2*x^56 + x^54 + x^53 + 2*x^52 + x^51 + x^50 + 2*x^49 + 2*x^48 + x^47 + x^46 + x^44 + x^43 + x^42 + 2*x^24 + 1)/(x^93 + x^85 + x^77 + 2*x^69 + 2*x^61 + 2*x^53))*y
decomposition_g8_pth_power ((2*x^87 + 2*x^84 + x^83 + x^82 + x^81 + x^80 + 2*x^78 + 2*x^77 + x^76 + 2*x^75 + 2*x^74 + x^73 + x^72 + 2*x^71 + 2*x^70 + 2*x^68 + 2*x^67 + x^63 + x^60 + 2*x^59 + 2*x^58 + 2*x^57 + 2*x^56 + x^54 + x^53 + 2*x^52 + x^51 + x^50 + 2*x^49 + 2*x^48 + x^47 + x^46 + x^44 + x^43 + x^42 + 2*x^24 + 1)/(x^93 + x^85 + x^77 + 2*x^69 + 2*x^61 + 2*x^53))*y
---------------------------------------------------------------------------
ArithmeticError Traceback (most recent call last)
Input In [15], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(4)]).coordinates(basis=B)
 
File <string>:103, in coordinates(self, basis)
 
File <string>:85, in div_by_p(self)
 
File <string>:70, in decomposition_g8_p2th_power(fct)
 
File <string>:62, in decomposition_g8_pth_power(fct, prec)
 
File <string>:14, in __init__(self, C, g)
 
File <string>:228, in reduction(C, g)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
159 print(type(C), C)
160 print(type(C._element_constructor), C._element_constructor)
--> 161 raise
162
163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
636 ring_one = self.ring().one()
637 try:
--> 638 return self._element_class(self, x, ring_one, coerce=coerce)
639 except (TypeError, ValueError):
640 pass
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
112 FieldElement.__init__(self, parent)
113 if coerce:
--> 114 self.__numerator = parent.ring()(numerator)
115 self.__denominator = parent.ring()(denominator)
116 else:
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
159 print(type(C), C)
160 print(type(C._element_constructor), C._element_constructor)
--> 161 raise
162
163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
1001
1002 try:
-> 1003 return self(str(element))
1004 except TypeError:
1005 pass
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
159 print(type(C), C)
160 print(type(C._element_constructor), C._element_constructor)
--> 161 raise
162
163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:988, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
986 try:
987 if '/' in element:
--> 988 element = sage_eval(element,d)
989 else:
990 element = element.replace("^","**")
 
File /ext/sage/9.7/src/sage/misc/sage_eval.py:198, in sage_eval(source, locals, cmds, preparse)
196 return locals['_sage_eval_returnval_']
197 else:
--> 198 return eval(source, sage.all.__dict__, locals)
 
File <string>:1, in <module>
 
File /ext/sage/9.7/src/sage/rings/big_oh.py:166, in O(*x, **kwds)
164 elif hasattr(x, 'O'):
165 return x.O(**kwds)
--> 166 raise ArithmeticError("O(%s) not defined" % (x,))
 
ArithmeticError: O(y^53) not defined
sage: ff = ((2*C.x^87 + 2*C.x^84 + C.x^83 + C.x^82 + C.x^81 + C.x^80 + 2*C.x^78 + 2*C.x^77 + C.x^76 + 2*C.x^75 + 2*C.x^74 + C.x+73 + C.x^72 + 2*C.x^71 + 2*C.x^70
....: 2*C.x^68 + 2*C.x^67 + C.x^63 + C.x^60 + 2*C.x^59 + 2*C.x^58 + 2*C.x^57 + 2*C.x^56 + C.x^54 + C.x^53 + 2*C.x^52 + C.x^51 x C.x^50 + 2*C.x^49 + 2*C.x^48 + C.
....: ^47 + C.x^46 + C.x^44 + C.x^43 + C.x^42 + 2*C.x^24 + 1)/(C.x^93 + C.x^85 + C.x^77 + 2*C.x^69 + 2*C.x^61 + 2*C.x^53))*C.y
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [16], in <cell line: 1>()
----> 1 ff = ((Integer(2)*C.x**Integer(87) + Integer(2)*C.x**Integer(84) + C.x**Integer(83) + C.x**Integer(82) + C.x**Integer(81) + C.x**Integer(80) + Integer(2)*C.x**Integer(78) + Integer(2)*C.x**Integer(77) + C.x**Integer(76) + Integer(2)*C.x**Integer(75) + Integer(2)*C.x**Integer(74) + C.x**Integer(73) + C.x**Integer(72) + Integer(2)*C.x**Integer(71) + Integer(2)*C.x**Integer(70) + Integer(2)*C.x**Integer(68) + Integer(2)*C.x**Integer(67) + C.x**Integer(63) + C.x**Integer(60) + Integer(2)*C.x**Integer(59) + Integer(2)*C.x**Integer(58) + Integer(2)*C.x**Integer(57) + Integer(2)*C.x**Integer(56) + C.x**Integer(54) + C.x**Integer(53) + Integer(2)*C.x**Integer(52) + C.x**Integer(51) + C.x**Integer(50) + Integer(2)*C.x**Integer(49) + Integer(2)*C.x**Integer(48) + C.x**Integer(47) + C.x**Integer(46) + C.x**Integer(44) + C.x**Integer(43) + C.x**Integer(42) + Integer(2)*C.x**Integer(24) + Integer(1))/(C.x**Integer(93) + C.x**Integer(85) + C.x**Integer(77) + Integer(2)*C.x**Integer(69) + Integer(2)*C.x**Integer(61) + Integer(2)*C.x**Integer(53)))*C.y
 
File <string>:38, in __add__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
493 """
--> 494 return self.getattr_from_category(name)
495
496 cdef getattr_from_category(self, name):
 
File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
505 else:
506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
508
509 def __dir__(self):
 
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
359 dummy_error_message.cls = type(self)
360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
362 attribute = <object>attr
363 # Check for a descriptor (__get__ in Python)
 
AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function'
sage: ff = ((2*C.x^87 + 2*C.x^84 + C.x^83 + C.x^82 + C.x^81 + C.x^80 + 2*C.x^78 + 2*C.x^77 + C.x^76 + 2*C.x^75 + 2*C.x^74 + C.x+73 + C.x^72 + 2*C.x^71 + 2*C.x^70
....: 2*C.x^68 + 2*C.x^67 + C.x^63 + C.x^60 + 2*C.x^59 + 2*C.x^58 + 2*C.x^57 + 2*C.x^56 + C.x^54 + C.x^53 + 2*C.x^52 + C.x^51 x C.x^50 + 2*C.x^49 + 2*C.x^48 + C.
....: ^47 + C.x^46 + C.x^44 + C.x^43 + C.x^42 + 2*C.x^24 + C.one)/(C.x^93 + C.x^85 + C.x^77 + 2*C.x^69 + 2*C.x^61 + 2*C.x^53))*C.y
sage: decomposition_g8_pth_power(ff)
decomposition_g8_pth_power ((2*x^87 + 2*x^84 + x^83 + x^82 + x^81 + x^80 + 2*x^78 + 2*x^77 + x^76 + 2*x^75 + 2*x^74 + x^73 + x^72 + 2*x^71 + 2*x^70 + 2*x^68 + 2*x^67 + x^63 + x^60 + 2*x^59 + 2*x^58 + 2*x^57 + 2*x^56 + x^54 + x^53 + 2*x^52 + x^51 + x^50 + 2*x^49 + 2*x^48 + x^47 + x^46 + x^44 + x^43 + x^42 + 2*x^24 + 1)/(x^93 + x^85 + x^77 + 2*x^69 + 2*x^61 + 2*x^53))*y
---------------------------------------------------------------------------
ArithmeticError Traceback (most recent call last)
Input In [18], in <cell line: 1>()
----> 1 decomposition_g8_pth_power(ff)
 
File <string>:62, in decomposition_g8_pth_power(fct, prec)
 
File <string>:14, in __init__(self, C, g)
 
File <string>:228, in reduction(C, g)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
159 print(type(C), C)
160 print(type(C._element_constructor), C._element_constructor)
--> 161 raise
162
163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
636 ring_one = self.ring().one()
637 try:
--> 638 return self._element_class(self, x, ring_one, coerce=coerce)
639 except (TypeError, ValueError):
640 pass
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
112 FieldElement.__init__(self, parent)
113 if coerce:
--> 114 self.__numerator = parent.ring()(numerator)
115 self.__denominator = parent.ring()(denominator)
116 else:
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
159 print(type(C), C)
160 print(type(C._element_constructor), C._element_constructor)
--> 161 raise
162
163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
1001
1002 try:
-> 1003 return self(str(element))
1004 except TypeError:
1005 pass
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
159 print(type(C), C)
160 print(type(C._element_constructor), C._element_constructor)
--> 161 raise
162
163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:988, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
986 try:
987 if '/' in element:
--> 988 element = sage_eval(element,d)
989 else:
990 element = element.replace("^","**")
 
File /ext/sage/9.7/src/sage/misc/sage_eval.py:198, in sage_eval(source, locals, cmds, preparse)
196 return locals['_sage_eval_returnval_']
197 else:
--> 198 return eval(source, sage.all.__dict__, locals)
 
File <string>:1, in <module>
 
File /ext/sage/9.7/src/sage/rings/big_oh.py:166, in O(*x, **kwds)
164 elif hasattr(x, 'O'):
165 return x.O(**kwds)
--> 166 raise ArithmeticError("O(%s) not defined" % (x,))
 
ArithmeticError: O(y^53) not defined
[6nsage: decomposition_g8_pth_power(ff, prec = 200)
decomposition_g8_pth_power ((2*x^87 + 2*x^84 + x^83 + x^82 + x^81 + x^80 + 2*x^78 + 2*x^77 + x^76 + 2*x^75 + 2*x^74 + x^73 + x^72 + 2*x^71 + 2*x^70 + 2*x^68 + 2*x^67 + x^63 + x^60 + 2*x^59 + 2*x^58 + 2*x^57 + 2*x^56 + x^54 + x^53 + 2*x^52 + x^51 + x^50 + 2*x^49 + 2*x^48 + x^47 + x^46 + x^44 + x^43 + x^42 + 2*x^24 + 1)/(x^93 + x^85 + x^77 + 2*x^69 + 2*x^61 + 2*x^53))*y
---------------------------------------------------------------------------
ArithmeticError Traceback (most recent call last)
Input In [19], in <cell line: 1>()
----> 1 decomposition_g8_pth_power(ff, prec = Integer(200))
 
File <string>:62, in decomposition_g8_pth_power(fct, prec)
 
File <string>:14, in __init__(self, C, g)
 
File <string>:228, in reduction(C, g)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
159 print(type(C), C)
160 print(type(C._element_constructor), C._element_constructor)
--> 161 raise
162
163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
636 ring_one = self.ring().one()
637 try:
--> 638 return self._element_class(self, x, ring_one, coerce=coerce)
639 except (TypeError, ValueError):
640 pass
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
112 FieldElement.__init__(self, parent)
113 if coerce:
--> 114 self.__numerator = parent.ring()(numerator)
115 self.__denominator = parent.ring()(denominator)
116 else:
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
159 print(type(C), C)
160 print(type(C._element_constructor), C._element_constructor)
--> 161 raise
162
163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
1001
1002 try:
-> 1003 return self(str(element))
1004 except TypeError:
1005 pass
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
159 print(type(C), C)
160 print(type(C._element_constructor), C._element_constructor)
--> 161 raise
162
163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:988, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
986 try:
987 if '/' in element:
--> 988 element = sage_eval(element,d)
989 else:
990 element = element.replace("^","**")
 
File /ext/sage/9.7/src/sage/misc/sage_eval.py:198, in sage_eval(source, locals, cmds, preparse)
196 return locals['_sage_eval_returnval_']
197 else:
--> 198 return eval(source, sage.all.__dict__, locals)
 
File <string>:1, in <module>
 
File /ext/sage/9.7/src/sage/rings/big_oh.py:166, in O(*x, **kwds)
164 elif hasattr(x, 'O'):
165 return x.O(**kwds)
--> 166 raise ArithmeticError("O(%s) not defined" % (x,))
 
ArithmeticError: O(y^203) not defined
sage: ff.expansion_at_infty()
2*t^3 + 2*t^9 + t^11 + t^13 + t^15 + t^17 + 2*t^21 + O(t^23)
[6nsage: laurent_analytic_part(ff.expansion_at_infty())
0
[6nsage: laurent_analytic_part(ff.expansion_at_infty())
0
sage: load('superelliptic_drw/superelliptic_drw_auxilliaries.sage')
sage: decomposition_g8_pth_power(ff)
decomposition_g8_pth_power ((2*x^87 + 2*x^84 + x^83 + x^82 + x^81 + x^80 + 2*x^78 + 2*x^77 + x^76 + 2*x^75 + 2*x^74 + x^73 + x^72 + 2*x^71 + 2*x^70 + 2*x^68 + 2*x^67 + x^63 + x^60 + 2*x^59 + 2*x^58 + 2*x^57 + 2*x^56 + x^54 + x^53 + 2*x^52 + x^51 + x^50 + 2*x^49 + 2*x^48 + x^47 + x^46 + x^44 + x^43 + x^42 + 2*x^24 + 1)/(x^93 + x^85 + x^77 + 2*x^69 + 2*x^61 + 2*x^53))*y
(((2*x^87 + 2*x^84 + x^83 + x^82 + x^81 + x^80 + 2*x^78 + 2*x^77 + x^76 + 2*x^75 + 2*x^74 + x^73 + x^72 + 2*x^71 + 2*x^70 + 2*x^68 + 2*x^67 + x^63 + x^60 + 2*x^59 + 2*x^58 + 2*x^57 + 2*x^56 + x^54 + x^53 + 2*x^52 + x^51 + x^50 + 2*x^49 + 2*x^48 + x^47 + x^46 + x^44 + x^43 + x^42 + 2*x^24 + 1)/(x^93 + x^85 + x^77 + 2*x^69 + 2*x^61 + 2*x^53))*y,
0)
[6nsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
sage: B = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)
omega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(2*x^5/(x^8 + 2))*y] d[x] + V(((-x^27 - x^19)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]) 0
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift 0 [(1/(x^12 + 2*x^4))*y] d[x] + V(((x^8 + 1)/(x^24*y - x^16*y)) dx) + dV([(1/(x^32 + 2*x^24))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^3/(x^8 + 2))*y] d[x] + V(((-x^29 - x^21 + x^13)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]) [(2/(x^13 + 2*x^5))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^35*y - x^27*y)) dx) + dV([(2/(x^35 + 2*x^27))*y])
result.omega8 == compare True
result.omega8 - compare 0
(1, 1, 0, 2, 1, 2, 1, 2)
decomposition_omega8_hpdh ((x^28 - x^26 + x^25 - x^24 + x^23 - x^22 - x^21 + x^20 + x^19 + x^18 + x^17 + x^15 - x^14 + x^13 + x^12 + x^11 - x^10 - x^8 - x^7 + x^6 - x^5 + x^4 + x^2 + x - 1)/(x^16*y - x^15*y + x^14*y - x^13*y + x^12*y - x^11*y + x^10*y - x^9*y - x^8*y + x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y)) dx
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [26], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(4)]).coordinates(basis=B)
 
File <string>:103, in coordinates(self, basis)
 
File <string>:83, in div_by_p(self)
 
File <string>:33, in decomposition_omega8_hpdh(omega, prec)
 
NameError: name 'T' is not defined
[6nsage: load('superelliptic_drw/superelliptic_drw_auxilliaries.sage')
[6nsage: load('init.sage')
[6nsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
[6nsage: B = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)
omega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(2*x^5/(x^8 + 2))*y] d[x] + V(((-x^27 - x^19)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]) 0
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift 0 [(1/(x^12 + 2*x^4))*y] d[x] + V(((x^8 + 1)/(x^24*y - x^16*y)) dx) + dV([(1/(x^32 + 2*x^24))*y])
result.omega8 == compare True
result.omega8 - compare 0
omega0_lift, omega8_lift [(x^3/(x^8 + 2))*y] d[x] + V(((-x^29 - x^21 + x^13)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]) [(2/(x^13 + 2*x^5))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^35*y - x^27*y)) dx) + dV([(2/(x^35 + 2*x^27))*y])
result.omega8 == compare True
result.omega8 - compare 0
(1, 1, 0, 2, 1, 2, 1, 2)
decomposition_omega8_hpdh ((x^28 - x^26 + x^25 - x^24 + x^23 - x^22 - x^21 + x^20 + x^19 + x^18 + x^17 + x^15 - x^14 + x^13 + x^12 + x^11 - x^10 - x^8 - x^7 + x^6 - x^5 + x^4 + x^2 + x - 1)/(x^16*y - x^15*y + x^14*y - x^13*y + x^12*y - x^11*y + x^10*y - x^9*y - x^8*y + x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y)) dx
omega_analytic t^-18 + t^-16 + 2*t^-14 + t^-4
omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + O(t^32)
omega_analytic ((x^72 + x^71 - x^70 + x^65 - x^64 - x^62 - x^56 - x^55 - x^49 - x^48 + x^47 - x^46 - x^40 - x^38 - x^32 - x^31 - x^24 + x^23 - x^22 - x^16 - x^14 - x^8 - x^7 + 1)/(x^60*y)) dx
omega8 ((x^78 - x^76 - x^75 - x^74 + x^73 + x^72 - x^71 - x^69 - x^67 - x^66 + x^65 - x^64 + x^63 - x^60 + x^59 + x^58 - x^57 - x^56 + x^55 - x^54 + x^48 - x^47 + x^46 + x^45 - x^44 + x^43 - x^42 + x^41 - x^40 + x^39 - x^38 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 + x^21 - x^20 + x^19 - x^18 + x^17 - x^16 - x^15 - x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1)/(x^75*y - x^74*y + x^73*y - x^72*y + x^71*y - x^70*y + x^69*y - x^68*y - x^67*y + x^66*y - x^65*y + x^64*y - x^63*y + x^62*y - x^61*y + x^60*y)) dx
dh ((x^24 + x^22 - x^16 + x^14 - x^8 + 1)/(x^18*y)) dx
omega8.expansion_at_infty() 1 + t^2 + 2*t^4 + t^6 + t^8 + 2*t^12 + 2*t^16 + t^18 + t^20 + 2*t^22 + t^32 + 2*t^40 + t^48 + O(t^50)
decomposition_g8_p2th_power ((2*x^87 + 2*x^84 + x^83 + x^82 + x^81 + x^80 + 2*x^78 + 2*x^77 + x^76 + 2*x^75 + 2*x^74 + x^73 + x^72 + 2*x^71 + 2*x^70 + 2*x^68 + 2*x^67 + x^63 + x^60 + 2*x^59 + 2*x^58 + 2*x^57 + 2*x^56 + x^54 + x^53 + 2*x^52 + x^51 + x^50 + 2*x^49 + 2*x^48 + x^47 + x^46 + x^44 + x^43 + x^42 + 2*x^24 + 1)/(x^93 + x^85 + x^77 + 2*x^69 + 2*x^61 + 2*x^53))*y
decomposition_g8_pth_power ((2*x^87 + 2*x^84 + x^83 + x^82 + x^81 + x^80 + 2*x^78 + 2*x^77 + x^76 + 2*x^75 + 2*x^74 + x^73 + x^72 + 2*x^71 + 2*x^70 + 2*x^68 + 2*x^67 + x^63 + x^60 + 2*x^59 + 2*x^58 + 2*x^57 + 2*x^56 + x^54 + x^53 + 2*x^52 + x^51 + x^50 + 2*x^49 + 2*x^48 + x^47 + x^46 + x^44 + x^43 + x^42 + 2*x^24 + 1)/(x^93 + x^85 + x^77 + 2*x^69 + 2*x^61 + 2*x^53))*y
decomposition_g8_pth_power 0
aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True
[4, 1, 3, 2, 1, 8, 1, 2]
[6nsassage: C.genus()
4
[6sage: quit()
[23;0t
~/Research/2021 De Rham/DeRhamComputation/sage$ cd ..
~/Research/2021 De Rham/DeRhamComputation$ git add -u
~/Research/2021 De Rham/DeRhamComputation$ git status
On branch master
Your branch is up to date with 'origin/master'.
 
Changes to be committed:
(use "git restore --staged <file>..." to unstage)
modified: sage/.run.term-0.term
modified: sage/superelliptic/superelliptic_class.sage
modified: sage/superelliptic_drw/superelliptic_drw_auxilliaries.sage
modified: sage/superelliptic_drw/superelliptic_drw_cech.sage
modified: sage/tests.sage
 
Untracked files:
(use "git add <file>..." to include in what will be committed)
.crystalline_p2.ipynb.sage-jupyter2
.deRhamComputation.ipynb.sage-jupyter2
.elementary_covers_of_superelliptic_curves.ipynb.sage-jupyter2
.git.x11-0.term
.superelliptic.ipynb.sage-jupyter2
.superelliptic_alpha.ipynb.sage-jupyter2
.superelliptic_arbitrary_field.ipynb.sage-jupyter2
git.x11
sage/auxilliaries/laurent_analytic_part.sage
sage/drafty/.2023-03-06-file-1.ipynb.sage-jupyter2
sage/drafty/2gpcovers.sage
sage/drafty/as_cartier.sage
sage/drafty/better_trace.sage
sage/drafty/cartier_image_representation.sage
sage/drafty/convert_superelliptic_into_AS.sage
sage/drafty/draft4.sage
sage/drafty/draft5.sage
sage/drafty/draft6.sage
sage/drafty/draft7.sage
sage/drafty/draft8.sage
sage/drafty/draft_klein_covers.sage
sage/drafty/lift_to_de_rham.sage
sage/drafty/pole_numbers.sage
~/Research/2021 De Rham/DeRhamComputation$
~/Research/2021 De Rham/DeRhamComputation$ y.t add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/su[1@p
~/Research/2021 De Rham/DeRhamComputation$ git commit -m "dziala[1Pja wspolrzedne crystalline cohomology!!!!".sage sage/superelliptic_drw/regular_form.sage sage/sup[1@e
git commit -m "dzialaja wspolrzedne crystalline cohomologygit add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/superelliptic/tests/expansion_at_infty.sage sage/auxilliaries/laurent_analytic_part.sagegit add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/superelliptic/tests/expansion_at_infty.sage sage/auxilliaries/laurent_analytic_part.sage"
[master a9d055a] dzialaja wspolrzedne crystalline cohomologygit add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/superelliptic/tests/expansion_at_infty.sage sage/auxilliaries/laurent_analytic_part.sagegit add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/superelliptic/tests/expansion_at_infty.sage sage/auxilliaries/laurent_analytic_part.sage
9 files changed, 1398 insertions(+), 27 deletions(-)/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/supe[1P
create mode 100644 sage/auxilliaries/laurent_analytic_part.sageptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/sup[1P
create mode 100644 sage/superelliptic/tests/expansion_at_infty.sagec_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/su[1Prelliptic/tests/expansion_at_infty.sage sage/auxilliaries/laurent_analytic_part.sage
create mode 100644 sage/superelliptic_drw/regular_form.sageerelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/superelliptic/tests/expansion_at_infty.sage sage/auxilliaries/laurent_analytic_part.sage
create mode 100644 sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage
~/Research/2021 De Rham/DeRhamComputation$ git push
Username for 'https://git.wmi.amu.edu.pl': jgarnek
Password for 'https://jgarnek@git.wmi.amu.edu.pl':
Enumerating objects: 29, done.
Counting objects: 100% (29/29), done.
Delta compression using up to 4 threads
Compressing objects: 100% (17/17), done.
Writing objects: 100% (17/17), 11.83 KiB | 84.00 KiB/s, done.
Total 17 (delta 11), reused 0 (delta 0)
remote: . Processing 1 references
remote: Processed 1 references in total
To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git
995d5f0..a9d055a master -> master
~/Research/2021 De Rham/DeRhamComputation$ cd sage/
~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
[22;0t[6nsage: load('init.sage')
[6nsage: M
[4 6]
[1 4]
[6nsage: M^3
[1 0]
[0 1]
[6nsasage: load('init.sage')
---------------------------------------------------------------------------
IndexError Traceback (most recent call last)
Input In [4], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:32, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:19, in <module>
 
File <string>:10, in crystalline_matrix(C)
 
File <string>:39, in crystalline_cohomology_basis(self, prec)
 
File <string>:29, in de_rham_witt_lift(cech_class, prec)
 
File <string>:7, in decomposition_g0_g8(fct, prec)
 
File <string>:107, in coordinates(self, basis, basis_holo, prec)
 
File <string>:79, in serre_duality_pairing(self, fct, prec)
 
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__()
542 return type(self)(self._parent, f, self.__n)
543
--> 544 return self.__u[i - self.__n]
545
546 def __iter__(self):
 
File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__()
451 return self.base_ring().zero()
452 else:
--> 453 raise IndexError("coefficient not known")
454 return self.__f[n]
455
 
IndexError: coefficient not known
[6nsasage: load('init.sage')
---------------------------------------------------------------------------
IndexError Traceback (most recent call last)
Input In [5], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:32, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:19, in <module>
 
File <string>:10, in crystalline_matrix(C)
 
File <string>:39, in crystalline_cohomology_basis(self, prec)
 
File <string>:29, in de_rham_witt_lift(cech_class, prec)
 
File <string>:7, in decomposition_g0_g8(fct, prec)
 
File <string>:107, in coordinates(self, basis, basis_holo, prec)
 
File <string>:79, in serre_duality_pairing(self, fct, prec)
 
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__()
542 return type(self)(self._parent, f, self.__n)
543
--> 544 return self.__u[i - self.__n]
545
546 def __iter__(self):
 
File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__()
451 return self.base_ring().zero()
452 else:
--> 453 raise IndexError("coefficient not known")
454 return self.__f[n]
455
 
IndexError: coefficient not known
[6nsasage: load('init.sage')
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [6], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:32, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:19, in <module>
 
File <string>:16, in crystalline_matrix(C, prec)
 
TypeError: superelliptic_drw_cech.coordinates() got an unexpected keyword argument 'prec'
[6nsasage: load('init.sage')
[1 0 0 0 0 0 6 0]
[1 1 0 3 0 6 6 0]
[1 2 1 6 6 3 6 6]
[4 3 3 1 0 0 3 0]
[4 1 3 2 1 8 1 2]
[8 3 3 4 0 1 7 3]
[3 6 3 3 0 0 1 6]
[4 1 6 7 0 3 3 1]
[1 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0]
[0 0 0 1 0 0 0 0]
[0 0 0 0 1 0 0 0]
[0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 1]
~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
[22;0t[6nsage: load('init.sage')
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
File <string>:59, in __mul__(self, other)
 
File <string>:235, in reduction(C, g)
 
File /ext/sage/9.7/src/sage/arith/misc.py:1971, in xgcd(a, b)
1970 try:
-> 1971 return a.xgcd(b)
1972 except AttributeError:
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
 
During handling of the above exception, another exception occurred:
 
AttributeError Traceback (most recent call last)
Input In [1], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:32, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:19, in <module>
 
File <string>:10, in crystalline_matrix(C, prec)
 
File <string>:39, in crystalline_cohomology_basis(self, prec)
 
File <string>:26, in de_rham_witt_lift(cech_class, prec)
 
File <string>:73, in diffn(self, dy_w)
 
File <string>:177, in dy_w(C)
 
File /ext/sage/9.7/src/sage/rings/rational.pyx:2414, in sage.rings.rational.Rational.__mul__()
2412 return x
2413
-> 2414 return coercion_model.bin_op(left, right, operator.mul)
2415
2416 cpdef _mul_(self, right):
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:48, in __rmul__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
1526 if not err:
1527 return (<Element>right)._mul_long(value)
-> 1528 return coercion_model.bin_op(left, right, mul)
1529 except TypeError:
1530 return NotImplemented
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:43, in __rmul__(self, other)
 
File <string>:31, in __add__(self, other)
 
File <string>:63, in __mul__(self, other)
 
AttributeError: 'superelliptic_function' object has no attribute 'form'
[6nsage: load('init.sage')
[6nssage: B = C.crystalline_cohomology_basis(prec = 100)
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [3], in <cell line: 1>()
----> 1 B = C.crystalline_cohomology_basis(prec = Integer(100))
 
File <string>:39, in crystalline_cohomology_basis(self, prec)
 
File <string>:24, in de_rham_witt_lift(cech_class, prec)
 
File <string>:6, in de_rham_witt_lift_form0(omega)
 
File <string>:73, in diffn(self, dy_w)
 
File <string>:177, in dy_w(C)
 
File /ext/sage/9.7/src/sage/rings/rational.pyx:2414, in sage.rings.rational.Rational.__mul__()
2412 return x
2413
-> 2414 return coercion_model.bin_op(left, right, operator.mul)
2415
2416 cpdef _mul_(self, right):
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:48, in __rmul__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
1526 if not err:
1527 return (<Element>right)._mul_long(value)
-> 1528 return coercion_model.bin_op(left, right, mul)
1529 except TypeError:
1530 return NotImplemented
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:43, in __rmul__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
1526 if not err:
1527 return (<Element>right)._mul_long(value)
-> 1528 return coercion_model.bin_op(left, right, mul)
1529 except TypeError:
1530 return NotImplemented
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:43, in __rmul__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
1526 if not err:
1527 return (<Element>right)._mul_long(value)
-> 1528 return coercion_model.bin_op(left, right, mul)
1529 except TypeError:
1530 return NotImplemented
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:43, in __rmul__(self, other)
 
File <string>:31, in __add__(self, other)
 
File <string>:82, in __pow__(self, exp)
 
File <string>:14, in __init__(self, C, g)
 
File <string>:228, in reduction(C, g)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
636 ring_one = self.ring().one()
637 try:
--> 638 return self._element_class(self, x, ring_one, coerce=coerce)
639 except (TypeError, ValueError):
640 pass
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
112 FieldElement.__init__(self, parent)
113 if coerce:
--> 114 self.__numerator = parent.ring()(numerator)
115 self.__denominator = parent.ring()(denominator)
116 else:
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
1001
1002 try:
-> 1003 return self(str(element))
1004 except TypeError:
1005 pass
 
File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
192 except AttributeError:
193 return super().__repr__()
--> 194 result = reprfunc()
195 if isinstance(result, str):
196 return result
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_()
2688 NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3
2689 """
-> 2690 return self._repr()
2691
2692 def _latex_(self, name=None):
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2656, in sage.rings.polynomial.polynomial_element.Polynomial._repr()
2654 if n != m-1:
2655 s += " + "
-> 2656 x = y = repr(x)
2657 if y.find("-") == 0:
2658 y = y[1:]
 
File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
192 except AttributeError:
193 return super().__repr__()
--> 194 result = reprfunc()
195 if isinstance(result, str):
196 return result
 
File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:340, in sage.rings.fraction_field_FpT.FpTElement._repr_()
338 return repr(self.numer())
339 else:
--> 340 numer_s = repr(self.numer())
341 denom_s = repr(self.denom())
342 if '-' in numer_s or '+' in numer_s:
 
File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
192 except AttributeError:
193 return super().__repr__()
--> 194 result = reprfunc()
195 if isinstance(result, str):
196 return result
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_()
2688 NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3
2689 """
-> 2690 return self._repr()
2691
2692 def _latex_(self, name=None):
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2656, in sage.rings.polynomial.polynomial_element.Polynomial._repr()
2654 if n != m-1:
2655 s += " + "
-> 2656 x = y = repr(x)
2657 if y.find("-") == 0:
2658 y = y[1:]
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: C
Superelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
[6nsage: B = C.crystalline_cohomology_basis(prec = 100)
[6nsage: B
[([(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), V(((x^2 + 1)/x)*y), [(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y])),
([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))]
[6nsage: B[0].reguler_form()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [7], in <cell line: 1>()
----> 1 B[Integer(0)].reguler_form()
 
AttributeError: 'superelliptic_drw_cech' object has no attribute 'reguler_form'
[6nsage: B[0].regular_form()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [8], in <cell line: 1>()
----> 1 B[Integer(0)].regular_form()
 
AttributeError: 'superelliptic_drw_cech' object has no attribute 'regular_form'
[6nssage: B0 = B[0]
sage: B0.omega0.regular_form()
[0] d[x] + [1] d[y] + V(((x^5 + x^3)/y) dx) + dV(0)
~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
sage: load('init.sage')
sage: C
Superelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
[sage: B = C.crystalline_cohomology_basis(prec = 100, info = 1)
Computing 0. basis element
Computing 1. basis element
[6nsage: B
[([(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), V(((x^2 + 1)/x)*y), [(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y])),
([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))]
[6nsage: B[0].omega0.regular_form()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [5], in <cell line: 1>()
----> 1 B[Integer(0)].omega0.regular_form()
 
File <string>:81, in regular_drw_form(omega)
 
AttributeError: 'superelliptic_drw_form' object has no attribute 'omega0'
[6nsage: sage: load('init.sage')
[6nsage: sage: B = C.crystalline_cohomology_basis(prec = 100, info = 1)
Computing 0. basis element
Computing 1. basis element
[6nsage: B[0].omega0.regular_form()
[0] d[x] + [1] d[y] + V((x^21 + 2*x^19 + 2*x^15 + x^13) dy) + dV((2*x^15 + x^13 + 2*x^9 + x^7)*y)
[6nsage: B[1].omega0.regular_form()
[0] d[x] + [x] d[y] + V((0) dy) + dV((x^6 + 2*x^4)*y)
[6nsage: load('init.sage')
[6nsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)
[6nsage: B = C.crystalline_cohomology_basis(prec = 100, info = 1)
Computing 0. basis element
Computing 1. basis element
Computing 2. basis element
Computing 3. basis element
Computing 4. basis element
Computing 5. basis element
Computing 6. basis element
Computing 7. basis element
[6nsage: B[0].regular_form()
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [13], in <cell line: 1>()
----> 1 B[Integer(0)].regular_form()
 
File <string>:90, in regular_drw_cech(cocycle)
 
TypeError: can only concatenate str (not "superelliptic_regular_drw_form") to str
[6nsage: B[0].omega0.regular_form()
[0] d[x] + [1] d[y] + V((0) dy) + dV((x^9 + 2*x)*y)
[6nsage: B[7].omega0.regular_form()
[0] d[x] + [x^4] d[y] + V((0) dy) + dV(0)
sage: def regular_drw_cech(cocycle):
....: print("( " + str(cocycle.omega0.regular_form()) + ", " + str(cocycle.f) + " )")
....:
....: superelliptic_drw_cech.regular_form = regular_drw_cech
[6nsage:
[6nsage: B[0].regular_form()
( [0] d[x] + [1] d[y] + V((0) dy) + dV((x^9 + 2*x)*y), V(x*y) )
sage: for i in range(8):
....: print(B[i].regular_form())
....:
( [0] d[x] + [1] d[y] + V((0) dy) + dV((x^9 + 2*x)*y), V(x*y) )
None
( [0] d[x] + [x] d[y] + V((2*x^36 + x^28 + x^12 + 2*x^4) dy) + dV((x^12 + 2*x^4)*y), V(((x^8 + 1)/x^4)*y) )
None
( [0] d[x] + [x^2] d[y] + V((x^63 + 2*x^55 + 2*x^39 + x^31) dy) + dV((2*x^39 + x^31 + 2*x^15 + x^7)*y), V(((x^8 + 1)/x)*y) )
None
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [18], in <cell line: 1>()
1 for i in range(Integer(8)):
----> 2 print(B[i].regular_form())
 
Input In [16], in regular_drw_cech(cocycle)
1 def regular_drw_cech(cocycle):
----> 2 print("( " + str(cocycle.omega0.regular_form()) + ", " + str(cocycle.f) + " )")
 
File <string>:80, in regular_drw_form(omega)
 
File <string>:73, in diffn(self, dy_w)
 
File <string>:177, in dy_w(C)
 
File <string>:149, in auxilliary_derivative(P)
 
File <string>:84, in __add__(self, other)
 
File <string>:65, in __mul__(self, other)
 
File <string>:28, in __sub__(self, other)
 
File <string>:7, in __init__(self, C, g)
 
File <string>:252, in reduction_form(C, g)
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:647, in PolynomialRing(base_ring, *args, **kwds)
644 raise TypeError("variable names specified twice inconsistently: %r and %r" % (names, kwnames))
646 if multivariate or len(names) != 1:
--> 647 return _multi_variate(base_ring, names, **kwds)
648 else:
649 return _single_variate(base_ring, names, **kwds)
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:762, in _multi_variate(base_ring, names, sparse, order, implementation)
760 from sage.rings.polynomial.term_order import TermOrder
761 n = len(names)
--> 762 order = TermOrder(order, n)
764 # "implementation" must be last
765 key = [base_ring, names, n, order, implementation]
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
sage: for i in range(8):
....: B[i].regular_form()
....:
( [0] d[x] + [1] d[y] + V((0) dy) + dV((x^9 + 2*x)*y), V(x*y) )
( [0] d[x] + [x] d[y] + V((2*x^36 + x^28 + x^12 + 2*x^4) dy) + dV((x^12 + 2*x^4)*y), V(((x^8 + 1)/x^4)*y) )
( [0] d[x] + [x^2] d[y] + V((x^63 + 2*x^55 + 2*x^39 + x^31) dy) + dV((2*x^39 + x^31 + 2*x^15 + x^7)*y), V(((x^8 + 1)/x)*y) )
( [0] d[x] + [x^3] d[y] + V((0) dy) + dV(0), V((x^10 + x^2)*y) )
( [0] d[x] + [x^7] d[y] + V((x^54 + 2*x^46 + 2*x^30 + x^22) dy) + dV((2*x^30 + x^22)*y), [2/x*y] + V(((x^24 + x^16 + x^8 + 2)/x^2)*y) )
( [0] d[x] + [2*x^6] d[y] + V((0) dy) + dV((2*x^27 + x^19)*y), [2/x^2*y] + V((2*x^19 + 2*x^11 + 2*x^3)*y) )
( [0] d[x] + [0] d[y] + V((x^72 + 2*x^64 + 2*x^48 + x^40) dy) + dV((2*x^48 + x^40 + 2*x^24 + x^16)*y), [2/x^3*y] )
( [0] d[x] + [x^4] d[y] + V((0) dy) + dV(0), [2/x^4*y] + V(((x^16 + x^8 + 1)/x^3)*y) )
[6nsage: C
Superelliptic curve with the equation y^2 = x^9 + 2*x over Finite Field of size 3
[6nsasage: C1 = superelliptic(x^3 + x, 2)
[6nsage: B1 = C1.crystalline_cohomology_basis(prec = 100, info = 1)
Computing 0. basis element
Computing 1. basis element
^C---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
File <string>:58, in __mul__(self, other)
 
AttributeError: 'superelliptic_form' object has no attribute 'function'
 
During handling of the above exception, another exception occurred:
 
KeyboardInterrupt Traceback (most recent call last)
Input In [22], in <cell line: 1>()
----> 1 B1 = C1.crystalline_cohomology_basis(prec = Integer(100), info = Integer(1))
 
File <string>:41, in crystalline_cohomology_basis(self, prec, info)
 
File <string>:33, in de_rham_witt_lift(cech_class, prec)
 
File <string>:6, in __init__(self, omega0, f)
 
File <string>:90, in diffn(self, dy_w)
 
File <string>:73, in diffn(self, dy_w)
 
File <string>:177, in dy_w(C)
 
File <string>:65, in __mul__(self, other)
 
File <string>:65, in __mul__(self, other)
 
File <string>:7, in __init__(self, C, g)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce)
704 x0, y0 = x, y
705 try:
--> 706 x, y = resolve_fractions(x0, y0)
707 except (AttributeError, TypeError):
708 raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
709 x0, y0, self))
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:688, in FractionField_generic._element_constructor_.<locals>.resolve_fractions(x, y)
686 yd = y.denominator()
687 try:
--> 688 return (xn * yd, yn * xd)
689 except (AttributeError, TypeError, ValueError):
690 pass
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
1514 return (<Element>left)._mul_(right)
1515 if BOTH_ARE_ELEMENT(cl):
-> 1516 return coercion_model.bin_op(left, right, mul)
1517
1518 cdef long value
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1200, in sage.structure.coerce.CoercionModel.bin_op()
1198 # Now coerce to a common parent and do the operation there
1199 try:
-> 1200 xy = self.canonical_coercion(x, y)
1201 except TypeError:
1202 self._record_exception()
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1311, in sage.structure.coerce.CoercionModel.canonical_coercion()
1309 x_map, y_map = coercions
1310 if x_map is not None:
-> 1311 x_elt = (<Map>x_map)._call_(x)
1312 else:
1313 x_elt = x
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
285 raise TypeError("Cannot coerce {} to {}".format(x, C))
286 cdef Map m
--> 287 cdef Element e = method(C)
288 if e is None:
289 raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x)))
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:198, in sage.rings.polynomial.multi_polynomial.MPolynomial._polynomial_()
196 var = R.variable_name()
197 if var in self._parent.variable_names():
--> 198 return R(self.polynomial(self._parent(var)))
199 else:
200 return R([self])
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:419, in sage.rings.polynomial.multi_polynomial.MPolynomial.polynomial()
417 w = {remove_from_tuple(e, ind): val
418 for e, val in self.dict().iteritems() if not e[ind]}
--> 419 v = [B(w)] # coefficients that don't involve var
420 z = var
421 for i in range(1,d+1):
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:309, in PolynomialRing_general._element_constructor_(self, x, check, is_gen, construct, **kwds)
306 args = (self.base_ring(), self.variable_names(), None, self.is_sparse())
307 return unpickle_PolynomialRing, args
--> 309 def _element_constructor_(self, x=None, check=True, is_gen=False,
310 construct=False, **kwds):
311 r"""
312 Convert ``x`` into this univariate polynomial ring,
313 possibly non-canonically.
(...)
412 λ^2
413 """
414 C = self.element_class
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: B1 = C1.crystalline_cohomology_basis(prec = 100, info = 1)
Computing 0. basis element
Computing 1. basis element
sage: for i in range(2):
....: print(B1[i].regular_form())
....:
( [0] d[x] + [2] d[y] + V((x^21 + x^19 + x^15 + x^13) dy) + dV((x^15 + x^13 + 2*x^9 + 2*x^7)*y), V(((x^2 + 2)/x)*y) )
None
( [0] d[x] + [2*x] d[y] + V((0) dy) + dV((2*x^6 + 2*x^4)*y), [2/x*y] + V((x^4 + 2*x^2 + 1)*y) )
None
[6nsage: adic_expansion((x^63 + 2*x^55 + 2*x^39 + x^31), x^3 - x)
[0, 0, 0, 0, x, 1, x, 2, 0, 1, x, 1, x, 0, 0, 2, 0, 0, 0, 1, 0, 1]
[6nsage: adic_expansion(x^3 - x, x^3 - x)
[0, 1]
[6nsage: Rxt.<t> = PolynomialRing(Rx)
[6nsage: coo = adic_expansion(x^3 - x, x^3 - x)
[6nsage: coo = adic_expansion((x^63 + 2*x^55 + 2*x^39 + x^31), x^3 - x)
[6nsagsage: FF = Rxt(0)
[6nsage: sage: FF = sum(a*t^i for i, a in enumerate(coo))
[6nsage: FF
t^21 + t^19 + 2*t^15 + x*t^12 + t^11 + x*t^10 + t^9 + 2*t^7 + x*t^6 + t^5 + x*t^4
[6nsage: C.de_rham_basis()
[((1/y) dx, 0, (1/y) dx),
((x/y) dx, 0, (x/y) dx),
((x^2/y) dx, 0, (x^2/y) dx),
((x^3/y) dx, 0, (x^3/y) dx),
((x^7/y) dx, 2/x*y, ((-1)/(x*y)) dx),
(((-x^6)/y) dx, 2/x^2*y, 0 dx),
(0 dx, 2/x^3*y, (1/(x^3*y)) dx),
((x^4/y) dx, 2/x^4*y, ((-1)/(x^4*y)) dx)]
[6nsage: (C.y/C.x^3).expansion_at_infty()
t^-3 + t^13 + O(t^17)
[6nsage:
[6nsage: (C.y/C.x).expansion_at_infty()
t^-7 + O(t^13)
[6nsage: (C.y/C.x^4).expansion_at_infty()
t^-1 + O(t^19)
[6nsage: (C.y/C.x^5).expansion_at_infty()
t + 2*t^17 + O(t^21)
[6nsage: (C.y/C.x^5).diffn()
(x^3/y) dx
[6nsage: (C.y/C.x^7).diffn()
((-x^8 - 1)/(x^7*y)) dx
[6nsage: (C.x^5*C.y.diffn()).int()
---------------------------------------------------------------------------
ZeroDivisionError Traceback (most recent call last)
Input In [40], in <cell line: 1>()
----> 1 (C.x**Integer(5)*C.y.diffn()).int()
 
File <string>:198, in int(self)
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:3994, in sage.rings.polynomial.polynomial_element.Polynomial.integral()
3992 cdef Py_ssize_t n
3993 zero = Q.zero()
-> 3994 p = [zero] + [cm.bin_op(Q(self.get_unsafe(n)), n + 1, operator.truediv)
3995 if self.get_unsafe(n) else zero for n in range(self.degree() + 1)]
3996 return S(p)
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
1202 self._record_exception()
1203 else:
-> 1204 return PyObject_CallObject(op, xy)
1205
1206 if op is mul:
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
1735 cdef int cl = classify_elements(left, right)
1736 if HAVE_SAME_PARENT(cl):
-> 1737 return (<Element>left)._div_(right)
1738 if BOTH_ARE_ELEMENT(cl):
1739 return coercion_model.bin_op(left, right, truediv)
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
2622 if right_inverse is None:
-> 2623 raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
2624 else:
2625 return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)
 
ZeroDivisionError: inverse of Mod(0, 3) does not exist
[6nsage: (C.x^5*C.y.diffn()).cartier()
(x^4/y) dx
[6nsage: (C.x^5*C.y.diffn()).cartier().inv_cartier()
((x^21 - x^13)/y) dx
[6nsage: ((C.x^5 - C.x^3)*C.y.diffn()).cartier()
(x^4/y) dx
[6nsage: adic_expansion(x^7, x^3 - x)
[x, 2*x^2 + 1, x]
[6nsage: sage: x
x
[6nsage: parent(x)
Univariate Polynomial Ring in x over Finite Field of size 3
[6nsage: sage: load('init.sage')
Computing 0. basis element
Computing 1. basis element
Computing 0. basis element
---------------------------------------------------------------------------
IndexError Traceback (most recent call last)
Input In [47], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:32, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:12, in <module>
 
File <string>:41, in crystalline_cohomology_basis(self, prec, info)
 
File <string>:29, in de_rham_witt_lift(cech_class, prec)
 
File <string>:7, in decomposition_g0_g8(fct, prec)
 
File <string>:107, in coordinates(self, basis, basis_holo, prec)
 
File <string>:79, in serre_duality_pairing(self, fct, prec)
 
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__()
542 return type(self)(self._parent, f, self.__n)
543
--> 544 return self.__u[i - self.__n]
545
546 def __iter__(self):
 
File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__()
451 return self.base_ring().zero()
452 else:
--> 453 raise IndexError("coefficient not known")
454 return self.__f[n]
455
 
IndexError: coefficient not known
[6nsage: load('init.sage')
Computing 0. basis element
Computing 1. basis element
Computing 0. basis element
Computing 1. basis element
Computing 2. basis element
Computing 3. basis element
---------------------------------------------------------------------------
IndexError Traceback (most recent call last)
Input In [48], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:32, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:12, in <module>
 
File <string>:41, in crystalline_cohomology_basis(self, prec, info)
 
File <string>:32, in de_rham_witt_lift(cech_class, prec)
 
File <string>:36, in decomposition_omega0_omega8(omega, prec)
 
File /ext/sage/9.7/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds)
583 return expression.sum(*args, **kwds)
584 elif max(len(args),len(kwds)) <= 1:
--> 585 return sum(expression, *args, **kwds)
586 else:
587 from sage.symbolic.ring import SR
 
File <string>:36, in <genexpr>(.0)
 
File <string>:156, in residue(self, place, prec)
 
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__()
542 return type(self)(self._parent, f, self.__n)
543
--> 544 return self.__u[i - self.__n]
545
546 def __iter__(self):
 
File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__()
451 return self.base_ring().zero()
452 else:
--> 453 raise IndexError("coefficient not known")
454 return self.__f[n]
455
 
IndexError: coefficient not known
[6nsage: load('init.sage')
Computing 0. basis element
^C---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
File <string>:58, in __mul__(self, other)
 
AttributeError: 'superelliptic_form' object has no attribute 'function'
 
During handling of the above exception, another exception occurred:
 
KeyboardInterrupt Traceback (most recent call last)
Input In [49], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:32, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:11, in <module>
 
File <string>:41, in crystalline_cohomology_basis(self, prec, info)
 
File <string>:25, in de_rham_witt_lift(cech_class, prec)
 
File <string>:15, in de_rham_witt_lift_form8(omega)
 
File <string>:90, in diffn(self, dy_w)
 
File <string>:73, in diffn(self, dy_w)
 
File <string>:177, in dy_w(C)
 
File <string>:65, in __mul__(self, other)
 
File <string>:65, in __mul__(self, other)
 
File <string>:7, in __init__(self, C, g)
 
File <string>:271, in reduction_form(C, g)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
636 ring_one = self.ring().one()
637 try:
--> 638 return self._element_class(self, x, ring_one, coerce=coerce)
639 except (TypeError, ValueError):
640 pass
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
112 FieldElement.__init__(self, parent)
113 if coerce:
--> 114 self.__numerator = parent.ring()(numerator)
115 self.__denominator = parent.ring()(denominator)
116 else:
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1009, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
1007 try:
1008 # now try calling the base ring's __call__ methods
-> 1009 element = self.base_ring()(element)
1010 _p = p_NSet(sa2si(element,_ring), _ring)
1011 return new_MP(self,_p)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x)
1143 """
1144 TESTS::
1145
(...)
1182 True
1183 """
1184 try:
-> 1185 return integer_mod.IntegerMod(self, x)
1186 except (NotImplementedError, PariError):
1187 raise TypeError("error coercing to finite field")
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod()
199 return a
200 t = modulus.element_class()
--> 201 return t(parent, value)
202
203
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:380, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
378 else:
379 try:
--> 380 z = integer_ring.Z(value)
381 except (TypeError, ValueError):
382 from sage.structure.element import Expression
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
285 raise TypeError("Cannot coerce {} to {}".format(x, C))
286 cdef Map m
--> 287 cdef Element e = method(C)
288 if e is None:
289 raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x)))
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:831, in sage.rings.fraction_field_element.FractionFieldElement._conversion()
829 return R(self.__numerator)
830 else:
--> 831 self.reduce()
832 num = R(self.__numerator)
833 inv_den = R(self.__denominator).inverse_of_unit()
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:1239, in sage.rings.fraction_field_element.FractionFieldElement_1poly_field.reduce()
1237 if self._is_reduced:
1238 return
-> 1239 super(self.__class__, self).reduce()
1240 self.normalize_leading_coefficients()
1241
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:164, in sage.rings.fraction_field_element.FractionFieldElement.reduce()
162 return codomain.coerce(nnum/nden)
163
--> 164 cpdef reduce(self):
165 """
166 Reduce this fraction.
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:197, in sage.rings.fraction_field_element.FractionFieldElement.reduce()
195 return
196 try:
--> 197 g = self.__numerator.gcd(self.__denominator)
198 if not g.is_unit():
199 self.__numerator //= g
 
File /ext/sage/9.7/src/sage/structure/element.pyx:4494, in sage.structure.element.coerce_binop.new_method()
4492 def new_method(self, other, *args, **kwargs):
4493 if have_same_parent(self, other):
-> 4494 return method(self, other, *args, **kwargs)
4495 else:
4496 a, b = coercion_model.canonical_coercion(self, other)
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:4913, in sage.rings.polynomial.polynomial_element.Polynomial.gcd()
4911 raise NotImplementedError("%s does not provide a gcd implementation for univariate polynomials"%self._parent._base)
4912 else:
-> 4913 return doit(self, other)
4914
4915 @coerce_binop
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:944, in FractionField_generic._gcd_univariate_polynomial(self, f, g)
942 Pol = f.parent()
943 Num = Pol.change_ring(self.base())
--> 944 f1 = Num(f.numerator())
945 g1 = Num(g.numerator())
946 return Pol(f1.gcd(g1)).monic()
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:452, in PolynomialRing_general._element_constructor_(self, x, check, is_gen, construct, **kwds)
450 except NameError:
451 raise TypeError("Unable to coerce string")
--> 452 elif isinstance(x, FractionFieldElement):
453 if x.denominator().is_unit():
454 x = x.numerator() * x.denominator().inverse_of_unit()
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
sage: try:
....: print(0/0)
....: except IndexError:
....: print("a")
....:
---------------------------------------------------------------------------
ZeroDivisionError Traceback (most recent call last)
Input In [50], in <cell line: 1>()
1 try:
----> 2 print(Integer(0)/Integer(0))
3 except IndexError:
4 print("a")
 
File /ext/sage/9.7/src/sage/rings/integer.pyx:2022, in sage.rings.integer.Integer.__truediv__()
2020 if type(left) is type(right):
2021 if mpz_sgn((<Integer>right).value) == 0:
-> 2022 raise ZeroDivisionError("rational division by zero")
2023 x = <Rational> Rational.__new__(Rational)
2024 mpq_div_zz(x.value, (<Integer>left).value, (<Integer>right).value)
 
ZeroDivisionError: rational division by zero
sage: try:
....: print(0/0)
....: except ZeroDivisionError:
....: print("a")
....:
a
[6nsage: load('init.sage')
Computing 0. basis element
Computing 1. basis element
Computing 0. basis element
Computing 1. basis element
Computing 2. basis element
Computing 3. basis element
Computing 4. basis element
Computing 5. basis element
Computing 6. basis element
Computing 7. basis element
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
File <string>:60, in __mul__(self, other)
 
File <string>:14, in __init__(self, C, g)
 
File <string>:228, in reduction(C, g)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
637 try:
--> 638 return self._element_class(self, x, ring_one, coerce=coerce)
639 except (TypeError, ValueError):
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
113 if coerce:
--> 114 self.__numerator = parent.ring()(numerator)
115 self.__denominator = parent.ring()(denominator)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
1002 try:
-> 1003 return self(str(element))
1004 except TypeError:
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:991, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
990 element = element.replace("^","**")
--> 991 element = eval(element, d, {})
992 except (SyntaxError, NameError):
 
File <string>:1, in <module>
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
 
During handling of the above exception, another exception occurred:
 
AttributeError Traceback (most recent call last)
Input In [52], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:32, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:12, in <module>
 
File <string>:44, in crystalline_cohomology_basis(self, prec, info)
 
File <string>:26, in de_rham_witt_lift(cech_class, prec)
 
File <string>:90, in diffn(self, dy_w)
 
File <string>:73, in diffn(self, dy_w)
 
File <string>:177, in dy_w(C)
 
File <string>:149, in auxilliary_derivative(P)
 
File <string>:149, in auxilliary_derivative(P)
 
File <string>:147, in auxilliary_derivative(P)
 
File <string>:35, in __sub__(self, other)
 
File <string>:31, in __add__(self, other)
 
File <string>:63, in __mul__(self, other)
 
AttributeError: 'superelliptic_function' object has no attribute 'form'
[6nsage: quit()
[23;0t
~/Research/2021 De Rham/DeRhamComputation/sage$ cd ..
~/Research/2021 De Rham/DeRhamComputation$ git status
On branch master
Your branch is up to date with 'origin/master'.
 
Changes not staged for commit:
(use "git add <file>..." to update what will be committed)
(use "git restore <file>..." to discard changes in working directory)
modified: sage/.run.term-0.term
modified: sage/drafty/draft.sage
modified: sage/superelliptic_drw/de_rham_witt_lift.sage
modified: sage/superelliptic_drw/regular_form.sage
modified: sage/superelliptic_drw/superelliptic_drw_auxilliaries.sage
modified: sage/superelliptic_drw/superelliptic_drw_cech.sage
 
Untracked files:
(use "git add <file>..." to include in what will be committed)
.crystalline_p2.ipynb.sage-jupyter2
.deRhamComputation.ipynb.sage-jupyter2
.elementary_covers_of_superelliptic_curves.ipynb.sage-jupyter2
.git.x11-0.term
.superelliptic.ipynb.sage-jupyter2
.superelliptic_alpha.ipynb.sage-jupyter2
.superelliptic_arbitrary_field.ipynb.sage-jupyter2
git.x11
sage/drafty/.2023-03-06-file-1.ipynb.sage-jupyter2
sage/drafty/2gpcovers.sage
sage/drafty/as_cartier.sage
sage/drafty/better_trace.sage
sage/drafty/cartier_image_representation.sage
sage/drafty/convert_superelliptic_into_AS.sage
sage/drafty/draft4.sage
sage/drafty/draft5.sage
sage/drafty/draft6.sage
sage/drafty/draft7.sage
sage/drafty/draft8.sage
sage/drafty/draft_klein_covers.sage
sage/drafty/lift_to_de_rham.sage
sage/drafty/pole_numbers.sage
sage/superelliptic/frobenius_kernel.sage
superelliptic_arbitrary_field.ipynb
 
no changes added to commit (use "git add" and/or "git commit -a")
~/Research/2021 De Rham/DeRhamComputation$ git add -u
~/Research/2021 De Rham/DeRhamComputation$ git commit -[1Pm "przed zmin[1[1Pana w expansion at infty w superelliptic"
[master eda1cca] przed zmiana w expansion at infty w superelliptic
6 files changed, 1599 insertions(+), 62 deletions(-)
rewrite sage/drafty/draft.sage (94%)
~/Research/2021 De Rham/DeRhamComputation$ git push
Username for 'https://git.wmi.amu.edu.pl': jgarnek
Password for 'https://jgarnek@git.wmi.amu.edu.pl':
Enumerating objects: 21, done.
Counting objects: 100% (21/21), done.
Delta compression using up to 4 threads
Compressing objects: 100% (11/11), done.
Writing objects: 100% (11/11), 12.06 KiB | 81.00 KiB/s, done.
Total 11 (delta 9), reused 0 (delta 0)
remote: . Processing 1 references
remote: Processed 1 references in total
To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git
a9d055a..eda1cca master -> master
~/Research/2021 De Rham/DeRhamComputation$ cd sage/; sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
sage: load('tests.sage')
Expansion at infty test:
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [1], in <cell line: 1>()
----> 1 load('tests.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:3, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:7, in <module>
 
NameError: name 'superelliptic' is not defined
[6nsage: load('init.sage')
[6nsage: load('tests.sage')
Expansion at infty test:
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [3], in <cell line: 1>()
----> 1 load('tests.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:3, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:8, in <module>
 
File <string>:120, in expansion_at_infty(self, place, prec)
 
NameError: name 'fct' is not defined
[6nsage: load('init.sage')
[6nsage: load('tests.sage')
Expansion at infty test:
---------------------------------------------------------------------------
UnboundLocalError Traceback (most recent call last)
Input In [5], in <cell line: 1>()
----> 1 load('tests.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:3, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:8, in <module>
 
File <string>:115, in expansion_at_infty(self, place, prec)
 
UnboundLocalError: local variable 'f' referenced before assignment
[6nssage: load('init.sage')
[6nsage: load('tests.sage')
Expansion at infty test:
True
True True
[6nsage: load('init.sage')
Computing 0. basis element
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [8], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:32, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:11, in <module>
 
File <string>:44, in crystalline_cohomology_basis(self, prec, info)
 
File <string>:29, in de_rham_witt_lift(cech_class, prec)
 
File <string>:7, in decomposition_g0_g8(fct, prec)
 
File <string>:107, in coordinates(self, basis, basis_holo, prec)
 
File <string>:79, in serre_duality_pairing(self, fct, prec)
 
File <string>:143, in expansion_at_infty(self, place, prec)
 
TypeError: can't multiply sequence by non-int of type 'sage.rings.laurent_series_ring_element.LaurentSeries'
[6nsage: load('init.sage')
Computing 0. basis element
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [9], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:32, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:11, in <module>
 
File <string>:44, in crystalline_cohomology_basis(self, prec, info)
 
File <string>:29, in de_rham_witt_lift(cech_class, prec)
 
File <string>:7, in decomposition_g0_g8(fct, prec)
 
File <string>:107, in coordinates(self, basis, basis_holo, prec)
 
File <string>:79, in serre_duality_pairing(self, fct, prec)
 
File <string>:143, in expansion_at_infty(self, place, prec)
 
TypeError: can't multiply sequence by non-int of type 'sage.rings.laurent_series_ring_element.LaurentSeries'
[6nsage: C.y.diffn().expansion_at_infty()
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [10], in <cell line: 1>()
----> 1 C.y.diffn().expansion_at_infty()
 
File <string>:143, in expansion_at_infty(self, place, prec)
 
TypeError: can't multiply sequence by non-int of type 'sage.rings.laurent_series_ring_element.LaurentSeries'
[6nsage: load('init.sage')
Traceback (most recent call last):
 
File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
exec(code_obj, self.user_global_ns, self.user_ns)
 
Input In [11] in <cell line: 1>
load('init.sage')
 
File sage/misc/persist.pyx:175 in sage.misc.persist.load
sage.repl.load.load(filename, globals())
 
File /ext/sage/9.7/src/sage/repl/load.py:272 in load
exec(preparse_file(f.read()) + "\n", globals)
 
File <string>:3 in <module>
 
File sage/misc/persist.pyx:175 in sage.misc.persist.load
sage.repl.load.load(filename, globals())
 
File /ext/sage/9.7/src/sage/repl/load.py:272 in load
exec(preparse_file(f.read()) + "\n", globals)
 
File <string>:144
dx_series = C.x_series[place = place]
^
SyntaxError: invalid syntax. Maybe you meant '==' or ':=' instead of '='?
 
[6nsage: load('init.sage')
Computing 0. basis element
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [12], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:32, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:11, in <module>
 
File <string>:44, in crystalline_cohomology_basis(self, prec, info)
 
File <string>:29, in de_rham_witt_lift(cech_class, prec)
 
File <string>:7, in decomposition_g0_g8(fct, prec)
 
File <string>:107, in coordinates(self, basis, basis_holo, prec)
 
File <string>:79, in serre_duality_pairing(self, fct, prec)
 
File <string>:145, in expansion_at_infty(self, place, prec)
 
TypeError: can't multiply sequence by non-int of type 'sage.rings.laurent_series_ring_element.LaurentSeries'
[6nsage: C.y.diffn().expansion_at_infty()
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [13], in <cell line: 1>()
----> 1 C.y.diffn().expansion_at_infty()
 
File <string>:145, in expansion_at_infty(self, place, prec)
 
TypeError: can't multiply sequence by non-int of type 'sage.rings.laurent_series_ring_element.LaurentSeries'
[6nsage: load('init.sage')
Computing 0. basis element
Computing 1. basis element
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [14], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:32, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:11, in <module>
 
File <string>:44, in crystalline_cohomology_basis(self, prec, info)
 
File <string>:32, in de_rham_witt_lift(cech_class, prec)
 
File <string>:37, in decomposition_omega0_omega8(omega, prec)
 
ValueError: (((4*x^50 + x^46 + 2*x^44 + 2*x^40 + 4*x^38 + 4*x^36 + 4*x^34 + x^32 + 2*x^28 + 3*x^22 + 4*x^18 + x^16 + x^14 + x^12 + 3*x^10 + 3*x^6 + 4*x^4 + 1)/(x^30 + 3*x^28 + 3*x^26 + x^24))*y) dx has non zero residue!
[6nsage: C
Superelliptic curve with the equation y^2 = x^3 + x over Finite Field of size 5
[6nsage: 2*C.y*C.y.diffn()
(-2*x^2 + 1) dx
[6nsage: 2*C.y*C.y.diffn().expansion_at_infty()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
File <string>:58, in __mul__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
493 """
--> 494 return self.getattr_from_category(name)
495
 
File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
508
 
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
362 attribute = <object>attr
 
AttributeError: 'sage.rings.laurent_series_ring_element.LaurentSeries' object has no attribute 'form'
 
During handling of the above exception, another exception occurred:
 
AttributeError Traceback (most recent call last)
Input In [17], in <cell line: 1>()
----> 1 Integer(2)*C.y*C.y.diffn().expansion_at_infty()
 
File <string>:63, in __mul__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
493 """
--> 494 return self.getattr_from_category(name)
495
496 cdef getattr_from_category(self, name):
 
File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
505 else:
506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
508
509 def __dir__(self):
 
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
359 dummy_error_message.cls = type(self)
360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
362 attribute = <object>attr
363 # Check for a descriptor (__get__ in Python)
 
AttributeError: 'sage.rings.laurent_series_ring_element.LaurentSeries' object has no attribute 'form'
[6nsage: (2*C.y*C.y.diffn()).expansion_at_infty()
3*t^-6 + 2*t^-2 + 4*t^2 + t^6 + 4*t^10 + 3*t^14 + 2*t^18 + 3*t^22 + 2*t^26 + 3*t^30 + 4*t^34 + t^38 + 4*t^42 + t^46 + 4*t^50 + O(t^94)
[6nsage: (-C.x).expansion_at_infty()
4*t^-2 + t^2 + t^6 + 2*t^10 + 4*t^18 + 2*t^22 + 2*t^26 + 4*t^30 + 2*t^38 + t^42 + t^46 + 2*t^50 + O(t^98)
[6nsage: (-C.dx).expansion_at_infty()
4*t^-2 + t^2 + t^6 + 2*t^10 + 4*t^18 + 2*t^22 + 2*t^26 + 4*t^30 + 2*t^38 + t^42 + t^46 + 2*t^50 + O(t^98)
[6nsage: C.x.diffn().expansion_at_infty()
t^-2 + 4*t^2 + 4*t^6 + 3*t^10 + t^18 + 3*t^22 + 3*t^26 + t^30 + 3*t^38 + 4*t^42 + 4*t^46 + 3*t^50 + O(t^98)
[6nsage: -C.x.diffn().expansion_at_infty()
4*t^-2 + t^2 + t^6 + 2*t^10 + 4*t^18 + 2*t^22 + 2*t^26 + 4*t^30 + 2*t^38 + t^42 + t^46 + 2*t^50 + O(t^98)
[6nsage: C.y.expansion_at_infty(prec = 100)
t^-3 + 4*t + 4*t^5 + 3*t^9 + t^17 + 3*t^21 + 3*t^25 + t^29 + 3*t^37 + 4*t^41 + 4*t^45 + 3*t^49 + O(t^97)
[6nsage: C.x.expansion_at_infty()
t^-2 + 4*t^2 + 4*t^6 + 3*t^10 + t^18 + 3*t^22 + 3*t^26 + t^30 + 3*t^38 + 4*t^42 + 4*t^46 + 3*t^50 + O(t^98)
[6nsage: yy = C.y.expansion_at_infty(prec = 100)
[6nsage: xx = C.x.expansion_at_infty(prec = 100)
[6nsage: yy^2 - (xx^3 - xx)
2*t^-2 + 3*t^2 + 3*t^6 + t^10 + 2*t^18 + t^22 + t^26 + 2*t^30 + t^38 + 3*t^42 + 3*t^46 + t^50 + O(t^94)
[6nsage: C
Superelliptic curve with the equation y^2 = x^3 + x over Finite Field of size 5
[6nsage: yy^2 - (xx^3 + xx)
O(t^94)
[6nsage: C.y.diffn().expansion_at_infty()
4*t^-3 + t^5 + 2*t^9 + 4*t^17 + 2*t^21 + 2*t^25 + 4*t^29 + 2*t^37 + t^41 + t^45 + 2*t^49 + O(t^97)
[6nsage: sage: C.y.diffn()
((-x^2 - 2)/y) dx
[6nsage: C.x.diffn()
1 dx
[6nsage: C.x.diffn().expansion_at_infty()
t^-2 + 4*t^2 + 4*t^6 + 3*t^10 + t^18 + 3*t^22 + 3*t^26 + t^30 + 3*t^38 + 4*t^42 + 4*t^46 + 3*t^50 + O(t^98)
[6nsage: C.dx.expansion_at_infty()
t^-2 + 4*t^2 + 4*t^6 + 3*t^10 + t^18 + 3*t^22 + 3*t^26 + t^30 + 3*t^38 + 4*t^42 + 4*t^46 + 3*t^50 + O(t^98)
[6nsage: load('init.sage')
Computing 0. basis element
Computing 1. basis element
Computing 0. basis element
Computing 1. basis element
Computing 2. basis element
Computing 3. basis element
Computing 4. basis element
Computing 5. basis element
Computing 6. basis element
Computing 7. basis element
Computing 8. basis element
Computing 9. basis element
Computing 10. basis element
Computing 11. basis element
Computing 12. basis element
Computing 13. basis element
[6nsage:
[6nsage:
[6nsage:
[6nsage:
[6nsage:
[6nsage:
[6nsage:
[6nsage:
[6nsage:
[6nsage:
[6nsage:
[6nsage:
[6nsage:
[6nsage:
[6nsage:
[6nsage:
[6nsage:
[6nsage:
[6nsage: B1
[([(1/(x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x))*y] d[x] + V(((2*x^36 - 2*x^34 - x^32 + x^24 + x^22 + 2*x^20 + 2*x^18 - 2*x^16 - 2*x^14 + x^10 + 2*x^8 + x^6 - x^4 - 2*x^2 - 1)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^114 + 3*x^110 + x^108 + 2*x^106 + 3*x^104 + x^100 + x^90 + 3*x^88 + 2*x^84 + 3*x^82 + 2*x^80 + 2*x^78 + 3*x^76 + 2*x^70 + x^66 + 3*x^64 + 4*x^62 + x^60 + x^58 + 3*x^56 + 2*x^48 + 3*x^44 + 3*x^42 + 2*x^36 + x^34 + 2*x^32 + 4*x^30 + 2*x^28 + 4*x^26 + 2*x^24 + 3*x^20 + 2*x^18 + 4*x^16 + 3*x^14 + 4*x^10 + 4*x^8 + 4*x^6 + 4*x^4)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(((2*x^80 + 4*x^76 + x^74 + 3*x^72 + 4*x^68 + 2*x^66 + 4*x^64 + 2*x^60 + x^58 + 3*x^56 + x^54 + 3*x^52 + x^50 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 4*x^38 + 3*x^36 + x^34 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 4*x^20 + x^18 + 2*x^16 + 4*x^14 + x^12 + x^10 + 4*x^8 + 2*x^6 + 4*x^4 + 3)/x^4)*y), [(1/(x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x))*y] d[x] + V(((2*x^36 - 2*x^34 - x^32 + x^24 + x^22 + 2*x^20 + 2*x^18 - 2*x^16 - 2*x^14 + x^10 + 2*x^8 + x^6 - x^4 - 2*x^2 - 1)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^34 + 4*x^32 + 4*x^30 + 3*x^28 + 3*x^26 + 3*x^24 + 2*x^22 + 4*x^20 + 4*x^16 + x^14 + x^12 + 3*x^10 + x^8 + 4*x^6 + 3*x^4 + x^2 + 2)/(x^42 + 2*x^38 + 3*x^34 + 3*x^32 + 4*x^30 + 2*x^28 + 2*x^22 + x^18 + 3*x^12 + 4*x^10 + x^8 + 3*x^6 + x^4))*y])),
([(1/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((x^37 - 2*x^33 - 2*x^31 + 2*x^25 - 2*x^23 + x^21 - 2*x^19 + x^17 - x^15 - x^13 + 2*x^11 - 2*x^9 - 2*x^7 + x^5 + x^3 + x)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^119 + 3*x^115 + x^113 + 2*x^111 + 3*x^109 + x^105 + x^95 + 3*x^93 + 2*x^89 + 3*x^87 + 2*x^85 + 2*x^83 + 3*x^81 + 2*x^75 + x^71 + 3*x^69 + 4*x^67 + x^65 + x^63 + 3*x^61 + 2*x^53 + 3*x^49 + 3*x^47 + 2*x^41 + x^39 + 2*x^37 + 4*x^35 + 2*x^33 + 4*x^31 + 2*x^29 + 3*x^25 + 2*x^23 + 4*x^21 + 3*x^19 + 4*x^15 + 4*x^13 + 4*x^11 + 4*x^9)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(((2*x^88 + 4*x^84 + x^82 + 3*x^80 + 4*x^76 + 2*x^74 + 4*x^72 + 2*x^68 + x^66 + 3*x^64 + x^62 + 3*x^60 + x^58 + 3*x^56 + 2*x^54 + 3*x^52 + x^50 + 4*x^46 + 3*x^44 + x^42 + 2*x^40 + x^38 + 3*x^36 + 2*x^34 + 4*x^28 + x^26 + 2*x^24 + 4*x^22 + x^20 + x^18 + 4*x^16 + 2*x^14 + 4*x^12 + 3*x^8 + 3*x^4 + 4*x^2 + 3)/x^7)*y), [(1/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((x^37 - 2*x^33 - 2*x^31 + 2*x^25 - 2*x^23 + x^21 - 2*x^19 + x^17 - x^15 - x^13 + 2*x^11 - 2*x^9 - 2*x^7 + x^5 + x^3 + x)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^34 + 2*x^32 + 4*x^30 + 3*x^28 + 3*x^24 + 3*x^20 + 4*x^18 + 2*x^16 + x^14 + 4*x^12 + 2*x^10 + 4*x^8 + 2*x^4 + 2*x^2 + 2)/(x^45 + 2*x^41 + 3*x^37 + 3*x^35 + 4*x^33 + 2*x^31 + 2*x^25 + x^21 + 3*x^15 + 4*x^13 + x^11 + 3*x^9 + x^7))*y])),
([(x/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 - x^34 + x^32 - 2*x^30 + 2*x^28 - x^26 - 2*x^24 - 2*x^20 - 2*x^18 - 2*x^16 + x^14 + x^12 + x^10 - 2*x^8 + x^6 + 2*x^4 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^124 + 3*x^120 + x^118 + 2*x^116 + 3*x^114 + x^110 + x^100 + 3*x^98 + 2*x^94 + 3*x^92 + 2*x^90 + 2*x^88 + 3*x^86 + 2*x^80 + x^76 + 3*x^74 + 4*x^72 + x^70 + x^68 + 3*x^66 + 2*x^58 + 3*x^54 + 3*x^52 + 2*x^46 + x^44 + 2*x^42 + 4*x^40 + 2*x^38 + 4*x^36 + 2*x^34 + 3*x^30 + 2*x^28 + 4*x^26 + 3*x^24 + 4*x^20 + 4*x^18 + 4*x^16 + 4*x^14)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(((2*x^92 + 4*x^88 + x^86 + 3*x^84 + 4*x^80 + 2*x^78 + 4*x^76 + 2*x^72 + x^70 + 3*x^68 + x^66 + 3*x^64 + x^62 + 3*x^60 + 2*x^58 + 3*x^56 + x^54 + 4*x^50 + 3*x^48 + x^46 + 2*x^44 + x^42 + 3*x^40 + 2*x^38 + 4*x^32 + x^30 + 2*x^28 + 4*x^26 + x^24 + x^22 + 4*x^20 + 2*x^18 + 4*x^16 + 3*x^12 + 3*x^8 + 4*x^6 + 3*x^4 + 3)/x^6)*y), [(x/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 - x^34 + x^32 - 2*x^30 + 2*x^28 - x^26 - 2*x^24 - 2*x^20 - 2*x^18 - 2*x^16 + x^14 + x^12 + x^10 - 2*x^8 + x^6 + 2*x^4 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^36 + 3*x^34 + 3*x^32 + x^30 + 4*x^28 + 3*x^26 + 2*x^24 + 4*x^22 + 2*x^20 + 4*x^16 + 4*x^14 + 4*x^12 + 3*x^8 + 4*x^4 + x^2 + 2)/(x^44 + 2*x^40 + 3*x^36 + 3*x^34 + 4*x^32 + 2*x^30 + 2*x^24 + x^20 + 3*x^14 + 4*x^12 + x^10 + 3*x^8 + x^6))*y])),
([(x^2/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((x^33 + 2*x^31 + x^29 - x^27 + x^25 - x^21 - x^19 + 2*x^17 + 2*x^15 - x^13 - 2*x^11 + 2*x^9 + x^7 + 2*x^5 + x^3 + 2*x)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^129 + 3*x^125 + x^123 + 2*x^121 + 3*x^119 + x^115 + x^105 + 3*x^103 + 2*x^99 + 3*x^97 + 2*x^95 + 2*x^93 + 3*x^91 + 2*x^85 + x^81 + 3*x^79 + 4*x^77 + x^75 + x^73 + 3*x^71 + 2*x^63 + 3*x^59 + 3*x^57 + 2*x^51 + x^49 + 2*x^47 + 4*x^45 + 2*x^43 + 4*x^41 + 2*x^39 + 3*x^35 + 2*x^33 + 4*x^31 + 3*x^29 + 4*x^25 + 4*x^23 + 4*x^21 + 4*x^19)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 4)/x^7)*y), [(x^2/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((x^33 + 2*x^31 + x^29 - x^27 + x^25 - x^21 - x^19 + 2*x^17 + 2*x^15 - x^13 - 2*x^11 + 2*x^9 + x^7 + 2*x^5 + x^3 + 2*x)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^32 + 3*x^30 + x^28 + 2*x^24 + 3*x^20 + 4*x^18 + 2*x^16 + 4*x^14 + 4*x^12 + 2*x^10 + 2*x^6 + 1)/(x^45 + 2*x^41 + 3*x^37 + 3*x^35 + 4*x^33 + 2*x^31 + 2*x^25 + x^21 + 3*x^15 + 4*x^13 + x^11 + 3*x^9 + x^7))*y])),
([(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^134 + 3*x^130 + x^128 + 2*x^126 + 3*x^124 + x^120 + x^110 + 3*x^108 + 2*x^104 + 3*x^102 + 2*x^100 + 2*x^98 + 3*x^96 + 2*x^90 + x^86 + 3*x^84 + 4*x^82 + x^80 + x^78 + 3*x^76 + 2*x^68 + 3*x^64 + 3*x^62 + 2*x^56 + x^54 + 2*x^52 + 4*x^50 + 2*x^48 + 4*x^46 + 2*x^44 + 3*x^40 + 2*x^38 + 4*x^36 + 3*x^34 + 4*x^30 + 4*x^28 + 4*x^26 + 4*x^24)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 4)/x^2)*y), [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^32 + 3*x^30 + x^28 + 2*x^24 + 3*x^20 + 4*x^18 + 2*x^16 + 4*x^14 + 4*x^12 + 2*x^10 + 2*x^6 + 1)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y])),
([(x^4/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((x^37 - 2*x^33 + x^31 - x^29 - 2*x^27 + 2*x^23 - x^21 + x^19 + 2*x^15 + x^13 - x^11 - x^9 + x^5 + x^3 - x)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^139 + 3*x^135 + x^133 + 2*x^131 + 3*x^129 + x^125 + x^115 + 3*x^113 + 2*x^109 + 3*x^107 + 2*x^105 + 2*x^103 + 3*x^101 + 2*x^95 + x^91 + 3*x^89 + 4*x^87 + x^85 + x^83 + 3*x^81 + 2*x^73 + 3*x^69 + 3*x^67 + 2*x^61 + x^59 + 2*x^57 + 4*x^55 + 2*x^53 + 4*x^51 + 2*x^49 + 3*x^45 + 2*x^43 + 4*x^41 + 3*x^39 + 4*x^35 + 4*x^33 + 4*x^31 + 4*x^29)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(((2*x^106 + 4*x^102 + x^100 + 3*x^98 + 4*x^94 + 2*x^92 + 4*x^90 + 2*x^86 + x^84 + 3*x^82 + x^80 + 3*x^78 + x^76 + 3*x^74 + 2*x^72 + 3*x^70 + x^68 + 4*x^64 + 3*x^62 + x^60 + 2*x^58 + x^56 + 3*x^54 + 2*x^52 + 4*x^46 + x^44 + 2*x^42 + 4*x^40 + x^38 + x^36 + 4*x^34 + 2*x^32 + 4*x^30 + 3*x^26 + 3*x^22 + 4*x^20 + 3*x^18 + 3*x^14 + 2*x^12 + 3*x^10 + 4*x^8 + 3*x^2 + 3)/x^5)*y), [(x^4/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((x^37 - 2*x^33 + x^31 - x^29 - 2*x^27 + 2*x^23 - x^21 + x^19 + 2*x^15 + x^13 - x^11 - x^9 + x^5 + x^3 - x)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^34 + 3*x^32 + 2*x^30 + 2*x^28 + x^26 + x^24 + 4*x^22 + 3*x^20 + x^18 + 2*x^16 + 4*x^14 + x^10 + 3*x^4 + 3*x^2 + 2)/(x^43 + 2*x^39 + 3*x^35 + 3*x^33 + 4*x^31 + 2*x^29 + 2*x^23 + x^19 + 3*x^13 + 4*x^11 + x^9 + 3*x^7 + x^5))*y])),
([(x^5/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-2*x^42 + x^38 - 2*x^36 - 2*x^32 + x^30 + 2*x^28 - 2*x^24 + x^22 - x^20 + 2*x^18 - 2*x^14 - 2*x^10 + 2*x^8 + x^6 - 2*x^4 + 2*x^2 - 1)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^144 + 3*x^140 + x^138 + 2*x^136 + 3*x^134 + x^130 + x^120 + 3*x^118 + 2*x^114 + 3*x^112 + 2*x^110 + 2*x^108 + 3*x^106 + 2*x^100 + x^96 + 3*x^94 + 4*x^92 + x^90 + x^88 + 3*x^86 + 2*x^78 + 3*x^74 + 3*x^72 + 2*x^66 + x^64 + 2*x^62 + 4*x^60 + 2*x^58 + 4*x^56 + 2*x^54 + 3*x^50 + 2*x^48 + 4*x^46 + 3*x^44 + 4*x^40 + 4*x^38 + 4*x^36 + 4*x^34)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(((2*x^112 + 4*x^108 + x^106 + 3*x^104 + 4*x^100 + 2*x^98 + 4*x^96 + 2*x^92 + x^90 + 3*x^88 + x^86 + 3*x^84 + x^82 + 3*x^80 + 2*x^78 + 3*x^76 + x^74 + 4*x^70 + 3*x^68 + x^66 + 2*x^64 + x^62 + 3*x^60 + 2*x^58 + 4*x^52 + x^50 + 2*x^48 + 4*x^46 + x^44 + x^42 + 4*x^40 + 2*x^38 + 4*x^36 + 3*x^32 + 3*x^28 + 4*x^26 + 3*x^24 + 3*x^20 + 2*x^18 + 3*x^16 + 4*x^14 + 3*x^8 + 3*x^6 + 4*x^2 + 3)/x^6)*y), [(x^5/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-2*x^42 + x^38 - 2*x^36 - 2*x^32 + x^30 + 2*x^28 - 2*x^24 + x^22 - x^20 + 2*x^18 - 2*x^14 - 2*x^10 + 2*x^8 + x^6 - 2*x^4 + 2*x^2 - 1)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^36 + x^34 + 4*x^32 + 4*x^28 + 3*x^26 + 2*x^22 + x^20 + 4*x^18 + 2*x^16 + 2*x^14 + x^10 + 3*x^8 + x^6 + 2*x^2 + 2)/(x^44 + 2*x^40 + 3*x^36 + 3*x^34 + 4*x^32 + 2*x^30 + 2*x^24 + x^20 + 3*x^14 + 4*x^12 + x^10 + 3*x^8 + x^6))*y])),
([((3*x^12 + 3*x^8 + 3*x^2 + 4)/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-2*x^77 - x^73 - 2*x^69 - x^67 - x^65 + 2*x^61 + x^59 - 2*x^57 - x^55 - x^49 + 2*x^45 + 2*x^43 + x^41 - x^37 - x^35 + 2*x^33 + x^31 + x^29 - x^25 + x^23 - x^21 + 2*x^17 - 2*x^15 - x^13 + 2*x^11 - x^7 + 2*x^5 - 2*x)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((x^179 + 4*x^175 + 3*x^173 + x^171 + 4*x^169 + 3*x^165 + x^159 + 2*x^155 + 2*x^153 + x^151 + 4*x^147 + 4*x^145 + x^143 + 4*x^141 + 4*x^135 + 4*x^133 + 3*x^131 + x^129 + x^127 + 3*x^125 + 2*x^123 + 4*x^121 + 2*x^119 + x^115 + x^111 + x^107 + 2*x^103 + 4*x^99 + 2*x^95 + x^91 + 3*x^89 + x^87 + 3*x^85 + 4*x^83 + 3*x^81 + x^79 + 3*x^77 + x^73 + 2*x^71 + x^67 + 3*x^65 + x^63 + 4*x^61 + 3*x^59 + 4*x^57 + 2*x^55 + 3*x^51 + 2*x^49 + 3*x^47 + 2*x^45 + x^43 + 3*x^37 + 4*x^33 + 3*x^31 + 2*x^29 + 4*x^25 + 3*x^21 + 4*x^19 + x^15 + x^13 + x^11 + x^9)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), [2/x*y] + V(((x^146 + 2*x^142 + 3*x^140 + 4*x^138 + 2*x^134 + x^132 + 2*x^130 + 2*x^126 + 3*x^124 + x^122 + x^120 + 3*x^118 + 3*x^116 + x^114 + 2*x^112 + x^110 + 3*x^108 + x^106 + 3*x^102 + x^100 + 2*x^96 + 3*x^94 + 4*x^92 + 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + x^80 + x^78 + 2*x^76 + 4*x^72 + x^70 + 4*x^68 + 2*x^66 + x^64 + 3*x^62 + 2*x^60 + 2*x^58 + 2*x^56 + 4*x^52 + x^50 + 2*x^48 + 2*x^46 + x^42 + 2*x^38 + 3*x^36 + 3*x^34 + 2*x^32 + 4*x^30 + 3*x^28 + x^26 + x^24 + 3*x^18 + 4*x^14 + x^12 + 4*x^10 + 2*x^8 + 3*x^6 + 4*x^4 + 3*x^2 + 1)/x^5)*y), [(4/(x^16 + 2*x^12 + 3*x^8 + x^6 + 4*x^4 + 4*x^2))*y] d[x] + V(((x^40 - x^38 + 2*x^34 - 2*x^32 - 2*x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - 2*x^16 + x^14 - x^12 - 2*x^10 - 2*x^8 + 2*x^6 - 2*x^4 - x^2 + 2)/(x^41*y + 2*x^37*y - 2*x^33*y - 2*x^31*y - x^29*y + 2*x^27*y + 2*x^21*y + x^17*y - 2*x^11*y - x^9*y + x^7*y - 2*x^5*y + x^3*y)) dx) + dV([((2*x^34 + x^30 + x^28 + 2*x^26 + 3*x^24 + x^20 + 3*x^18 + x^16 + 4*x^14 + x^12 + x^10 + 4*x^8 + 2*x^6 + 4*x^2 + 4)/(x^43 + 2*x^39 + 3*x^35 + 3*x^33 + 4*x^31 + 2*x^29 + 2*x^23 + x^19 + 3*x^13 + 4*x^11 + x^9 + 3*x^7 + x^5))*y])),
([((x^12 + 4*x^8 + 4*x^4 + x^2 + 1)/(x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x))*y] d[x] + V(((2*x^68 + 2*x^62 + x^60 - x^58 - 2*x^56 + x^54 - 2*x^52 + 2*x^50 - 2*x^42 - x^40 - 2*x^36 + 2*x^34 - x^32 + x^30 + 2*x^28 + x^26 + x^22 - 2*x^20 + 2*x^18 + 2*x^16 - 2*x^14 - 2*x^12 + x^10 + x^8 - x^6 + 2*x^4 + 1)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^174 + 3*x^170 + x^168 + 2*x^166 + 3*x^164 + x^160 + 3*x^154 + 3*x^150 + 2*x^148 + 3*x^146 + 4*x^144 + 3*x^142 + x^140 + 2*x^138 + 3*x^136 + 3*x^134 + 3*x^130 + x^128 + 4*x^126 + x^122 + x^120 + 2*x^116 + x^110 + x^106 + x^104 + x^102 + 4*x^100 + x^96 + 3*x^94 + x^86 + 3*x^84 + x^82 + x^80 + 3*x^78 + 3*x^76 + 2*x^72 + 3*x^70 + x^68 + 4*x^66 + 2*x^64 + x^62 + 3*x^60 + x^58 + 2*x^56 + 4*x^54 + x^52 + 2*x^50 + x^48 + 4*x^46 + 3*x^44 + x^40 + 2*x^36 + 2*x^32 + 3*x^30 + 4*x^26 + x^24 + 2*x^20 + x^18 + 3*x^16 + 2*x^14 + 4*x^10 + 4*x^8 + 4*x^6 + 4*x^4)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), [2/x^2*y] + V(((2*x^142 + 4*x^138 + x^136 + 3*x^134 + 4*x^130 + 2*x^128 + 4*x^126 + x^120 + 4*x^118 + x^112 + 4*x^110 + 4*x^106 + x^104 + x^102 + 3*x^100 + x^98 + 4*x^96 + x^94 + 2*x^92 + x^90 + 2*x^88 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + 2*x^76 + 4*x^74 + x^72 + 3*x^70 + 3*x^68 + x^66 + 2*x^64 + 2*x^62 + 4*x^60 + 3*x^58 + 3*x^56 + 4*x^54 + 4*x^52 + 3*x^50 + 3*x^48 + 3*x^46 + 2*x^44 + 4*x^42 + x^40 + 3*x^38 + x^36 + 3*x^34 + 3*x^32 + 4*x^28 + 3*x^26 + 3*x^24 + 3*x^22 + x^18 + 3*x^16 + 4*x^14 + 4*x^6 + 3*x^4 + 4)/x^6)*y), [(2/(x^17 + 2*x^13 + 3*x^9 + x^7 + 4*x^5 + 4*x^3))*y] d[x] + V(((x^44 - x^42 - 2*x^40 - x^36 + 2*x^34 - x^32 - x^28 + x^26 - 2*x^24 + x^20 + 2*x^18 + x^12 - 2*x^10 - x^8 + 2*x^6 - 2*x^4 - 1)/(x^46*y + 2*x^42*y - 2*x^38*y - 2*x^36*y - x^34*y + 2*x^32*y + 2*x^26*y + x^22*y - 2*x^16*y - x^14*y + x^12*y - 2*x^10*y + x^8*y)) dx) + dV([((4*x^34 + 3*x^32 + 3*x^30 + 2*x^28 + 2*x^26 + 4*x^24 + 3*x^22 + x^20 + x^14 + 2*x^10 + 3*x^6 + 2*x^2 + 2)/(x^42 + 2*x^38 + 3*x^34 + 3*x^32 + 4*x^30 + 2*x^28 + 2*x^22 + x^18 + 3*x^12 + 4*x^10 + x^8 + 3*x^6 + x^4))*y])),
([((4*x^10 + 3*x^2 + 4)/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^67 + x^63 + 2*x^59 + 2*x^57 - 2*x^55 - 2*x^53 - 2*x^49 + x^47 - x^45 - 2*x^43 + x^41 - 2*x^39 + 2*x^37 + 2*x^35 + 2*x^33 - 2*x^27 - x^25 - x^23 - 2*x^21 + x^17 + 2*x^11 - x^9 + 2*x^5 + 2*x^3)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^169 + 2*x^165 + 4*x^163 + 3*x^161 + 2*x^159 + 4*x^155 + 4*x^145 + 2*x^143 + 3*x^139 + 2*x^137 + 3*x^135 + 3*x^133 + 2*x^131 + x^129 + 2*x^125 + 3*x^123 + 4*x^119 + x^117 + 4*x^115 + 3*x^113 + 2*x^109 + 2*x^105 + 2*x^103 + 3*x^99 + x^97 + 3*x^93 + 2*x^91 + 2*x^89 + x^83 + x^81 + 2*x^79 + 2*x^77 + 3*x^75 + x^73 + 4*x^71 + 4*x^69 + x^67 + x^63 + 3*x^61 + 4*x^57 + 3*x^53 + x^51 + 3*x^47 + 2*x^45 + x^43 + 3*x^37 + 4*x^33 + 3*x^31 + 2*x^29 + 4*x^25 + 3*x^21 + 4*x^19 + x^15 + x^13 + x^11 + x^9)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), [2/x^3*y] + V(((3*x^138 + x^134 + 4*x^132 + 2*x^130 + x^126 + 3*x^124 + x^122 + 3*x^118 + 4*x^116 + 2*x^114 + 4*x^112 + 2*x^110 + 4*x^108 + 2*x^106 + 3*x^104 + 2*x^102 + 4*x^100 + x^98 + x^96 + 4*x^94 + 2*x^92 + 2*x^90 + 2*x^88 + 4*x^86 + x^82 + 2*x^80 + 2*x^78 + 3*x^76 + 3*x^70 + 4*x^66 + x^64 + 4*x^62 + x^58 + 4*x^56 + 4*x^54 + x^52 + 2*x^50 + 3*x^48 + 2*x^46 + x^44 + x^42 + 4*x^40 + x^38 + x^34 + 4*x^32 + 3*x^30 + 3*x^26 + 2*x^22 + 3*x^20 + 3*x^18 + x^16 + x^14 + 4*x^12 + 2*x^10 + 2*x^8 + 4*x^6 + 3*x^4 + 2*x^2 + 4)/x^7)*y), [(2/(x^16 + 2*x^12 + 3*x^8 + x^6 + 4*x^4 + 4*x^2))*y] d[x] + V(((2*x^44 + x^36 + x^34 - 2*x^32 - x^30 + x^24 + x^22 + 2*x^20 - 2*x^18 - 2*x^16 - x^14 - 2*x^12 - 2*x^10 + x^6 + x^4 - x^2 - 1)/(x^51*y + 2*x^47*y - 2*x^43*y - 2*x^41*y - x^39*y + 2*x^37*y + 2*x^31*y + x^27*y - 2*x^21*y - x^19*y + x^17*y - 2*x^15*y + x^13*y)) dx) + dV([((3*x^40 + 4*x^38 + 2*x^36 + x^34 + 2*x^32 + 2*x^30 + 3*x^26 + 2*x^24 + 3*x^22 + x^20 + x^18 + x^14 + x^12 + x^10 + 2*x^8 + 4*x^2 + 4)/(x^49 + 2*x^45 + 3*x^41 + 3*x^39 + 4*x^37 + 2*x^35 + 2*x^29 + x^25 + 3*x^19 + 4*x^17 + x^15 + 3*x^13 + x^11))*y])),
([(2/(x^5 + 4*x))*y] d[x] + V(((x^32 - x^24 + 2*x^22 + x^18 + x^16 - x^14 + x^12 - 2*x^10 + x^6 - 2*x^4 + 2*x^2 - 1)/(x^8*y - 2*x^4*y + y)) dx) + dV([((4*x^134 + 2*x^128 + 4*x^126 + x^124 + 4*x^122 + x^120 + 3*x^118 + 2*x^116 + 3*x^114 + x^112 + x^110 + 4*x^108 + 3*x^104 + 2*x^102 + 4*x^98 + 2*x^96 + x^94 + x^92 + 4*x^88 + x^84 + 3*x^82 + 4*x^80 + 2*x^78 + 3*x^76 + 3*x^74 + x^70 + 4*x^68 + 3*x^66 + 2*x^64 + x^62 + 2*x^60 + 3*x^58 + 4*x^54 + 3*x^48 + 4*x^46 + 3*x^44 + x^42 + 2*x^38 + 3*x^36 + 3*x^34 + 3*x^30 + 4*x^28 + 4*x^26 + x^22 + 3*x^18 + x^14 + 2*x^8 + 4*x^6 + 3*x^4)/(x^8 + 3*x^4 + 1))*y]), [2/x^4*y] + V(((4*x^132 + 3*x^128 + 2*x^126 + x^124 + 3*x^120 + 4*x^118 + 3*x^116 + x^112 + 2*x^110 + 3*x^106 + 4*x^104 + 2*x^102 + x^98 + 2*x^94 + x^92 + 4*x^90 + 2*x^88 + 3*x^84 + 2*x^82 + 2*x^80 + 3*x^78 + 3*x^76 + 2*x^74 + 2*x^72 + x^70 + 2*x^68 + 4*x^66 + 4*x^62 + 4*x^60 + x^58 + x^56 + 3*x^54 + 2*x^52 + 3*x^48 + 3*x^44 + 3*x^42 + 4*x^40 + x^38 + 2*x^36 + 2*x^34 + 3*x^32 + 3*x^30 + 2*x^28 + 3*x^26 + 3*x^22 + 4*x^20 + 3*x^18 + x^16 + 3*x^14 + 2*x^12 + 3*x^10 + 3*x^8 + 4*x^6 + x^4 + 2)/x^6)*y), [(3/(x^19 + 2*x^15 + 3*x^11 + x^9 + 4*x^7 + 4*x^5))*y] d[x] + V(((2*x^54 - x^52 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 + 2*x^40 - 2*x^36 - 2*x^32 - x^30 - 2*x^28 - 2*x^26 + x^22 + 2*x^20 + 2*x^18 + x^16 - x^14 + x^12 + x^10 + 2*x^8 - x^4 - 2*x^2 - 1)/(x^56*y + 2*x^52*y - 2*x^48*y - 2*x^46*y - x^44*y + 2*x^42*y + 2*x^36*y + x^32*y - 2*x^26*y - x^24*y + x^22*y - 2*x^20*y + x^18*y)) dx) + dV([((3*x^46 + 4*x^44 + x^42 + 2*x^40 + 3*x^38 + 4*x^34 + x^32 + x^28 + x^26 + 3*x^24 + 2*x^22 + 2*x^20 + 3*x^18 + 2*x^16 + 3*x^14 + 2*x^12 + 4*x^6 + 4*x^4 + 4*x^2 + 4)/(x^54 + 2*x^50 + 3*x^46 + 3*x^44 + 4*x^42 + 2*x^40 + 2*x^34 + x^30 + 3*x^24 + 4*x^22 + x^20 + 3*x^18 + x^16))*y])),
([((2*x^4 + 1)/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((x^57 - 2*x^53 - 2*x^49 + x^47 - x^45 + x^43 - 2*x^41 - x^37 + 2*x^35 - 2*x^33 - x^31 + x^29 + 2*x^23 + x^21 + x^19 + x^17 - x^15 - x^13 - 2*x^11 + x^9 + x^7 + x^5 - 2*x^3 + x)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^139 + x^135 + 2*x^133 + 4*x^131 + x^129 + 2*x^125 + 2*x^119 + 2*x^113 + 2*x^111 + 2*x^109 + x^107 + 4*x^103 + x^101 + 3*x^93 + 2*x^91 + 3*x^89 + x^87 + 4*x^85 + 4*x^83 + 4*x^81 + 2*x^75 + 4*x^73 + x^71 + 4*x^69 + x^65 + x^63 + 2*x^61 + 2*x^59 + 4*x^57 + 3*x^55 + x^53 + 3*x^51 + 2*x^49 + 3*x^47 + x^45 + 4*x^43 + 2*x^39 + 2*x^37 + 2*x^35 + 2*x^31 + 3*x^25 + 2*x^23 + 4*x^21 + 3*x^19 + 4*x^15 + 4*x^13 + 4*x^11 + 4*x^9)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), [2/x^5*y] + V(((4*x^106 + 3*x^102 + 2*x^100 + x^98 + 3*x^94 + 4*x^92 + 3*x^90 + x^86 + 2*x^84 + 3*x^80 + 4*x^78 + 2*x^76 + x^72 + 2*x^68 + 2*x^66 + 4*x^64 + 4*x^62 + 3*x^60 + 2*x^58 + 3*x^56 + 4*x^54 + x^52 + 3*x^50 + x^48 + 3*x^46 + x^44 + 2*x^42 + 4*x^40 + 4*x^38 + 3*x^36 + x^34 + x^32 + 3*x^30 + x^24 + 3*x^22 + 2*x^20 + 2*x^18 + x^16 + x^12 + 3*x^8 + x^6 + 4)/x^5)*y), [((3*x^2 + 1)/(x^20 + 2*x^16 + 3*x^12 + x^10 + 4*x^8 + 4*x^6))*y] d[x] + V(((-x^60 + 2*x^56 - x^54 - x^52 - 2*x^50 + x^48 - 2*x^46 - x^44 + x^42 + x^40 - x^34 - 2*x^32 + x^30 - 2*x^24 - x^22 + x^20 - x^18 + 2*x^16 - 2*x^14 - x^12 + x^10 - 2*x^6 + x^4 + x^2 + 1)/(x^61*y + 2*x^57*y - 2*x^53*y - 2*x^51*y - x^49*y + 2*x^47*y + 2*x^41*y + x^37*y - 2*x^31*y - x^29*y + x^27*y - 2*x^25*y + x^23*y)) dx) + dV([((3*x^50 + 4*x^46 + x^44 + x^42 + x^40 + 2*x^38 + 4*x^36 + 2*x^34 + 4*x^32 + 4*x^30 + 4*x^28 + x^26 + 3*x^18 + 3*x^16 + x^14 + 3*x^12 + 2*x^10 + 4*x^6 + 4*x^4 + 4*x^2 + 4)/(x^59 + 2*x^55 + 3*x^51 + 3*x^49 + 4*x^47 + 2*x^45 + 2*x^39 + x^35 + 3*x^29 + 4*x^27 + x^25 + 3*x^23 + x^21))*y])),
([((3*x^7 + 3*x^3)/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((x^52 - 2*x^48 + x^44 - 2*x^40 + x^38 - x^36 + x^30 - x^28 + 2*x^26 + x^24 + x^22 + x^20 - 2*x^18 + 2*x^16 + 2*x^14 + 2*x^12 - 2*x^10 - 2*x^8 + x^6 + x^4 + 1)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((x^154 + 4*x^150 + 3*x^148 + x^146 + 4*x^144 + 3*x^140 + x^134 + 2*x^130 + 2*x^128 + x^126 + 4*x^122 + 4*x^120 + x^118 + 4*x^116 + 4*x^110 + 4*x^108 + 3*x^106 + x^102 + 4*x^100 + 4*x^98 + 3*x^96 + x^90 + x^88 + 3*x^86 + 3*x^84 + x^82 + 3*x^80 + 3*x^78 + 3*x^74 + x^72 + 2*x^70 + 2*x^68 + 2*x^66 + 4*x^62 + 4*x^60 + x^58 + 3*x^56 + 2*x^54 + x^52 + 4*x^50 + 3*x^48 + 4*x^46 + 3*x^44 + 4*x^40 + x^38 + 2*x^36 + 4*x^34 + 2*x^30 + 2*x^28 + 2*x^26 + 2*x^24)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), [2/x^6*y] + V(((x^120 + 2*x^116 + 3*x^114 + 4*x^112 + 2*x^108 + x^106 + 2*x^104 + 2*x^100 + 3*x^98 + x^96 + x^94 + 3*x^92 + 3*x^90 + x^88 + 2*x^86 + x^84 + 3*x^82 + x^80 + 3*x^76 + x^74 + x^70 + 3*x^68 + 2*x^66 + 4*x^64 + 3*x^62 + 2*x^60 + 4*x^52 + x^50 + x^48 + 2*x^46 + 2*x^44 + x^40 + 3*x^38 + 4*x^34 + 2*x^32 + 3*x^30 + x^28 + 2*x^26 + x^24 + 2*x^22 + 4*x^20 + 3*x^16 + x^14 + 4*x^12 + 2*x^10 + 3*x^8 + 3*x^6 + 2*x^4 + 2)/x^4)*y), [((2*x^2 + 4)/(x^19 + 4*x^17 + 3*x^15 + 2*x^13 + x^11 + 4*x^7))*y] d[x] + V(((-x^60 - 2*x^58 - 2*x^56 + x^54 - x^52 - x^50 + x^48 - x^46 + x^40 - 2*x^38 - 2*x^36 - x^30 - 2*x^28 + 2*x^24 + 2*x^22 + x^18 + x^14 - 2*x^12 + 2*x^10 - x^8 + 2*x^6 - x^4 - 2*x^2 + 1)/(x^62*y - x^60*y - 2*x^58*y + 2*x^56*y + x^54*y + 2*x^52*y + 2*x^50*y + 2*x^42*y - 2*x^40*y - 2*x^38*y + 2*x^36*y - 2*x^34*y - x^30*y + 2*x^28*y + x^26*y)) dx) + dV([((x^52 + x^46 + 2*x^44 + 2*x^42 + 3*x^40 + x^38 + 3*x^36 + x^34 + 3*x^30 + 3*x^28 + 3*x^26 + x^24 + 2*x^22 + 2*x^20 + 4*x^18 + 4*x^16 + 3*x^14 + 2*x^12 + 4*x^10 + 3*x^8 + 2*x^6 + 3*x^4 + x^2 + 4)/(x^60 + 3*x^58 + 2*x^54 + 4*x^52 + 3*x^50 + 4*x^48 + x^46 + 4*x^44 + x^42 + x^40 + 2*x^38 + x^36 + x^34 + 2*x^32 + 3*x^30 + x^28 + x^26))*y])),
([(x^2/(x^10 + 3*x^6 + x^2 + 1))*y] d[x] + V(((-2*x^39 + 2*x^35 - 2*x^31 + 2*x^29 - x^27 + x^25 + 2*x^23 + x^19 - x^9 + 2*x^7 + 2*x^5 - x^3 - 2*x)/(x^30*y - x^26*y - 2*x^20*y - 2*x^16*y - 2*x^12*y + 2*x^10*y - 2*x^8*y - 2*x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^141 + 2*x^137 + x^135 + 4*x^133 + x^129 + 3*x^125 + 3*x^121 + x^117 + 2*x^115 + 2*x^113 + 3*x^111 + x^109 + 2*x^105 + 3*x^101 + 2*x^95 + 3*x^93 + 2*x^89 + 2*x^87 + 4*x^83 + 3*x^81 + x^79 + 4*x^77 + 4*x^73 + 4*x^71 + 3*x^69 + 2*x^67 + x^65 + 4*x^63 + 3*x^59 + 3*x^57 + 2*x^55 + 4*x^49 + x^47 + 4*x^43 + 3*x^41 + x^37 + 3*x^35 + 4*x^33 + 3*x^31 + 2*x^29 + 3*x^25 + 3*x^23 + x^21 + x^19)/(x^30 + 4*x^26 + 3*x^20 + 3*x^16 + 3*x^12 + 2*x^10 + 3*x^8 + 3*x^4 + 3*x^2 + 1))*y]), [2/x^7*y] + V(((2*x^118 + 4*x^114 + x^112 + 3*x^110 + 4*x^106 + 2*x^104 + 4*x^102 + x^96 + 4*x^94 + x^88 + 4*x^86 + 4*x^82 + x^80 + 3*x^78 + 3*x^76 + 4*x^70 + 2*x^62 + 4*x^60 + 4*x^58 + 2*x^56 + 4*x^54 + 3*x^52 + 4*x^50 + x^46 + 4*x^42 + 4*x^38 + 4*x^36 + x^34 + 2*x^30 + 4*x^28 + 4*x^26 + 4*x^22 + 4*x^20 + 2*x^18 + 4*x^12 + 2*x^10 + 4*x^8 + 2*x^4 + 3*x^2 + 2)/x^7)*y), [((x^6 + 4*x^4 + 4*x^2 + 2)/(x^22 + 2*x^18 + 3*x^14 + x^12 + 4*x^10 + 4*x^8))*y] d[x] + V(((x^70 + 2*x^68 - x^66 - 2*x^64 - x^62 - 2*x^60 + x^56 + 2*x^54 - x^52 - 2*x^50 - x^48 - 2*x^46 + 2*x^44 - 2*x^42 + x^40 - x^38 - 2*x^36 - x^34 - 2*x^32 + x^30 + x^28 + x^26 - 2*x^24 + 2*x^20 + x^14 + 2*x^12 + x^10 - x^8 + x^6 - x^4 - x^2 + 2)/(x^71*y + 2*x^67*y - 2*x^63*y - 2*x^61*y - x^59*y + 2*x^57*y + 2*x^51*y + x^47*y - 2*x^41*y - x^39*y + x^37*y - 2*x^35*y + x^33*y)) dx) + dV([((x^60 + 2*x^56 + 4*x^54 + 4*x^52 + 2*x^50 + 3*x^46 + 2*x^44 + 4*x^40 + 3*x^38 + 3*x^36 + 4*x^34 + 2*x^32 + 4*x^28 + 2*x^26 + x^24 + 2*x^22 + 4*x^20 + 2*x^16 + x^14 + 3*x^12 + 2*x^10 + 4*x^6 + 4*x^4 + 4*x^2 + 4)/(x^69 + 2*x^65 + 3*x^61 + 3*x^59 + 4*x^57 + 2*x^55 + 2*x^49 + x^45 + 3*x^39 + 4*x^37 + x^35 + 3*x^33 + x^31))*y]))]
[6nsage:
[6nsage:
[6nsage:
[6nsage:
[6nsage:
[6nsage:
sage: for b in B:
....: print(b.regular_form())
....:
( [3*x*y] d[x] + [3*x^2 + 2] d[y] + V((0) dy) + dV((x^16 + 2*x^14 + x^12 + 2*x^6 + 4*x^4 + 2*x^2)*y), V((4*x^14 + x^12 + 3*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 4)*y) )
( [3*x^2*y] d[x] + [3*x^3 + 2*x] d[y] + V((0) dy) + dV((3*x^21 + x^19 + 3*x^17)*y), [2/x*y] + V(((4*x^20 + x^18 + 3*x^16 + 3*x^14 + x^12 + x^10 + 3*x^8 + 4*x^6 + 4*x^4 + 3*x^2 + 4)/x)*y) )
sage: bor b in B1:
....:
....:
Input In [38]
bor b in B1:
^
SyntaxError: invalid syntax
 
sage: for b in B1:
....: print(b.regular_form())
....:
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [39], in <cell line: 1>()
1 for b in B1:
----> 2 print(b.regular_form())
 
File <string>:90, in regular_drw_cech(cocycle)
 
File <string>:83, in regular_drw_form(omega)
 
File <string>:12, in decomposition_g0_p2th_power(fct)
 
File <string>:5, in decomposition_g0_pth_power(fct)
 
File <string>:51, in int(self)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
1329 normalize(x._numer, x._denom, self.p)
1330 if nmod_poly_degree(x._denom) != 0:
-> 1331 raise ValueError("not integral")
1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:
 
ValueError: not integral
[6nsage: sage: B1[0].omega0.regular_form()
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [40], in <cell line: 1>()
----> 1 B1[Integer(0)].omega0.regular_form()
 
File <string>:83, in regular_drw_form(omega)
 
File <string>:12, in decomposition_g0_p2th_power(fct)
 
File <string>:5, in decomposition_g0_pth_power(fct)
 
File <string>:51, in int(self)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
1329 normalize(x._numer, x._denom, self.p)
1330 if nmod_poly_degree(x._denom) != 0:
-> 1331 raise ValueError("not integral")
1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:
 
ValueError: not integral
[6nsage: autom(B1[0]).coordinates()
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
File <string>:60, in __mul__(self, other)
 
File <string>:14, in __init__(self, C, g)
 
File <string>:253, in reduction(C, g)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
637 try:
--> 638 return self._element_class(self, x, ring_one, coerce=coerce)
639 except (TypeError, ValueError):
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
113 if coerce:
--> 114 self.__numerator = parent.ring()(numerator)
115 self.__denominator = parent.ring()(denominator)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
1002 try:
-> 1003 return self(str(element))
1004 except TypeError:
 
File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
193 return super().__repr__()
--> 194 result = reprfunc()
195 if isinstance(result, str):
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_()
2689 """
-> 2690 return self._repr()
2691
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2656, in sage.rings.polynomial.polynomial_element.Polynomial._repr()
2655 s += " + "
-> 2656 x = y = repr(x)
2657 if y.find("-") == 0:
 
File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
193 return super().__repr__()
--> 194 result = reprfunc()
195 if isinstance(result, str):
 
File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:338, in sage.rings.fraction_field_FpT.FpTElement._repr_()
337 if nmod_poly_degree(self._denom) == 0 and nmod_poly_get_coeff_ui(self._denom, 0) == 1:
--> 338 return repr(self.numer())
339 else:
 
File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
193 return super().__repr__()
--> 194 result = reprfunc()
195 if isinstance(result, str):
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_()
2689 """
-> 2690 return self._repr()
2691
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2656, in sage.rings.polynomial.polynomial_element.Polynomial._repr()
2655 s += " + "
-> 2656 x = y = repr(x)
2657 if y.find("-") == 0:
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
 
During handling of the above exception, another exception occurred:
 
AttributeError Traceback (most recent call last)
Input In [41], in <cell line: 1>()
----> 1 autom(B1[Integer(0)]).coordinates()
 
File <string>:97, in coordinates(self, basis, prec)
 
File <string>:44, in crystalline_cohomology_basis(self, prec, info)
 
File <string>:25, in de_rham_witt_lift(cech_class, prec)
 
File <string>:15, in de_rham_witt_lift_form8(omega)
 
File <string>:90, in diffn(self, dy_w)
 
File <string>:99, in diffn(self, dy_w)
 
File <string>:73, in diffn(self, dy_w)
 
File <string>:177, in dy_w(C)
 
File <string>:149, in auxilliary_derivative(P)
 
File <string>:55, in __rmul__(self, other)
 
File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
1962 return y
1963
-> 1964 return coercion_model.bin_op(left, right, operator.mul)
1965
1966 cpdef _mul_(self, right):
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:55, in __rmul__(self, other)
 
File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
1962 return y
1963
-> 1964 return coercion_model.bin_op(left, right, operator.mul)
1965
1966 cpdef _mul_(self, right):
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
[... skipping similar frames: __rmul__ at line 55 (4 times), sage.rings.integer.Integer.__mul__ at line 1964 (3 times), sage.structure.coerce.CoercionModel.bin_op at line 1242 (3 times)]
 
File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
1962 return y
1963
-> 1964 return coercion_model.bin_op(left, right, operator.mul)
1965
1966 cpdef _mul_(self, right):
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:55, in __rmul__(self, other)
 
File <string>:84, in __add__(self, other)
 
File <string>:31, in __add__(self, other)
 
File <string>:63, in __mul__(self, other)
 
AttributeError: 'superelliptic_function' object has no attribute 'form'
[6nsage: autom(B1[0]).coordinates(basis = B1)
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [42], in <cell line: 1>()
----> 1 autom(B1[Integer(0)]).coordinates(basis = B1)
 
File <string>:26, in autom(self)
 
File <string>:23, in autom(self)
 
File <string>:73, in diffn(self, dy_w)
 
File <string>:177, in dy_w(C)
 
File <string>:82, in __pow__(self, exp)
 
File <string>:14, in __init__(self, C, g)
 
File <string>:253, in reduction(C, g)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
636 ring_one = self.ring().one()
637 try:
--> 638 return self._element_class(self, x, ring_one, coerce=coerce)
639 except (TypeError, ValueError):
640 pass
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
112 FieldElement.__init__(self, parent)
113 if coerce:
--> 114 self.__numerator = parent.ring()(numerator)
115 self.__denominator = parent.ring()(denominator)
116 else:
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
1001
1002 try:
-> 1003 return self(str(element))
1004 except TypeError:
1005 pass
 
File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
192 except AttributeError:
193 return super().__repr__()
--> 194 result = reprfunc()
195 if isinstance(result, str):
196 return result
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:482, in sage.rings.fraction_field_element.FractionFieldElement._repr_()
480 if self.is_zero():
481 return "0"
--> 482 s = "%s" % self.__numerator
483 if self.__denominator != 1:
484 denom_string = str( self.__denominator )
 
File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
192 except AttributeError:
193 return super().__repr__()
--> 194 result = reprfunc()
195 if isinstance(result, str):
196 return result
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_()
2688 NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3
2689 """
-> 2690 return self._repr()
2691
2692 def _latex_(self, name=None):
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2667, in sage.rings.polynomial.polynomial_element.Polynomial._repr()
2665 else:
2666 var = ""
-> 2667 s += "%s%s"%(x,var)
2668 s = s.replace(" + -", " - ")
2669 s = re.sub(r' 1(\.0+)?\*',' ', s)
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsagsage: OM = B[0].omega0
sage: om = OM.r()
sage: OM - de_rham_witt_lift_form0(OM)
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [45], in <cell line: 1>()
----> 1 OM - de_rham_witt_lift_form0(OM)
 
File <string>:4, in de_rham_witt_lift_form0(omega)
 
File <string>:80, in regular_drw_form(omega)
 
File <string>:99, in diffn(self, dy_w)
 
File <string>:73, in diffn(self, dy_w)
 
File <string>:177, in dy_w(C)
 
File /ext/sage/9.7/src/sage/rings/rational.pyx:2414, in sage.rings.rational.Rational.__mul__()
2412 return x
2413
-> 2414 return coercion_model.bin_op(left, right, operator.mul)
2415
2416 cpdef _mul_(self, right):
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:48, in __rmul__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
1526 if not err:
1527 return (<Element>right)._mul_long(value)
-> 1528 return coercion_model.bin_op(left, right, mul)
1529 except TypeError:
1530 return NotImplemented
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:43, in __rmul__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
1526 if not err:
1527 return (<Element>right)._mul_long(value)
-> 1528 return coercion_model.bin_op(left, right, mul)
1529 except TypeError:
1530 return NotImplemented
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:43, in __rmul__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
1526 if not err:
1527 return (<Element>right)._mul_long(value)
-> 1528 return coercion_model.bin_op(left, right, mul)
1529 except TypeError:
1530 return NotImplemented
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:43, in __rmul__(self, other)
 
File <string>:31, in __add__(self, other)
 
File <string>:82, in __pow__(self, exp)
 
File <string>:14, in __init__(self, C, g)
 
File <string>:261, in reduction(C, g)
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2321, in sage.rings.polynomial.polynomial_element.Polynomial.__truediv__()
2319 # Same parents => bypass coercion
2320 if have_same_parent(left, right):
-> 2321 return (<Element>left)._div_(right)
2322
2323 # Try division of polynomial by a scalar
 
File /ext/sage/9.7/src/sage/structure/element.pyx:2739, in sage.structure.element.RingElement._div_()
2737 except AttributeError:
2738 raise bin_op_exception('/', self, other)
-> 2739 return frac(self, other)
2740
2741 def __divmod__(self, other):
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:899, in sage.structure.parent.Parent.__call__()
897 return mor._call_(x)
898 else:
--> 899 return mor._call_with_args(x, args, kwds)
900
901 raise TypeError(_LazyString("No conversion defined from %s to %s", (R, self), {}))
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:173, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args()
171 else:
172 if len(kwds) == 0:
--> 173 return C._element_constructor(x, *args)
174 else:
175 return C._element_constructor(x, *args, **kwds)
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:648, in FractionField_generic._element_constructor_(self, x, y, coerce)
646 x, y = x.numerator() * y.denominator(), y.numerator() * x.denominator()
647 try:
--> 648 return self._element_class(self, x, y, coerce=coerce)
649 except (TypeError, ValueError):
650 pass
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: OM - de_rham_witt_lift_form0(om)
V(((x^18 - x^16 + 2*x^14 + 2*x^12 + x^8 - 2*x^6 + 2*x^4 + 2*x^2 + 2)/y) dx)
[6nsage: OM.regular_form()
[3*x*y] d[x] + [3*x^2 + 2] d[y] + V((0) dy) + dV((x^16 + 2*x^14 + x^12 + 2*x^6 + 4*x^4 + 2*x^2)*y)
[6nsage: OM = B1[0].omega0
[6nsage: OM.regular_form()
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [49], in <cell line: 1>()
----> 1 OM.regular_form()
 
File <string>:83, in regular_drw_form(omega)
 
File <string>:12, in decomposition_g0_p2th_power(fct)
 
File <string>:5, in decomposition_g0_pth_power(fct)
 
File <string>:51, in int(self)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
1329 normalize(x._numer, x._denom, self.p)
1330 if nmod_poly_degree(x._denom) != 0:
-> 1331 raise ValueError("not integral")
1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:
 
ValueError: not integral
[6nsage: OM
[(1/(x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x))*y] d[x] + V(((2*x^36 - 2*x^34 - x^32 + x^24 + x^22 + 2*x^20 + 2*x^18 - 2*x^16 - 2*x^14 + x^10 + 2*x^8 + x^6 - x^4 - 2*x^2 - 1)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^114 + 3*x^110 + x^108 + 2*x^106 + 3*x^104 + x^100 + x^90 + 3*x^88 + 2*x^84 + 3*x^82 + 2*x^80 + 2*x^78 + 3*x^76 + 2*x^70 + x^66 + 3*x^64 + 4*x^62 + x^60 + x^58 + 3*x^56 + 2*x^48 + 3*x^44 + 3*x^42 + 2*x^36 + x^34 + 2*x^32 + 4*x^30 + 2*x^28 + 4*x^26 + 2*x^24 + 3*x^20 + 2*x^18 + 4*x^16 + 3*x^14 + 4*x^10 + 4*x^8 + 4*x^6 + 4*x^4)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y])
[6nssage: om = OM.r()
[6nsage: OM - de_rham_witt_lift_form0(om)
V(((2*x^94 + 2*x^90 + x^86 + x^84 + 2*x^82 + x^78 + 2*x^72 - 2*x^70 - x^68 + 2*x^66 - 2*x^64 - 2*x^62 - x^60 + 2*x^50 - x^48 + x^44 - x^42 - x^40 + 2*x^38 - x^36 + 2*x^34 - x^32 - 2*x^30 - 2*x^28 + 2*x^26 + 2*x^24 + 2*x^22 - 2*x^20 - x^18 - x^16 - x^12 + x^10 + x^8 - x^6 + x^4 - 2*x^2 - 1)/y) dx)
sage: def regular_drw_form(omega):
....: C = omega.curve
....: omega_aux = omega.r()
....: omega_aux = omega_aux.regular_form()
....: aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()
....: ^Iprint('aux', aux)
....: aux.omega, fct = decomposition_omega0_hpdh(aux.omega)
....: ^Iprint('aux.omega, fct', aux.omega, fct)
....: aux.h2 += fct^p
....: ^Iprint(aux.h2)
....: aux.h2 = decomposition_g0_p2th_power(aux.h2)[0]
....: result = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2)
....: return result
Input In [53]
print('aux', aux)
^
TabError: inconsistent use of tabs and spaces in indentation
 
[6nsage:
sage: def regular_drw_form(omega):
....: ^IC = omega.curve
....: ^Iomega_aux = omega.r()
....: ^Iomega_aux = omega_aux.regular_form()
....: ^Iaux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()
....: ^Iprint('aux', aux)
....: ^Iaux.omega, fct = decomposition_omega0_hpdh(aux.omega)
....: ^Iprint('aux.omega, fct', aux.omega, fct)
....: ^Iaux.h2 += fct^p
....: ^Iprint(aux.h2)
....: ^Iaux.h2 = decomposition_g0_p2th_power(aux.h2)[0]
....: ^Iresult = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2)
....: ^Ireturn result
....:
[6nsage: regular_drw_form(OM)
aux V(((2*x^94 + 2*x^90 + x^86 + x^84 + 2*x^82 + x^78 + 2*x^72 - 2*x^70 - x^68 + 2*x^66 - 2*x^64 - 2*x^62 - x^60 + 2*x^50 - x^48 + x^44 - x^42 - x^40 + 2*x^38 - x^36 + 2*x^34 - x^32 - 2*x^30 - 2*x^28 + 2*x^26 + 2*x^24 + 2*x^22 - 2*x^20 - x^18 - x^16 - x^12 + x^10 + x^8 - x^6 + x^4 - 2*x^2 - 1)/y) dx)
aux.omega, fct ((-2*x^790 + x^786 - x^782 + 2*x^780 + 2*x^778 - 2*x^776 + 2*x^774 - x^770 + x^766 + x^764 - 2*x^762 + 2*x^760 + x^756 + x^754 + x^752 + 2*x^744 - x^740 + x^736 - 2*x^732 - x^724 - x^720 - x^716 + x^714 - x^712 + 2*x^710 - x^708 - 2*x^706 - x^704 + x^702 + 2*x^700 - 2*x^698 + 2*x^696 - 2*x^694 + x^692 + 2*x^690 + 2*x^688 + 2*x^686 - 2*x^684 - x^682 - x^680 - x^678 - 2*x^676 - 2*x^672 + 2*x^666 + 2*x^664 - 2*x^662 - 2*x^660 - x^658 + 2*x^656 - 2*x^654 - x^646 - 2*x^644 + 2*x^640 + x^638 + 2*x^636 - 2*x^634 + x^632 - 2*x^630 - 2*x^628 + x^626 + x^624 - x^622 + x^620 + 2*x^616 - x^614 + x^612 - x^606 - 2*x^604 - 2*x^602 - 2*x^598 - 2*x^596 + x^594 - x^592 - x^590 + 2*x^588 - x^586 - 2*x^584 - 2*x^582 - x^576 - x^574 - x^572 - 2*x^570 - 2*x^568 + 2*x^566 - 2*x^564 + 2*x^558 - 2*x^556 + 2*x^552 + x^548 - x^546 + x^544 + x^542 - 2*x^540 - x^538 + 2*x^536 - 2*x^534 + x^530 - 2*x^528 + x^526 - x^524 - x^522 - 2*x^516 + x^512 + x^510 + x^508 + x^502 + 2*x^498 + x^496 - 2*x^494 - x^492 - x^490 - x^488 + x^486 + x^484 - 2*x^482 + 2*x^480 - 2*x^476 + x^474 + x^470 + x^468 + 2*x^466 - 2*x^464 - x^462 + x^460 - 2*x^458 - 2*x^456 - 2*x^454 - x^452 - x^450 - x^448 + 2*x^446 - x^444 - 2*x^442 + 2*x^438 + 2*x^436 + 2*x^434 - 2*x^430 + x^428 + x^426 + x^424 - 2*x^422 + x^418 - 2*x^416 + x^414 - x^410 - 2*x^408 + x^406 + x^404 - x^402 + 2*x^398 - x^396 + x^392 - x^390 + x^388 + x^386 + x^384 + 2*x^380 + x^378 + 2*x^376 + 2*x^372 + 2*x^370 + x^368 - x^366 - 2*x^362 + 2*x^358 + 2*x^356 - x^352 + x^350 - 2*x^348 + x^346 + x^344 - 2*x^342 - 2*x^340 + 2*x^336 - x^334 + x^332 + 2*x^330 - 2*x^328 - 2*x^326 - 2*x^324 + 2*x^318 - 2*x^314 + 2*x^310 - x^308 + x^306 + x^302 + 2*x^298 + 2*x^296 + x^294 + x^292 - 2*x^290 - x^288 - x^286 - x^284 + x^282 + 2*x^280 + x^278 - x^276 + 2*x^274 + x^272 + 2*x^270 - x^266 + 2*x^264 + x^262 - x^260 - 2*x^258 + 2*x^256 - 2*x^254 + 2*x^252 + x^250 + x^246 - 2*x^244 + x^242 - 2*x^240 - 2*x^236 - x^232 - x^224 + 2*x^222 + x^220 + x^218 + x^216 - x^214 + 2*x^212 + 2*x^210 + 2*x^208 + 2*x^206 + 2*x^204 + 2*x^200 + x^198 + 2*x^196 + x^194 + 2*x^192 - 2*x^188 + 2*x^186 - 2*x^180 + 2*x^178 + x^174 - 2*x^172 + x^170 - x^168 - x^166 + 2*x^164 + 2*x^160 - x^158 + x^156 - x^154 - 2*x^152 - 2*x^150 - x^148 - x^144 - 2*x^140 + 2*x^138 + 2*x^134 + 2*x^132 - 2*x^130 + x^128 - x^126 + x^122 + 2*x^116 + x^114 - x^112 - x^108 - x^106 - x^104 + x^102 - 2*x^100 + x^96 - x^94 - 2*x^92 + 2*x^90 - x^88 - x^86 + x^82 + 2*x^80 - x^78 + 2*x^74 - x^72 + x^70 - 2*x^68 + 2*x^66 + 2*x^64 - 2*x^62 - 2*x^60 + 2*x^58 - 2*x^56 + 2*x^54 - 2*x^50 + 2*x^48 - x^46 + x^42 - 2*x^40 + 2*x^38 + 2*x^36 + x^34 + 2*x^32 - x^30 - x^26 - x^24 - 2*x^22 - x^20 - 2*x^18 + x^12)/y) dx ((x^162 + 2*x^160 + 4*x^158 + x^156 + x^152 + 2*x^148 + 3*x^146 + x^144 + x^142 + 4*x^140 + 4*x^138 + x^134 + 2*x^132 + 2*x^130 + 2*x^128 + x^126 + x^122 + x^120 + 2*x^118 + 3*x^114 + 4*x^112 + 3*x^110 + 4*x^108 + x^104 + x^102 + 4*x^100 + 4*x^98 + 3*x^94 + 4*x^90 + x^88 + 3*x^84 + 3*x^82 + 4*x^78 + x^74 + 4*x^72 + 3*x^70 + x^68 + 4*x^66 + 3*x^64 + 2*x^62 + 2*x^60 + 2*x^58 + x^56 + 2*x^54 + x^48 + 2*x^46 + 4*x^44 + 4*x^40 + 4*x^38 + x^36 + 4*x^32 + 2*x^30 + 3*x^28 + x^26 + 2*x^24 + 4*x^22 + 3*x^20 + 2*x^16 + 2*x^12 + 4*x^10 + 4*x^8 + 4*x^6 + 4*x^4 + 4*x^2 + 2)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y
((x^816 + 2*x^814 + x^812 + 2*x^806 + 4*x^804 + 2*x^802 + 4*x^796 + 3*x^794 + 4*x^792 + x^786 + 2*x^784 + x^782 + x^766 + 2*x^764 + x^762 + 2*x^746 + 4*x^744 + 2*x^742 + 3*x^736 + x^734 + 3*x^732 + x^726 + 2*x^724 + x^722 + x^716 + 2*x^714 + x^712 + 4*x^706 + 3*x^704 + 4*x^702 + 4*x^696 + 3*x^694 + 4*x^692 + x^676 + 2*x^674 + x^672 + 2*x^666 + 4*x^664 + 2*x^662 + 2*x^656 + 4*x^654 + 2*x^652 + 2*x^646 + 4*x^644 + 2*x^642 + x^636 + 2*x^634 + x^632 + x^616 + 2*x^614 + x^612 + x^606 + 2*x^604 + x^602 + 2*x^596 + 4*x^594 + 2*x^592 + 3*x^576 + x^574 + 3*x^572 + 4*x^566 + 3*x^564 + 4*x^562 + 3*x^556 + x^554 + 3*x^552 + 4*x^546 + 3*x^544 + 4*x^542 + x^526 + 2*x^524 + x^522 + x^516 + 2*x^514 + x^512 + 4*x^506 + 3*x^504 + 4*x^502 + 4*x^496 + 3*x^494 + 4*x^492 + 3*x^476 + x^474 + 3*x^472 + 4*x^456 + 3*x^454 + 4*x^452 + x^446 + 2*x^444 + x^442 + 3*x^426 + x^424 + 3*x^422 + 3*x^416 + x^414 + 3*x^412 + 4*x^396 + 3*x^394 + 4*x^392 + x^376 + 2*x^374 + x^372 + 4*x^366 + 3*x^364 + 4*x^362 + 3*x^356 + x^354 + 3*x^352 + x^346 + 2*x^344 + x^342 + 4*x^336 + 3*x^334 + 4*x^332 + 3*x^326 + x^324 + 3*x^322 + 2*x^316 + 4*x^314 + 2*x^312 + 2*x^306 + 4*x^304 + 2*x^302 + 2*x^296 + 4*x^294 + 2*x^292 + x^286 + 2*x^284 + x^282 + 2*x^276 + 4*x^274 + 2*x^272 + x^246 + 2*x^244 + x^242 + 2*x^236 + 4*x^234 + 2*x^232 + 4*x^226 + 3*x^224 + 4*x^222 + 4*x^206 + 3*x^204 + 4*x^202 + 4*x^196 + 3*x^194 + 4*x^192 + x^186 + 2*x^184 + x^182 + 4*x^166 + 3*x^164 + 4*x^162 + 2*x^156 + 4*x^154 + 2*x^152 + 3*x^146 + x^144 + 3*x^142 + x^136 + 2*x^134 + x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 4*x^116 + 3*x^114 + 4*x^112 + 3*x^106 + x^104 + 3*x^102 + 2*x^86 + 4*x^84 + 2*x^82 + 2*x^66 + 4*x^64 + 2*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 4*x^46 + 3*x^44 + 4*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^26 + 3*x^24 + 4*x^22 + 4*x^16 + 3*x^14 + 4*x^12 + 2*x^6 + 4*x^4 + 2*x^2)/(x^156 + 2*x^154 + 2*x^152 + 2*x^150 + 2*x^148 + 2*x^146 + 2*x^144 + 3*x^142 + 4*x^140 + 3*x^138 + 4*x^136 + 3*x^134 + 4*x^132 + 3*x^130 + x^128 + 2*x^126 + 4*x^124 + 2*x^122 + x^120 + 3*x^118 + 2*x^116 + 3*x^114 + 3*x^112 + 2*x^108 + x^104 + x^102 + 4*x^100 + 2*x^98 + x^96 + 2*x^94 + 4*x^92 + 3*x^90 + 3*x^88 + x^84 + 3*x^82 + 4*x^80 + 3*x^78 + 4*x^76 + 4*x^74 + 4*x^72 + 3*x^70 + 4*x^66 + 2*x^64 + x^62 + 4*x^60 + 3*x^58 + 3*x^56 + 3*x^52 + 3*x^50 + 3*x^48 + 2*x^46 + 4*x^44 + 4*x^40 + 2*x^38 + 2*x^36 + 3*x^34 + 4*x^32 + x^30 + 2*x^26 + 2*x^22 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [55], in <cell line: 1>()
----> 1 regular_drw_form(OM)
 
Input In [54], in regular_drw_form(omega)
9 aux.h2 += fct**p
10 print(aux.h2)
---> 11 aux.h2 = decomposition_g0_p2th_power(aux.h2)[Integer(0)]
12 result = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2)
13 return result
 
File <string>:12, in decomposition_g0_p2th_power(fct)
 
File <string>:5, in decomposition_g0_pth_power(fct)
 
File <string>:51, in int(self)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
1329 normalize(x._numer, x._denom, self.p)
1330 if nmod_poly_degree(x._denom) != 0:
-> 1331 raise ValueError("not integral")
1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:
 
ValueError: not integral
sage: def regular_drw_form(omega):
....: ^IC = omega.curve
....: ^Iomega_aux = omega.r()
....: ^Iomega_aux = omega_aux.regular_form()
....: ^Iaux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()
....: ^Iprint('aux', aux)
....: ^Iaux.omega, fct = decomposition_omega0_hpdh(aux.omega)
....: ^Iprint('aux.omega, fct', aux.omega, fct)
....: ^Iaux.h2 += fct^p
....: ^Iprint('\n aux.h2', aux.h2, '\n')
....: ^Iaux.h2 = decomposition_g0_p2th_power(aux.h2)[0]
....: ^Iresult = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2)
....: ^Ireturn result
....:
sage: regular_drw_form(OM)
aux V(((2*x^94 + 2*x^90 + x^86 + x^84 + 2*x^82 + x^78 + 2*x^72 - 2*x^70 - x^68 + 2*x^66 - 2*x^64 - 2*x^62 - x^60 + 2*x^50 - x^48 + x^44 - x^42 - x^40 + 2*x^38 - x^36 + 2*x^34 - x^32 - 2*x^30 - 2*x^28 + 2*x^26 + 2*x^24 + 2*x^22 - 2*x^20 - x^18 - x^16 - x^12 + x^10 + x^8 - x^6 + x^4 - 2*x^2 - 1)/y) dx)
aux.omega, fct ((-2*x^790 + x^786 - x^782 + 2*x^780 + 2*x^778 - 2*x^776 + 2*x^774 - x^770 + x^766 + x^764 - 2*x^762 + 2*x^760 + x^756 + x^754 + x^752 + 2*x^744 - x^740 + x^736 - 2*x^732 - x^724 - x^720 - x^716 + x^714 - x^712 + 2*x^710 - x^708 - 2*x^706 - x^704 + x^702 + 2*x^700 - 2*x^698 + 2*x^696 - 2*x^694 + x^692 + 2*x^690 + 2*x^688 + 2*x^686 - 2*x^684 - x^682 - x^680 - x^678 - 2*x^676 - 2*x^672 + 2*x^666 + 2*x^664 - 2*x^662 - 2*x^660 - x^658 + 2*x^656 - 2*x^654 - x^646 - 2*x^644 + 2*x^640 + x^638 + 2*x^636 - 2*x^634 + x^632 - 2*x^630 - 2*x^628 + x^626 + x^624 - x^622 + x^620 + 2*x^616 - x^614 + x^612 - x^606 - 2*x^604 - 2*x^602 - 2*x^598 - 2*x^596 + x^594 - x^592 - x^590 + 2*x^588 - x^586 - 2*x^584 - 2*x^582 - x^576 - x^574 - x^572 - 2*x^570 - 2*x^568 + 2*x^566 - 2*x^564 + 2*x^558 - 2*x^556 + 2*x^552 + x^548 - x^546 + x^544 + x^542 - 2*x^540 - x^538 + 2*x^536 - 2*x^534 + x^530 - 2*x^528 + x^526 - x^524 - x^522 - 2*x^516 + x^512 + x^510 + x^508 + x^502 + 2*x^498 + x^496 - 2*x^494 - x^492 - x^490 - x^488 + x^486 + x^484 - 2*x^482 + 2*x^480 - 2*x^476 + x^474 + x^470 + x^468 + 2*x^466 - 2*x^464 - x^462 + x^460 - 2*x^458 - 2*x^456 - 2*x^454 - x^452 - x^450 - x^448 + 2*x^446 - x^444 - 2*x^442 + 2*x^438 + 2*x^436 + 2*x^434 - 2*x^430 + x^428 + x^426 + x^424 - 2*x^422 + x^418 - 2*x^416 + x^414 - x^410 - 2*x^408 + x^406 + x^404 - x^402 + 2*x^398 - x^396 + x^392 - x^390 + x^388 + x^386 + x^384 + 2*x^380 + x^378 + 2*x^376 + 2*x^372 + 2*x^370 + x^368 - x^366 - 2*x^362 + 2*x^358 + 2*x^356 - x^352 + x^350 - 2*x^348 + x^346 + x^344 - 2*x^342 - 2*x^340 + 2*x^336 - x^334 + x^332 + 2*x^330 - 2*x^328 - 2*x^326 - 2*x^324 + 2*x^318 - 2*x^314 + 2*x^310 - x^308 + x^306 + x^302 + 2*x^298 + 2*x^296 + x^294 + x^292 - 2*x^290 - x^288 - x^286 - x^284 + x^282 + 2*x^280 + x^278 - x^276 + 2*x^274 + x^272 + 2*x^270 - x^266 + 2*x^264 + x^262 - x^260 - 2*x^258 + 2*x^256 - 2*x^254 + 2*x^252 + x^250 + x^246 - 2*x^244 + x^242 - 2*x^240 - 2*x^236 - x^232 - x^224 + 2*x^222 + x^220 + x^218 + x^216 - x^214 + 2*x^212 + 2*x^210 + 2*x^208 + 2*x^206 + 2*x^204 + 2*x^200 + x^198 + 2*x^196 + x^194 + 2*x^192 - 2*x^188 + 2*x^186 - 2*x^180 + 2*x^178 + x^174 - 2*x^172 + x^170 - x^168 - x^166 + 2*x^164 + 2*x^160 - x^158 + x^156 - x^154 - 2*x^152 - 2*x^150 - x^148 - x^144 - 2*x^140 + 2*x^138 + 2*x^134 + 2*x^132 - 2*x^130 + x^128 - x^126 + x^122 + 2*x^116 + x^114 - x^112 - x^108 - x^106 - x^104 + x^102 - 2*x^100 + x^96 - x^94 - 2*x^92 + 2*x^90 - x^88 - x^86 + x^82 + 2*x^80 - x^78 + 2*x^74 - x^72 + x^70 - 2*x^68 + 2*x^66 + 2*x^64 - 2*x^62 - 2*x^60 + 2*x^58 - 2*x^56 + 2*x^54 - 2*x^50 + 2*x^48 - x^46 + x^42 - 2*x^40 + 2*x^38 + 2*x^36 + x^34 + 2*x^32 - x^30 - x^26 - x^24 - 2*x^22 - x^20 - 2*x^18 + x^12)/y) dx ((x^162 + 2*x^160 + 4*x^158 + x^156 + x^152 + 2*x^148 + 3*x^146 + x^144 + x^142 + 4*x^140 + 4*x^138 + x^134 + 2*x^132 + 2*x^130 + 2*x^128 + x^126 + x^122 + x^120 + 2*x^118 + 3*x^114 + 4*x^112 + 3*x^110 + 4*x^108 + x^104 + x^102 + 4*x^100 + 4*x^98 + 3*x^94 + 4*x^90 + x^88 + 3*x^84 + 3*x^82 + 4*x^78 + x^74 + 4*x^72 + 3*x^70 + x^68 + 4*x^66 + 3*x^64 + 2*x^62 + 2*x^60 + 2*x^58 + x^56 + 2*x^54 + x^48 + 2*x^46 + 4*x^44 + 4*x^40 + 4*x^38 + x^36 + 4*x^32 + 2*x^30 + 3*x^28 + x^26 + 2*x^24 + 4*x^22 + 3*x^20 + 2*x^16 + 2*x^12 + 4*x^10 + 4*x^8 + 4*x^6 + 4*x^4 + 4*x^2 + 2)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y
 
aux.h2 ((x^816 + 2*x^814 + x^812 + 2*x^806 + 4*x^804 + 2*x^802 + 4*x^796 + 3*x^794 + 4*x^792 + x^786 + 2*x^784 + x^782 + x^766 + 2*x^764 + x^762 + 2*x^746 + 4*x^744 + 2*x^742 + 3*x^736 + x^734 + 3*x^732 + x^726 + 2*x^724 + x^722 + x^716 + 2*x^714 + x^712 + 4*x^706 + 3*x^704 + 4*x^702 + 4*x^696 + 3*x^694 + 4*x^692 + x^676 + 2*x^674 + x^672 + 2*x^666 + 4*x^664 + 2*x^662 + 2*x^656 + 4*x^654 + 2*x^652 + 2*x^646 + 4*x^644 + 2*x^642 + x^636 + 2*x^634 + x^632 + x^616 + 2*x^614 + x^612 + x^606 + 2*x^604 + x^602 + 2*x^596 + 4*x^594 + 2*x^592 + 3*x^576 + x^574 + 3*x^572 + 4*x^566 + 3*x^564 + 4*x^562 + 3*x^556 + x^554 + 3*x^552 + 4*x^546 + 3*x^544 + 4*x^542 + x^526 + 2*x^524 + x^522 + x^516 + 2*x^514 + x^512 + 4*x^506 + 3*x^504 + 4*x^502 + 4*x^496 + 3*x^494 + 4*x^492 + 3*x^476 + x^474 + 3*x^472 + 4*x^456 + 3*x^454 + 4*x^452 + x^446 + 2*x^444 + x^442 + 3*x^426 + x^424 + 3*x^422 + 3*x^416 + x^414 + 3*x^412 + 4*x^396 + 3*x^394 + 4*x^392 + x^376 + 2*x^374 + x^372 + 4*x^366 + 3*x^364 + 4*x^362 + 3*x^356 + x^354 + 3*x^352 + x^346 + 2*x^344 + x^342 + 4*x^336 + 3*x^334 + 4*x^332 + 3*x^326 + x^324 + 3*x^322 + 2*x^316 + 4*x^314 + 2*x^312 + 2*x^306 + 4*x^304 + 2*x^302 + 2*x^296 + 4*x^294 + 2*x^292 + x^286 + 2*x^284 + x^282 + 2*x^276 + 4*x^274 + 2*x^272 + x^246 + 2*x^244 + x^242 + 2*x^236 + 4*x^234 + 2*x^232 + 4*x^226 + 3*x^224 + 4*x^222 + 4*x^206 + 3*x^204 + 4*x^202 + 4*x^196 + 3*x^194 + 4*x^192 + x^186 + 2*x^184 + x^182 + 4*x^166 + 3*x^164 + 4*x^162 + 2*x^156 + 4*x^154 + 2*x^152 + 3*x^146 + x^144 + 3*x^142 + x^136 + 2*x^134 + x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 4*x^116 + 3*x^114 + 4*x^112 + 3*x^106 + x^104 + 3*x^102 + 2*x^86 + 4*x^84 + 2*x^82 + 2*x^66 + 4*x^64 + 2*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 4*x^46 + 3*x^44 + 4*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^26 + 3*x^24 + 4*x^22 + 4*x^16 + 3*x^14 + 4*x^12 + 2*x^6 + 4*x^4 + 2*x^2)/(x^156 + 2*x^154 + 2*x^152 + 2*x^150 + 2*x^148 + 2*x^146 + 2*x^144 + 3*x^142 + 4*x^140 + 3*x^138 + 4*x^136 + 3*x^134 + 4*x^132 + 3*x^130 + x^128 + 2*x^126 + 4*x^124 + 2*x^122 + x^120 + 3*x^118 + 2*x^116 + 3*x^114 + 3*x^112 + 2*x^108 + x^104 + x^102 + 4*x^100 + 2*x^98 + x^96 + 2*x^94 + 4*x^92 + 3*x^90 + 3*x^88 + x^84 + 3*x^82 + 4*x^80 + 3*x^78 + 4*x^76 + 4*x^74 + 4*x^72 + 3*x^70 + 4*x^66 + 2*x^64 + x^62 + 4*x^60 + 3*x^58 + 3*x^56 + 3*x^52 + 3*x^50 + 3*x^48 + 2*x^46 + 4*x^44 + 4*x^40 + 2*x^38 + 2*x^36 + 3*x^34 + 4*x^32 + x^30 + 2*x^26 + 2*x^22 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y
 
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [57], in <cell line: 1>()
----> 1 regular_drw_form(OM)
 
Input In [56], in regular_drw_form(omega)
9 aux.h2 += fct**p
10 print('\n aux.h2', aux.h2, '\n')
---> 11 aux.h2 = decomposition_g0_p2th_power(aux.h2)[Integer(0)]
12 result = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2)
13 return result
 
File <string>:12, in decomposition_g0_p2th_power(fct)
 
File <string>:5, in decomposition_g0_pth_power(fct)
 
File <string>:51, in int(self)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
1329 normalize(x._numer, x._denom, self.p)
1330 if nmod_poly_degree(x._denom) != 0:
-> 1331 raise ValueError("not integral")
1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:
 
ValueError: not integral
sage: ((C1.x^816 + 2*C1.x^814 + C1.x^812 + 2*C1.x^806 + 4*C1.x^804 + 2*C1.x^802 + 4*C1.x^796 + 3*C1.x^794 + 4*C1.x^792 + C1.x^766 + 2*C1.x^784 + C1.x^782 + C1.x^7
....: 6 + 2*C1.x^764 + C1.x^762 + 2*C1.x^746 + 4*C1.x^744 + 2*C1.x^742 + 3*C1.x^736 + C1.x^734 + 3*C1.x^732 + C1.x^726 + 2*C1.x^724 + C1.x^722 + C1.x^716 + 2*C1.x
....: 714 + C1.x^712 + 4*C1.x^706 + 3*C1.x^704 + 4*C1.x^702 + 4*C1.x^696 + 3*C1.x^694 + 4*C1.x^692 + C1.x^676 + 2*C1.x^674 + C12x^672 + 2*C1.x^666 + 4*C1.x^664 +
....: *C1.x^662 + 2*C1.x^656 + 4*C1.x^654 + 2*C1.x^652 + 2*C1.x^646 + 4*C1.x^644 + 2*C1.x^642 + C1.x^636 + 2*C1.x^634 + C1.x^632 + C1.x^616 + 2*C1.x^614 + C1.x^61
....: + C1.x^606 + 2*C1.x^604 + C1.x^602 + 2*C1.x^596 + 4*C1.x^594 + 2*C1.x^592 + 3*C1.x^576 + C1.x^574 + 3*C1.x^572 + 4*C1.x^166 + 3*C1.x^564 + 4*C1.x^562 + 3*C
....: .x^556 + C1.x^554 + 3*C1.x^552 + 4*C1.x^546 + 3*C1.x^544 + 4*C1.x^542 + C1.x^526 + 2*C1.x^524 + C1.x^522 + C1.x^516 + 2*C*.x^514 + C1.x^512 + 4*C1.x^506 + 3
....: C1.x^504 + 4*C1.x^502 + 4*C1.x^496 + 3*C1.x^494 + 4*C1.x^492 + 3*C1.x^476 + C1.x^474 + 3*C1.x^472 + 4*C1.x^456 + 3*C1.x^4^4 + 4*C1.x^452 + C1.x^446 + 2*C1.x
....: 444 + C1.x^442 + 3*C1.x^426 + C1.x^424 + 3*C1.x^422 + 3*C1.x^416 + C1.x^414 + 3*C1.x^412 + 4*C1.x^396 + 3*C1.x^394 + 4*C1.x^392 + C1.x^376 + 2*C1.x^374 + C1
....: x^372 + 4*C1.x^366 + 3*C1.x^364 + 4*C1.x^362 + 3*C1.x^356 + C1.x^354 + 3*C1.x^352 + C1.x^346 + 2*C1.x^344 + C1.x^342 + 4*+1.x^336 + 3*C1.x^334 + 4*C1.x^332
....: 3*C1.x^326 + C1.x^324 + 3*C1.x^322 + 2*C1.x^316 + 4*C1.x^314 + 2*C1.x^312 + 2*C1.x^306 + 4*C1.x^304 + 2*C1.x^302 + 2*C1.1^296 + 4*C1.x^294 + 2*C1.x^292 + C
....: .x^286 + 2*C1.x^284 + C1.x^282 + 2*C1.x^276 + 4*C1.x^274 + 2*C1.x^272 + C1.x^246 + 2*C1.x^244 + C1.x^242 + 2*C1.x^236 + 4*C1.x^234 + 2*C1.x^232 + 4*C1.x^226
....: + 3*C1.x^224 + 4*C1.x^222 + 4*C1.x^206 + 3*C1.x^204 + 4*C1.x^202 + 4*C1.x^196 + 3*C1.x^194 + 4*C1.x^192 + C1.x^186 + 2*C1Cx^184 + C1.x^182 + 4*C1.x^166 + 3*
....: 1.x^164 + 4*C1.x^162 + 2*C1.x^156 + 4*C1.x^154 + 2*C1.x^152 + 3*C1.x^146 + C1.x^144 + 3*C1.x^142 + C1.x^136 + 2*C1.x^134 4 C1.x^132 + 2*C1.x^126 + 4*C1.x^12
....: + 2*C1.x^122 + 4*C1.x^116 + 3*C1.x^114 + 4*C1.x^112 + 3*C1.x^106 + C1.x^104 + 3*C1.x^102 + 2*C1.x^86 + 4*C1.x^84 + 2*C1..^82 + 2*C1.x^66 + 4*C1.x^64 + 2*C1
....: x^62 + 4*C1.x^56 + 3*C1.x^54 + 4*C1.x^52 + 4*C1.x^46 + 3*C1.x^44 + 4*C1.x^42 + 4*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + 4*C1.xx26 + 3*C1.x^24 + 4*C1.x^22 + 4*C1.
....: ^16 + 3*C1.x^14 + 4*C1.x^12 + 2*C1.x^6 + 4*C1.x^4 + 2*C1.x^2)/(C1.x^156 + 2*C1.x^154 + 2*C1.x^152 + 2*C1.x^150 + 2*C1.x^1.8 + 2*C1.x^146 + 2*C1.x^144 + 3*C1
....: x^142 + 4*C1.x^140 + 3*C1.x^138 + 4*C1.x^136 + 3*C1.x^134 + 4*C1.x^132 + 3*C1.x^130 + C1.x^128 + 2*C1.x^126 + 4*C1.x^124 8 2*C1.x^122 + C1.x^120 + 3*C1.x^11
....: + 2*C1.x^116 + 3*C1.x^114 + 3*C1.x^112 + 2*C1.x^108 + C1.x^104 + C1.x^102 + 4*C1.x^100 + 2*C1.x^98 + C1.x^96 + 2*C1.x^948+ 4*C1.x^92 + 3*C1.x^90 + 3*C1.x^8
....: + C1.x^84 + 3*C1.x^82 + 4*C1.x^80 + 3*C1.x^78 + 4*C1.x^76 + 4*C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + 4*C1.x^66 + 2*C1.x^64 + *1.x^62 + 4*C1.x^60 + 3*C1.x^58 + 3
....: C1.x^56 + 3*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 2*C1.x^46 + 4*C1.x^44 + 4*C1.x^40 + 2*C1.x^38 + 2*C1.x^36 + 3*C1.x^34 + 4*C..x^32 + C1.x^30 + 2*C1.x^26 + 2*C1
....: x^22 + 2*C1.x^18 + C1.x^14 + 4*C1.x^12 + C1.x^8 + C1.x^6 + 3*C1.x^4 + 4*C1.one))*C1.y
((x^816 + 2*x^814 + x^812 + 2*x^806 + 4*x^804 + 2*x^802 + 4*x^796 + 3*x^794 + 4*x^792 + x^786 + 2*x^784 + x^782 + x^766 + 2*x^764 + x^762 + 2*x^746 + 4*x^744 + 2*x^742 + 3*x^736 + x^734 + 3*x^732 + x^726 + 2*x^724 + x^722 + x^716 + 2*x^714 + x^712 + 4*x^706 + 3*x^704 + 4*x^702 + 4*x^696 + 3*x^694 + 4*x^692 + x^676 + 2*x^674 + x^672 + 2*x^666 + 4*x^664 + 2*x^662 + 2*x^656 + 4*x^654 + 2*x^652 + 2*x^646 + 4*x^644 + 2*x^642 + x^636 + 2*x^634 + x^632 + x^616 + 2*x^614 + x^612 + x^606 + 2*x^604 + x^602 + 2*x^596 + 4*x^594 + 2*x^592 + 3*x^576 + x^574 + 3*x^572 + 4*x^566 + 3*x^564 + 4*x^562 + 3*x^556 + x^554 + 3*x^552 + 4*x^546 + 3*x^544 + 4*x^542 + x^526 + 2*x^524 + x^522 + x^516 + 2*x^514 + x^512 + 4*x^506 + 3*x^504 + 4*x^502 + 4*x^496 + 3*x^494 + 4*x^492 + 3*x^476 + x^474 + 3*x^472 + 4*x^456 + 3*x^454 + 4*x^452 + x^446 + 2*x^444 + x^442 + 3*x^426 + x^424 + 3*x^422 + 3*x^416 + x^414 + 3*x^412 + 4*x^396 + 3*x^394 + 4*x^392 + x^376 + 2*x^374 + x^372 + 4*x^366 + 3*x^364 + 4*x^362 + 3*x^356 + x^354 + 3*x^352 + x^346 + 2*x^344 + x^342 + 4*x^336 + 3*x^334 + 4*x^332 + 3*x^326 + x^324 + 3*x^322 + 2*x^316 + 4*x^314 + 2*x^312 + 2*x^306 + 4*x^304 + 2*x^302 + 2*x^296 + 4*x^294 + 2*x^292 + x^286 + 2*x^284 + x^282 + 2*x^276 + 4*x^274 + 2*x^272 + x^246 + 2*x^244 + x^242 + 2*x^236 + 4*x^234 + 2*x^232 + 4*x^226 + 3*x^224 + 4*x^222 + 4*x^206 + 3*x^204 + 4*x^202 + 4*x^196 + 3*x^194 + 4*x^192 + x^186 + 2*x^184 + x^182 + 4*x^166 + 3*x^164 + 4*x^162 + 2*x^156 + 4*x^154 + 2*x^152 + 3*x^146 + x^144 + 3*x^142 + x^136 + 2*x^134 + x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 4*x^116 + 3*x^114 + 4*x^112 + 3*x^106 + x^104 + 3*x^102 + 2*x^86 + 4*x^84 + 2*x^82 + 2*x^66 + 4*x^64 + 2*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 4*x^46 + 3*x^44 + 4*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^26 + 3*x^24 + 4*x^22 + 4*x^16 + 3*x^14 + 4*x^12 + 2*x^6 + 4*x^4 + 2*x^2)/(x^156 + 2*x^154 + 2*x^152 + 2*x^150 + 2*x^148 + 2*x^146 + 2*x^144 + 3*x^142 + 4*x^140 + 3*x^138 + 4*x^136 + 3*x^134 + 4*x^132 + 3*x^130 + x^128 + 2*x^126 + 4*x^124 + 2*x^122 + x^120 + 3*x^118 + 2*x^116 + 3*x^114 + 3*x^112 + 2*x^108 + x^104 + x^102 + 4*x^100 + 2*x^98 + x^96 + 2*x^94 + 4*x^92 + 3*x^90 + 3*x^88 + x^84 + 3*x^82 + 4*x^80 + 3*x^78 + 4*x^76 + 4*x^74 + 4*x^72 + 3*x^70 + 4*x^66 + 2*x^64 + x^62 + 4*x^60 + 3*x^58 + 3*x^56 + 3*x^52 + 3*x^50 + 3*x^48 + 2*x^46 + 4*x^44 + 4*x^40 + 2*x^38 + 2*x^36 + 3*x^34 + 4*x^32 + x^30 + 2*x^26 + 2*x^22 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y
sage: f1 = ((C1.x^816 + 2*C1.x^814 + C1.x^812 + 2*C1.x^806 + 4*C1.x^804 + 2*C1.x^802 + 4*C1.x^796 + 3*C1.x^794 + 4*C1.x^792 + C1.x^786 + 2*C1.x^784 + C1.x^782 + C
....: .x^766 + 2*C1.x^764 + C1.x^762 + 2*C1.x^746 + 4*C1.x^744 + 2*C1.x^742 + 3*C1.x^736 + C1.x^734 + 3*C1.x^732 + C1.x^726 + 2*C1.x^724 + C1.x^722 + C1.x^716 + 2
....: C1.x^714 + C1.x^712 + 4*C1.x^706 + 3*C1.x^704 + 4*C1.x^702 + 4*C1.x^696 + 3*C1.x^694 + 4*C1.x^692 + C1.x^676 + 2*C1.x^6746+ C1.x^672 + 2*C1.x^666 + 4*C1.x^6
....: 4 + 2*C1.x^662 + 2*C1.x^656 + 4*C1.x^654 + 2*C1.x^652 + 2*C1.x^646 + 4*C1.x^644 + 2*C1.x^642 + C1.x^636 + 2*C1.x^634 + C1.x^632 + C1.x^616 + 2*C1.x^614 + C1
....: x^612 + C1.x^606 + 2*C1.x^604 + C1.x^602 + 2*C1.x^596 + 4*C1.x^594 + 2*C1.x^592 + 3*C1.x^576 + C1.x^574 + 3*C1.x^572 + 4*+1.x^566 + 3*C1.x^564 + 4*C1.x^562
....: 3*C1.x^556 + C1.x^554 + 3*C1.x^552 + 4*C1.x^546 + 3*C1.x^544 + 4*C1.x^542 + C1.x^526 + 2*C1.x^524 + C1.x^522 + C1.x^516 6 2*C1.x^514 + C1.x^512 + 4*C1.x^50
....: + 3*C1.x^504 + 4*C1.x^502 + 4*C1.x^496 + 3*C1.x^494 + 4*C1.x^492 + 3*C1.x^476 + C1.x^474 + 3*C1.x^472 + 4*C1.x^456 + 3*C*.x^454 + 4*C1.x^452 + C1.x^446 + 2
....: C1.x^444 + C1.x^442 + 3*C1.x^426 + C1.x^424 + 3*C1.x^422 + 3*C1.x^416 + C1.x^414 + 3*C1.x^412 + 4*C1.x^396 + 3*C1.x^394 + 4*C1.x^392 + C1.x^376 + 2*C1.x^374
....: + C1.x^372 + 4*C1.x^366 + 3*C1.x^364 + 4*C1.x^362 + 3*C1.x^356 + C1.x^354 + 3*C1.x^352 + C1.x^346 + 2*C1.x^344 + C1.x^342^+ 4*C1.x^336 + 3*C1.x^334 + 4*C1.x
....: 332 + 3*C1.x^326 + C1.x^324 + 3*C1.x^322 + 2*C1.x^316 + 4*C1.x^314 + 2*C1.x^312 + 2*C1.x^306 + 4*C1.x^304 + 2*C1.x^302 + 2*C1.x^296 + 4*C1.x^294 + 2*C1.x^29
....: + C1.x^286 + 2*C1.x^284 + C1.x^282 + 2*C1.x^276 + 4*C1.x^274 + 2*C1.x^272 + C1.x^246 + 2*C1.x^244 + C1.x^242 + 2*C1.x^23x + 4*C1.x^234 + 2*C1.x^232 + 4*C1.
....: ^226 + 3*C1.x^224 + 4*C1.x^222 + 4*C1.x^206 + 3*C1.x^204 + 4*C1.x^202 + 4*C1.x^196 + 3*C1.x^194 + 4*C1.x^192 + C1.x^186 + 2*C1.x^184 + C1.x^182 + 4*C1.x^166
....: + 3*C1.x^164 + 4*C1.x^162 + 2*C1.x^156 + 4*C1.x^154 + 2*C1.x^152 + 3*C1.x^146 + C1.x^144 + 3*C1.x^142 + C1.x^136 + 2*C1.x.134 + C1.x^132 + 2*C1.x^126 + 4*C1
....: x^124 + 2*C1.x^122 + 4*C1.x^116 + 3*C1.x^114 + 4*C1.x^112 + 3*C1.x^106 + C1.x^104 + 3*C1.x^102 + 2*C1.x^86 + 4*C1.x^84 + 2*C1.x^82 + 2*C1.x^66 + 4*C1.x^64 +
....: 2*C1.x^62 + 4*C1.x^56 + 3*C1.x^54 + 4*C1.x^52 + 4*C1.x^46 + 3*C1.x^44 + 4*C1.x^42 + 4*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + 44C1.x^26 + 3*C1.x^24 + 4*C1.x^22 +
....: *C1.x^16 + 3*C1.x^14 + 4*C1.x^12 + 2*C1.x^6 + 4*C1.x^4 + 2*C1.x^2)/(C1.x^156 + 2*C1.x^154 + 2*C1.x^152 + 2*C1.x^150 + 2*C1.x^148 + 2*C1.x^146 + 2*C1.x^144 +
....: 3*C1.x^142 + 4*C1.x^140 + 3*C1.x^138 + 4*C1.x^136 + 3*C1.x^134 + 4*C1.x^132 + 3*C1.x^130 + C1.x^128 + 2*C1.x^126 + 4*C1.x.124 + 2*C1.x^122 + C1.x^120 + 3*C1
....: x^118 + 2*C1.x^116 + 3*C1.x^114 + 3*C1.x^112 + 2*C1.x^108 + C1.x^104 + C1.x^102 + 4*C1.x^100 + 2*C1.x^98 + C1.x^96 + 2*C11x^94 + 4*C1.x^92 + 3*C1.x^90 + 3*C
....: .x^88 + C1.x^84 + 3*C1.x^82 + 4*C1.x^80 + 3*C1.x^78 + 4*C1.x^76 + 4*C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + 4*C1.x^66 + 2*C1.x^84 + C1.x^62 + 4*C1.x^60 + 3*C1.x^5
....: + 3*C1.x^56 + 3*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 2*C1.x^46 + 4*C1.x^44 + 4*C1.x^40 + 2*C1.x^38 + 2*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + C1.x^30 + 2*C1.x^26 +
....: 2*C1.x^22 + 2*C1.x^18 + C1.x^14 + 4*C1.x^12 + C1.x^8 + C1.x^6 + 3*C1.x^4 + 4*C1.one))*C1.y
sage: f1.diffn()
0 dx
sage: f1.diffn().int()
0
sage: decomposition_g0_p2th_power(f1)[0]
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [62], in <cell line: 1>()
----> 1 decomposition_g0_p2th_power(f1)[Integer(0)]
 
File <string>:12, in decomposition_g0_p2th_power(fct)
 
File <string>:5, in decomposition_g0_pth_power(fct)
 
File <string>:51, in int(self)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
1329 normalize(x._numer, x._denom, self.p)
1330 if nmod_poly_degree(x._denom) != 0:
-> 1331 raise ValueError("not integral")
1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:
 
ValueError: not integral
[6nsage: f2 = f1.pth_root()
[6nsage: decomposition_g0_p2th_power(f2)[0]
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [64], in <cell line: 1>()
----> 1 decomposition_g0_p2th_power(f2)[Integer(0)]
 
File <string>:11, in decomposition_g0_p2th_power(fct)
 
File <string>:5, in decomposition_g0_pth_power(fct)
 
File <string>:51, in int(self)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
1329 normalize(x._numer, x._denom, self.p)
1330 if nmod_poly_degree(x._denom) != 0:
-> 1331 raise ValueError("not integral")
1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:
 
ValueError: not integral
[6nsage: f2.diffn()
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
[6nsage: f2.diffn().int()
((x^162 + 2*x^160 + 4*x^158 + x^156 + x^152 + 2*x^148 + 3*x^146 + x^144 + x^142 + 4*x^140 + 4*x^138 + x^134 + 2*x^132 + 2*x^130 + 2*x^128 + x^126 + x^122 + x^120 + 2*x^118 + 3*x^114 + 4*x^112 + 3*x^110 + 4*x^108 + x^104 + x^102 + 4*x^100 + 4*x^98 + 3*x^94 + 4*x^90 + x^88 + 3*x^84 + 3*x^82 + 4*x^78 + x^74 + 4*x^72 + 3*x^70 + x^68 + 4*x^66 + 3*x^64 + 2*x^62 + 2*x^60 + 2*x^58 + x^56 + 2*x^54 + x^48 + 2*x^46 + 4*x^44 + 4*x^40 + 4*x^38 + x^36 + 4*x^32 + 2*x^30 + 3*x^28 + x^26 + 2*x^24 + 4*x^22 + 3*x^20 + 2*x^16 + 2*x^12 + 4*x^10 + 4*x^8 + 4*x^6 + 4*x^4 + 4*x^2 + 2)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y
[6nsage: decomposition_g0_pth_power(f2)[0]
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [67], in <cell line: 1>()
----> 1 decomposition_g0_pth_power(f2)[Integer(0)]
 
File <string>:5, in decomposition_g0_pth_power(fct)
 
File <string>:51, in int(self)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
1329 normalize(x._numer, x._denom, self.p)
1330 if nmod_poly_degree(x._denom) != 0:
-> 1331 raise ValueError("not integral")
1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:
 
ValueError: not integral
[6nsage: p
5
[6nsage: g0, A = decomposition_g0_pth_power(f1)
[6nsage: g0
0
[6nsage: A
((x^162 + 2*x^160 + 4*x^158 + x^156 + x^152 + 2*x^148 + 3*x^146 + x^144 + x^142 + 4*x^140 + 4*x^138 + x^134 + 2*x^132 + 2*x^130 + 2*x^128 + x^126 + x^122 + x^120 + 2*x^118 + 3*x^114 + 4*x^112 + 3*x^110 + 4*x^108 + x^104 + x^102 + 4*x^100 + 4*x^98 + 3*x^94 + 4*x^90 + x^88 + 3*x^84 + 3*x^82 + 4*x^78 + x^74 + 4*x^72 + 3*x^70 + x^68 + 4*x^66 + 3*x^64 + 2*x^62 + 2*x^60 + 2*x^58 + x^56 + 2*x^54 + x^48 + 2*x^46 + 4*x^44 + 4*x^40 + 4*x^38 + x^36 + 4*x^32 + 2*x^30 + 3*x^28 + x^26 + 2*x^24 + 4*x^22 + 3*x^20 + 2*x^16 + 2*x^12 + 4*x^10 + 4*x^8 + 4*x^6 + 4*x^4 + 4*x^2 + 2)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y
[6nsage: A0, A1 = decomposition_g0_pth_power(A)
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [72], in <cell line: 1>()
----> 1 A0, A1 = decomposition_g0_pth_power(A)
 
File <string>:5, in decomposition_g0_pth_power(fct)
 
File <string>:51, in int(self)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
1329 normalize(x._numer, x._denom, self.p)
1330 if nmod_poly_degree(x._denom) != 0:
-> 1331 raise ValueError("not integral")
1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:
 
ValueError: not integral
[6nsage: A
((x^162 + 2*x^160 + 4*x^158 + x^156 + x^152 + 2*x^148 + 3*x^146 + x^144 + x^142 + 4*x^140 + 4*x^138 + x^134 + 2*x^132 + 2*x^130 + 2*x^128 + x^126 + x^122 + x^120 + 2*x^118 + 3*x^114 + 4*x^112 + 3*x^110 + 4*x^108 + x^104 + x^102 + 4*x^100 + 4*x^98 + 3*x^94 + 4*x^90 + x^88 + 3*x^84 + 3*x^82 + 4*x^78 + x^74 + 4*x^72 + 3*x^70 + x^68 + 4*x^66 + 3*x^64 + 2*x^62 + 2*x^60 + 2*x^58 + x^56 + 2*x^54 + x^48 + 2*x^46 + 4*x^44 + 4*x^40 + 4*x^38 + x^36 + 4*x^32 + 2*x^30 + 3*x^28 + x^26 + 2*x^24 + 4*x^22 + 3*x^20 + 2*x^16 + 2*x^12 + 4*x^10 + 4*x^8 + 4*x^6 + 4*x^4 + 4*x^2 + 2)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y
[6nsage: A.diffn()
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
[6nsage: A.diffn().regular_form()
((3*x^145 + 3*x^141 + 3*x^137 + 3*x^135 + 3*x^133 + 2*x^131 + 3*x^127 + 4*x^125 + x^123 + 2*x^121 + x^119 + 4*x^117 + 2*x^115 + 4*x^111 + 3*x^109 + x^107 + 3*x^103 + 2*x^101 + 4*x^97 + 2*x^95 + 2*x^93 + 3*x^91 + 3*x^87 + 2*x^85 + 4*x^83 + 2*x^81 + 3*x^77 + x^75 + x^73 + 4*x^69 + 2*x^67 + 4*x^65 + 2*x^63 + 2*x^61 + 3*x^59 + 4*x^57 + 4*x^55 + 4*x^53 + 2*x^51 + 2*x^47 + 3*x^45 + x^43 + 2*x^41 + x^39 + 4*x^37 + 4*x^35 + 4*x^33 + 4*x^31 + 3*x^25 + 3*x^23 + 2*x^15 + 2*x^13 + x^11 + x^5 + x^3 + 2*x)*y) dx + (2*x^150 + 2*x^136 + 3*x^134 + 3*x^132 + 4*x^130 + 4*x^128 + 2*x^126 + 2*x^124 + x^122 + 3*x^118 + x^116 + 2*x^114 + 4*x^106 + 3*x^104 + 3*x^100 + 2*x^98 + x^96 + 2*x^94 + x^92 + 2*x^88 + 2*x^84 + 2*x^82 + 4*x^80 + 4*x^78 + 3*x^76 + 4*x^74 + 3*x^72 + 3*x^70 + x^68 + 4*x^64 + 3*x^62 + 3*x^60 + 2*x^58 + 3*x^56 + 4*x^54 + x^50 + 2*x^46 + 4*x^44 + x^42 + 4*x^40 + 4*x^38 + 4*x^36 + 4*x^34 + 2*x^32 + x^30 + 4*x^28 + x^26 + 3*x^22 + 3*x^20 + 4*x^18 + x^16 + 3*x^14 + x^12 + 2*x^10 + x^8 + 3*x^6 + 3*x^4 + x^2 + 3) dy
[6nsage: omega = A.diffn().regular_form()
[6nsage: g0 = omega.int()
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [77], in <cell line: 1>()
----> 1 g0 = omega.int()
 
File <string>:51, in int(self)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
1329 normalize(x._numer, x._denom, self.p)
1330 if nmod_poly_degree(x._denom) != 0:
-> 1331 raise ValueError("not integral")
1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:
 
ValueError: not integral
[6nsage: omega.int()
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [78], in <cell line: 1>()
----> 1 omega.int()
 
File <string>:51, in int(self)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
1329 normalize(x._numer, x._denom, self.p)
1330 if nmod_poly_degree(x._denom) != 0:
-> 1331 raise ValueError("not integral")
1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:
 
ValueError: not integral
[6nsage: omega
((3*x^145 + 3*x^141 + 3*x^137 + 3*x^135 + 3*x^133 + 2*x^131 + 3*x^127 + 4*x^125 + x^123 + 2*x^121 + x^119 + 4*x^117 + 2*x^115 + 4*x^111 + 3*x^109 + x^107 + 3*x^103 + 2*x^101 + 4*x^97 + 2*x^95 + 2*x^93 + 3*x^91 + 3*x^87 + 2*x^85 + 4*x^83 + 2*x^81 + 3*x^77 + x^75 + x^73 + 4*x^69 + 2*x^67 + 4*x^65 + 2*x^63 + 2*x^61 + 3*x^59 + 4*x^57 + 4*x^55 + 4*x^53 + 2*x^51 + 2*x^47 + 3*x^45 + x^43 + 2*x^41 + x^39 + 4*x^37 + 4*x^35 + 4*x^33 + 4*x^31 + 3*x^25 + 3*x^23 + 2*x^15 + 2*x^13 + x^11 + x^5 + x^3 + 2*x)*y) dx + (2*x^150 + 2*x^136 + 3*x^134 + 3*x^132 + 4*x^130 + 4*x^128 + 2*x^126 + 2*x^124 + x^122 + 3*x^118 + x^116 + 2*x^114 + 4*x^106 + 3*x^104 + 3*x^100 + 2*x^98 + x^96 + 2*x^94 + x^92 + 2*x^88 + 2*x^84 + 2*x^82 + 4*x^80 + 4*x^78 + 3*x^76 + 4*x^74 + 3*x^72 + 3*x^70 + x^68 + 4*x^64 + 3*x^62 + 3*x^60 + 2*x^58 + 3*x^56 + 4*x^54 + x^50 + 2*x^46 + 4*x^44 + x^42 + 4*x^40 + 4*x^38 + 4*x^36 + 4*x^34 + 2*x^32 + x^30 + 4*x^28 + x^26 + 3*x^22 + 3*x^20 + 4*x^18 + x^16 + 3*x^14 + x^12 + 2*x^10 + x^8 + 3*x^6 + 3*x^4 + x^2 + 3) dy
....: ^I^Ireturn 0*C.x
....: ^I#which = random.choice([0, 1])
....: ^IP = self.dx.function
....: ^IQ = self.dy.function
....: ^IPy, Px = P.quo_rem(y) #P = y*Py + Px
....: ^IQy, Qx = Q.quo_rem(y)
....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())
....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)
....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.
....: ^IW = Rx(0)
....: ^Iwhile(numerator != 0):
....: ^I^Id = numerator.degree()
....: ^I^Ir = f.degree()
....: ^I^In_lead = numerator.leading_coefficient()
....: ^I^If_lead = Rx(f).leading_coefficient()
....: ^I^Ia = d - (r-1)
....: ^I^Iif a >= 0:
....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))
....: ^I^I^IW += W_coeff*Rx(x^a)
....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()
....: ^I^I^Inumerator = Rx(numerator)
....: ^I^Iif a < 0:
....: ^I^I print('numerator', numerator)
....: ^I^I^IW += Rx(numerator/f.derivative())
....: ^I^I^Inumerator = Rx(0)
....: ^Iresult = result + superelliptic_function(C, y*W)
....: ^Ireturn result
Input In [80]
W += Rx(numerator/f.derivative())
^
TabError: inconsistent use of tabs and spaces in indentation
 
....: ^I#which = random.choice([0, 1])
....: ^IP = self.dx.function
....: ^IQ = self.dy.function
....: ^IPy, Px = P.quo_rem(y) #P = y*Py + Px
....: ^IQy, Qx = Q.quo_rem(y)
....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())
....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)
....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.
....: ^IW = Rx(0)
....: ^Iwhile(numerator != 0):
....: ^I^Id = numerator.degree()
....: ^I^Ir = f.degree()
....: ^I^In_lead = numerator.leading_coefficient()
....: ^I^If_lead = Rx(f).leading_coefficient()
....: ^I^Ia = d - (r-1)
....: ^I^Iif a >= 0:
....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))
....: ^I^I^IW += W_coeff*Rx(x^a)
....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()
....: ^I^I^Inumerator = Rx(numerator)
....: ^I^Iif a < 0:
....: ^I^I^Iprint('numerator', numerator)
....: ^I^I^IW += Rx(numerator/f.derivative())
....: ^I^I^Inumerator = Rx(0)
....: ^Iresult = result + superelliptic_function(C, y*W)
....: ^Ireturn result
....:
[6nsage: int(omega)
numerator 2*x^10 + 2*x^6 + x^2 + 2
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [82], in <cell line: 1>()
----> 1 int(omega)
 
Input In [81], in int(self)
32 if a < Integer(0):
33 print('numerator', numerator)
---> 34 W += Rx(numerator/f.derivative())
35 numerator = Rx(Integer(0))
36 result = result + superelliptic_function(C, y*W)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
1329 normalize(x._numer, x._denom, self.p)
1330 if nmod_poly_degree(x._denom) != 0:
-> 1331 raise ValueError("not integral")
1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:
 
ValueError: not integral
[6nsage: omega1 = (2*C1.x^10 + 2*C1.x^6 + C1.x^2 + 2*C1.one)/C1.y*C.dx
[6nsage: omega1
((2*x^10 + 2*x^6 + x^2 + 2)/y) dx
[6nsage: omega1.int()
((2*x^32 + 4*x^30 + 2*x^28 + 3*x^24 + 2*x^20 + 4*x^18 + 2*x^16 + 4*x^12 + x^10 + x^8 + 4*x^4 + 3*x^2 + 4)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y
[6nsage: omega1 = (2*C1.x^10 + 2*C1.x^6 + C1.x^2 + 2*C1.one)/C1.y*C1.dx
[6nsage: omega1.int()
((2*x^32 + 4*x^30 + 2*x^28 + 3*x^24 + 2*x^20 + 4*x^18 + 2*x^16 + 4*x^12 + x^10 + x^8 + 4*x^4 + 3*x^2 + 4)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y
[6nsage: C1
Superelliptic curve with the equation y^2 = x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x over Finite Field of size 5
[6nsage: omega1.regular_form()
((x^15 + 2*x^7 + x^5 + 2*x^3 + 4*x)*y) dx + (4*x^20 + x^16 + 3*x^12 + 3*x^6 + 2*x^4 + 2*x^2 + 1) dy
[6nsage: omega1
((2*x^10 + 2*x^6 + x^2 + 2)/y) dx
[6nsage: C1
Superelliptic curve with the equation y^2 = x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x over Finite Field of size 5
[6nsage: omega1 == 2*C1.y.diffn()
False
[6nsage: omega1, 2*C1.diffn()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [93], in <cell line: 1>()
----> 1 omega1, Integer(2)*C1.diffn()
 
AttributeError: 'superelliptic' object has no attribute 'diffn'
[6nsage: omega1, 2*C1.y.diffn()
(((2*x^10 + 2*x^6 + x^2 + 2)/y) dx, ((2*x^10 + x^6 + 2*x^2 - 1)/y) dx)
[6nsage: aux = (C1.y)^(-1)*C1.dx
[6nsage: aux.int()
---------------------------------------------------------------------------
ZeroDivisionError Traceback (most recent call last)
Input In [96], in <cell line: 1>()
----> 1 aux.int()
 
File <string>:198, in int(self)
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:3994, in sage.rings.polynomial.polynomial_element.Polynomial.integral()
3992 cdef Py_ssize_t n
3993 zero = Q.zero()
-> 3994 p = [zero] + [cm.bin_op(Q(self.get_unsafe(n)), n + 1, operator.truediv)
3995 if self.get_unsafe(n) else zero for n in range(self.degree() + 1)]
3996 return S(p)
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
1202 self._record_exception()
1203 else:
-> 1204 return PyObject_CallObject(op, xy)
1205
1206 if op is mul:
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
1735 cdef int cl = classify_elements(left, right)
1736 if HAVE_SAME_PARENT(cl):
-> 1737 return (<Element>left)._div_(right)
1738 if BOTH_ARE_ELEMENT(cl):
1739 return coercion_model.bin_op(left, right, truediv)
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_()
2621 right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
2622 if right_inverse is None:
-> 2623 raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
2624 else:
2625 return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)
 
ZeroDivisionError: inverse of Mod(0, 5) does not exist
[6nsage: omega1- 2*C1.y.diffn()
((x^6 - x^2 - 2)/y) dx
[6nsage: (omega1- 2*C1.y.diffn()).int()
((3*x^28 + 4*x^26 + 4*x^24 + x^22 + 4*x^20 + 4*x^16 + x^14 + 2*x^12 + 2*x^10 + 4*x^8 + 3*x^6 + 4*x^4 + 2*x^2 + 4)/(x^36 + 3*x^34 + 2*x^32 + 3*x^30 + 2*x^28 + 2*x^26 + 4*x^24 + 2*x^22 + 2*x^20 + 2*x^18 + 4*x^16 + 3*x^14 + 3*x^12 + 4*x^10 + 4*x^6 + x^2 + 1))*y
[6nsage: omega1.int()
((2*x^32 + 4*x^30 + 2*x^28 + 3*x^24 + 2*x^20 + 4*x^18 + 2*x^16 + 4*x^12 + x^10 + x^8 + 4*x^4 + 3*x^2 + 4)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y
[6nsage: (omega1- 2*C1.y.diffn()).regular_form.int()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [100], in <cell line: 1>()
----> 1 (omega1- Integer(2)*C1.y.diffn()).regular_form.int()
 
AttributeError: 'function' object has no attribute 'int'
[6nsage: (omega1- 2*C1.y.diffn()).regular_form().int()
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [101], in <cell line: 1>()
----> 1 (omega1- Integer(2)*C1.y.diffn()).regular_form().int()
 
File <string>:51, in int(self)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
1329 normalize(x._numer, x._denom, self.p)
1330 if nmod_poly_degree(x._denom) != 0:
-> 1331 raise ValueError("not integral")
1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:
 
ValueError: not integral
[6nsage:
[6nsage: omega1
((2*x^10 + 2*x^6 + x^2 + 2)/y) dx
[6nsage: C1
Superelliptic curve with the equation y^2 = x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x over Finite Field of size 5
[6nsage: int(omega)
numerator 2*x^10 + 2*x^6 + x^2 + 2
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [104], in <cell line: 1>()
----> 1 int(omega)
 
Input In [81], in int(self)
32 if a < Integer(0):
33 print('numerator', numerator)
---> 34 W += Rx(numerator/f.derivative())
35 numerator = Rx(Integer(0))
36 result = result + superelliptic_function(C, y*W)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
1329 normalize(x._numer, x._denom, self.p)
1330 if nmod_poly_degree(x._denom) != 0:
-> 1331 raise ValueError("not integral")
1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:
 
ValueError: not integral
[6nsage: C1
Superelliptic curve with the equation y^2 = x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x over Finite Field of size 5
[6nsage: C1.polynomial.derivative()
2*x^10 + x^6 + 2*x^2 + 4
[6nsage: omega1
((2*x^10 + 2*x^6 + x^2 + 2)/y) dx
[6nsage: B1[0].omega0.regular_form()
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [108], in <cell line: 1>()
----> 1 B1[Integer(0)].omega0.regular_form()
 
File <string>:83, in regular_drw_form(omega)
 
File <string>:12, in decomposition_g0_p2th_power(fct)
 
File <string>:5, in decomposition_g0_pth_power(fct)
 
File <string>:51, in int(self)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
1329 normalize(x._numer, x._denom, self.p)
1330 if nmod_poly_degree(x._denom) != 0:
-> 1331 raise ValueError("not integral")
1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:
 
ValueError: not integral
[6nsage: OM = B1[0].omega0
[6nsage: OM
[(1/(x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x))*y] d[x] + V(((2*x^36 - 2*x^34 - x^32 + x^24 + x^22 + 2*x^20 + 2*x^18 - 2*x^16 - 2*x^14 + x^10 + 2*x^8 + x^6 - x^4 - 2*x^2 - 1)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((2*x^114 + 3*x^110 + x^108 + 2*x^106 + 3*x^104 + x^100 + x^90 + 3*x^88 + 2*x^84 + 3*x^82 + 2*x^80 + 2*x^78 + 3*x^76 + 2*x^70 + x^66 + 3*x^64 + 4*x^62 + x^60 + x^58 + 3*x^56 + 2*x^48 + 3*x^44 + 3*x^42 + 2*x^36 + x^34 + 2*x^32 + 4*x^30 + 2*x^28 + 4*x^26 + 2*x^24 + 3*x^20 + 2*x^18 + 4*x^16 + 3*x^14 + 4*x^10 + 4*x^8 + 4*x^6 + 4*x^4)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y])
[6nsage: OM - de_rham_witt_lift_form0(om)
V(((2*x^94 + 2*x^90 + x^86 + x^84 + 2*x^82 + x^78 + 2*x^72 - 2*x^70 - x^68 + 2*x^66 - 2*x^64 - 2*x^62 - x^60 + 2*x^50 - x^48 + x^44 - x^42 - x^40 + 2*x^38 - x^36 + 2*x^34 - x^32 - 2*x^30 - 2*x^28 + 2*x^26 + 2*x^24 + 2*x^22 - 2*x^20 - x^18 - x^16 - x^12 + x^10 + x^8 - x^6 + x^4 - 2*x^2 - 1)/y) dx)
[6nsage: aux = OM - de_rham_witt_lift_form0(om)
[6nsage: sage: aom = aux.omega
[6nsage: aom
((2*x^94 + 2*x^90 + x^86 + x^84 + 2*x^82 + x^78 + 2*x^72 - 2*x^70 - x^68 + 2*x^66 - 2*x^64 - 2*x^62 - x^60 + 2*x^50 - x^48 + x^44 - x^42 - x^40 + 2*x^38 - x^36 + 2*x^34 - x^32 - 2*x^30 - 2*x^28 + 2*x^26 + 2*x^24 + 2*x^22 - 2*x^20 - x^18 - x^16 - x^12 + x^10 + x^8 - x^6 + x^4 - 2*x^2 - 1)/y) dx
sage: aom.is_regular_on_U0()
True
sage: aom0, h = decomposition_omega0_hpdh(aom)
sage: aom.verschiebung() == aom0.verschiebung() + mult_by_p(h.diffn())
True
[6nsagsage: mult_by_p(h.diffn()) == (0*C.dx).verschiebung()
False
[6nsage: mult_by_p(h.diffn()) == (h^(p-1)*h.diffn()).verschiebung()
True
[6nsage: mult_by_p(h.diffn()) == (h^p).verschiebung().diffn()
True
[6nsage: h1 = h^p
sage: decomposition_g0_p2th_power(h1)
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [122], in <cell line: 1>()
----> 1 decomposition_g0_p2th_power(h1)
 
File <string>:12, in decomposition_g0_p2th_power(fct)
 
File <string>:5, in decomposition_g0_pth_power(fct)
 
File <string>:51, in int(self)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
1329 normalize(x._numer, x._denom, self.p)
1330 if nmod_poly_degree(x._denom) != 0:
-> 1331 raise ValueError("not integral")
1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:
 
ValueError: not integral
[6nsage: h1
((x^816 + 2*x^814 + x^812 + 2*x^806 + 4*x^804 + 2*x^802 + 4*x^796 + 3*x^794 + 4*x^792 + x^786 + 2*x^784 + x^782 + x^766 + 2*x^764 + x^762 + 2*x^746 + 4*x^744 + 2*x^742 + 3*x^736 + x^734 + 3*x^732 + x^726 + 2*x^724 + x^722 + x^716 + 2*x^714 + x^712 + 4*x^706 + 3*x^704 + 4*x^702 + 4*x^696 + 3*x^694 + 4*x^692 + x^676 + 2*x^674 + x^672 + 2*x^666 + 4*x^664 + 2*x^662 + 2*x^656 + 4*x^654 + 2*x^652 + 2*x^646 + 4*x^644 + 2*x^642 + x^636 + 2*x^634 + x^632 + x^616 + 2*x^614 + x^612 + x^606 + 2*x^604 + x^602 + 2*x^596 + 4*x^594 + 2*x^592 + 3*x^576 + x^574 + 3*x^572 + 4*x^566 + 3*x^564 + 4*x^562 + 3*x^556 + x^554 + 3*x^552 + 4*x^546 + 3*x^544 + 4*x^542 + x^526 + 2*x^524 + x^522 + x^516 + 2*x^514 + x^512 + 4*x^506 + 3*x^504 + 4*x^502 + 4*x^496 + 3*x^494 + 4*x^492 + 3*x^476 + x^474 + 3*x^472 + 4*x^456 + 3*x^454 + 4*x^452 + x^446 + 2*x^444 + x^442 + 3*x^426 + x^424 + 3*x^422 + 3*x^416 + x^414 + 3*x^412 + 4*x^396 + 3*x^394 + 4*x^392 + x^376 + 2*x^374 + x^372 + 4*x^366 + 3*x^364 + 4*x^362 + 3*x^356 + x^354 + 3*x^352 + x^346 + 2*x^344 + x^342 + 4*x^336 + 3*x^334 + 4*x^332 + 3*x^326 + x^324 + 3*x^322 + 2*x^316 + 4*x^314 + 2*x^312 + 2*x^306 + 4*x^304 + 2*x^302 + 2*x^296 + 4*x^294 + 2*x^292 + x^286 + 2*x^284 + x^282 + 2*x^276 + 4*x^274 + 2*x^272 + x^246 + 2*x^244 + x^242 + 2*x^236 + 4*x^234 + 2*x^232 + 4*x^226 + 3*x^224 + 4*x^222 + 4*x^206 + 3*x^204 + 4*x^202 + 4*x^196 + 3*x^194 + 4*x^192 + x^186 + 2*x^184 + x^182 + 4*x^166 + 3*x^164 + 4*x^162 + 2*x^156 + 4*x^154 + 2*x^152 + 3*x^146 + x^144 + 3*x^142 + x^136 + 2*x^134 + x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 4*x^116 + 3*x^114 + 4*x^112 + 3*x^106 + x^104 + 3*x^102 + 2*x^86 + 4*x^84 + 2*x^82 + 2*x^66 + 4*x^64 + 2*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 4*x^46 + 3*x^44 + 4*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^26 + 3*x^24 + 4*x^22 + 4*x^16 + 3*x^14 + 4*x^12 + 2*x^6 + 4*x^4 + 2*x^2)/(x^156 + 2*x^154 + 2*x^152 + 2*x^150 + 2*x^148 + 2*x^146 + 2*x^144 + 3*x^142 + 4*x^140 + 3*x^138 + 4*x^136 + 3*x^134 + 4*x^132 + 3*x^130 + x^128 + 2*x^126 + 4*x^124 + 2*x^122 + x^120 + 3*x^118 + 2*x^116 + 3*x^114 + 3*x^112 + 2*x^108 + x^104 + x^102 + 4*x^100 + 2*x^98 + x^96 + 2*x^94 + 4*x^92 + 3*x^90 + 3*x^88 + x^84 + 3*x^82 + 4*x^80 + 3*x^78 + 4*x^76 + 4*x^74 + 4*x^72 + 3*x^70 + 4*x^66 + 2*x^64 + x^62 + 4*x^60 + 3*x^58 + 3*x^56 + 3*x^52 + 3*x^50 + 3*x^48 + 2*x^46 + 4*x^44 + 4*x^40 + 2*x^38 + 2*x^36 + 3*x^34 + 4*x^32 + x^30 + 2*x^26 + 2*x^22 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y
[6nsage: h1.diffn().regular_form().form() == h1.diffn()
True
[6nsage: h1.diffn().regular_form().int()
0
[6nsage: decomposition_g0_pth_power(h1)
(0,
((x^162 + 2*x^160 + 4*x^158 + x^156 + x^152 + 2*x^148 + 3*x^146 + x^144 + x^142 + 4*x^140 + 4*x^138 + x^134 + 2*x^132 + 2*x^130 + 2*x^128 + x^126 + x^122 + x^120 + 2*x^118 + 3*x^114 + 4*x^112 + 3*x^110 + 4*x^108 + x^104 + x^102 + 4*x^100 + 4*x^98 + 3*x^94 + 4*x^90 + x^88 + 3*x^84 + 3*x^82 + 4*x^78 + x^74 + 4*x^72 + 3*x^70 + x^68 + 4*x^66 + 3*x^64 + 2*x^62 + 2*x^60 + 2*x^58 + x^56 + 2*x^54 + x^48 + 2*x^46 + 4*x^44 + 4*x^40 + 4*x^38 + x^36 + 4*x^32 + 2*x^30 + 3*x^28 + x^26 + 2*x^24 + 4*x^22 + 3*x^20 + 2*x^16 + 2*x^12 + 4*x^10 + 4*x^8 + 4*x^6 + 4*x^4 + 4*x^2 + 2)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y)
[6nsage: A1, A = decomposition_g0_pth_power(h1)
[6nsage: A.diffn()
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
[6nsage: A.diffn().int()
((x^162 + 2*x^160 + 4*x^158 + x^156 + x^152 + 2*x^148 + 3*x^146 + x^144 + x^142 + 4*x^140 + 4*x^138 + x^134 + 2*x^132 + 2*x^130 + 2*x^128 + x^126 + x^122 + x^120 + 2*x^118 + 3*x^114 + 4*x^112 + 3*x^110 + 4*x^108 + x^104 + x^102 + 4*x^100 + 4*x^98 + 3*x^94 + 4*x^90 + x^88 + 3*x^84 + 3*x^82 + 4*x^78 + x^74 + 4*x^72 + 3*x^70 + x^68 + 4*x^66 + 3*x^64 + 2*x^62 + 2*x^60 + 2*x^58 + x^56 + 2*x^54 + x^48 + 2*x^46 + 4*x^44 + 4*x^40 + 4*x^38 + x^36 + 4*x^32 + 2*x^30 + 3*x^28 + x^26 + 2*x^24 + 4*x^22 + 3*x^20 + 2*x^16 + 2*x^12 + 4*x^10 + 4*x^8 + 4*x^6 + 4*x^4 + 4*x^2 + 2)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y
[6nsage: A.diffn().regular_form().int()
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [130], in <cell line: 1>()
----> 1 A.diffn().regular_form().int()
 
File <string>:51, in int(self)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
1329 normalize(x._numer, x._denom, self.p)
1330 if nmod_poly_degree(x._denom) != 0:
-> 1331 raise ValueError("not integral")
1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:
 
ValueError: not integral
[6nsage: int(A.diffn().regular_form())
numerator 2*x^10 + 2*x^6 + x^2 + 2
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [131], in <cell line: 1>()
----> 1 int(A.diffn().regular_form())
 
Input In [81], in int(self)
32 if a < Integer(0):
33 print('numerator', numerator)
---> 34 W += Rx(numerator/f.derivative())
35 numerator = Rx(Integer(0))
36 result = result + superelliptic_function(C, y*W)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
1329 normalize(x._numer, x._denom, self.p)
1330 if nmod_poly_degree(x._denom) != 0:
-> 1331 raise ValueError("not integral")
1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:
 
ValueError: not integral
[6nssage: A.diffn().regular_form()
((3*x^145 + 3*x^141 + 3*x^137 + 3*x^135 + 3*x^133 + 2*x^131 + 3*x^127 + 4*x^125 + x^123 + 2*x^121 + x^119 + 4*x^117 + 2*x^115 + 4*x^111 + 3*x^109 + x^107 + 3*x^103 + 2*x^101 + 4*x^97 + 2*x^95 + 2*x^93 + 3*x^91 + 3*x^87 + 2*x^85 + 4*x^83 + 2*x^81 + 3*x^77 + x^75 + x^73 + 4*x^69 + 2*x^67 + 4*x^65 + 2*x^63 + 2*x^61 + 3*x^59 + 4*x^57 + 4*x^55 + 4*x^53 + 2*x^51 + 2*x^47 + 3*x^45 + x^43 + 2*x^41 + x^39 + 4*x^37 + 4*x^35 + 4*x^33 + 4*x^31 + 3*x^25 + 3*x^23 + 2*x^15 + 2*x^13 + x^11 + x^5 + x^3 + 2*x)*y) dx + (2*x^150 + 2*x^136 + 3*x^134 + 3*x^132 + 4*x^130 + 4*x^128 + 2*x^126 + 2*x^124 + x^122 + 3*x^118 + x^116 + 2*x^114 + 4*x^106 + 3*x^104 + 3*x^100 + 2*x^98 + x^96 + 2*x^94 + x^92 + 2*x^88 + 2*x^84 + 2*x^82 + 4*x^80 + 4*x^78 + 3*x^76 + 4*x^74 + 3*x^72 + 3*x^70 + x^68 + 4*x^64 + 3*x^62 + 3*x^60 + 2*x^58 + 3*x^56 + 4*x^54 + x^50 + 2*x^46 + 4*x^44 + x^42 + 4*x^40 + 4*x^38 + 4*x^36 + 4*x^34 + 2*x^32 + x^30 + 4*x^28 + x^26 + 3*x^22 + 3*x^20 + 4*x^18 + x^16 + 3*x^14 + x^12 + 2*x^10 + x^8 + 3*x^6 + 3*x^4 + x^2 + 3) dy
....: ^IQ = self.dy.function
....: ^IPy, Px = P.quo_rem(y) #P = y*Py + Px
....: ^IQy, Qx = Q.quo_rem(y)
....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())
....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)
....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.
....: ^IW = Rx(0)
....: ^Iwhile(numerator != 0):
....: ^I^Iprint('numerator: ', numerator)
....: ^I^Iprint('W: ', W)
....: ^I^Id = numerator.degree()
....: ^I^Ir = f.degree()
....: ^I^In_lead = numerator.leading_coefficient()
....: ^I^If_lead = Rx(f).leading_coefficient()
....: ^I^Ia = d - (r-1)
....: ^I^Iif a >= 0:
....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))
....: ^I^I^IW += W_coeff*Rx(x^a)
....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()
....: ^I^I^Inumerator = Rx(numerator)
....: ^I^Iif a < 0:
....: ^I^I^Iprint('numerator', numerator)
....: ^I^I^IW += Rx(numerator/f.derivative())
....: ^I^I^Inumerator = Rx(0)
....: ^Iresult = result + superelliptic_function(C, y*W)
....: ^Ireturn result
....:
[6nsage: int(A.diffn().regular_form())
numerator: 2*x^140 + 4*x^136 + x^132 + 2*x^130 + 3*x^128 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: 0
numerator: 3*x^136 + 4*x^132 + 3*x^128 + 3*x^126 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126
numerator: 4*x^132 + 2*x^128 + 2*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122
numerator: x^128 + x^124 + 3*x^122 + 4*x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118
numerator: 3*x^122 + 3*x^118 + 4*x^116 + 3*x^114 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114
numerator: x^118 + 4*x^116 + x^114 + 4*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108
numerator: 4*x^116 + 3*x^108 + x^106 + 3*x^104 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104
numerator: 2*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102
numerator: 3*x^102 + x^98 + x^96 + x^94 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92
numerator: 4*x^98 + x^96 + 4*x^94 + x^92 + 3*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88
numerator: x^96 + x^92 + 4*x^88 + 3*x^86 + 4*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84
numerator: x^92 + 2*x^88 + 2*x^86 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82
numerator: 3*x^88 + 2*x^86 + 3*x^84 + x^82 + 4*x^80 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78
numerator: 2*x^86 + x^82 + 4*x^80 + 2*x^78 + 4*x^76 + 2*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74
numerator: x^82 + 4*x^80 + 3*x^78 + 2*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72
numerator: 4*x^80 + 4*x^78 + 2*x^76 + 4*x^74 + 4*x^72 + x^70 + x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68
numerator: 4*x^78 + 4*x^74 + 2*x^70 + x^68 + 3*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66
numerator: 2*x^70 + 2*x^68 + x^66 + 2*x^64 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64
numerator: 2*x^68 + 2*x^64 + 3*x^62 + 4*x^60 + 3*x^58 + 2*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56
numerator: 3*x^62 + 4*x^60 + x^58 + x^56 + x^54 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54
numerator: 4*x^60 + 4*x^58 + x^56 + 4*x^54 + 2*x^52 + 3*x^50 + 2*x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48
numerator: 4*x^58 + 4*x^56 + 4*x^54 + 3*x^52 + 4*x^50 + 2*x^48 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46
numerator: 4*x^56 + 3*x^52 + 4*x^50 + 3*x^48 + 3*x^46 + 3*x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44
numerator: 3*x^52 + 4*x^50 + 4*x^46 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42
numerator: 4*x^50 + 3*x^48 + 4*x^46 + 3*x^44 + 4*x^42 + 2*x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38
numerator: 3*x^48 + 2*x^46 + 3*x^44 + x^40 + 2*x^38 + 2*x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36
numerator: 2*x^46 + x^40 + 4*x^38 + 3*x^36 + 4*x^34 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34
numerator: x^40 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32
numerator: 3*x^36 + x^32 + 3*x^28 + x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26
numerator: x^32 + 2*x^28 + 3*x^26 + 2*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22
numerator: 3*x^28 + 3*x^26 + 3*x^24 + x^22 + 4*x^20 + x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18
numerator: 3*x^26 + x^22 + 4*x^20 + 3*x^18 + x^16 + 3*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14
numerator: x^22 + 4*x^20 + 2*x^18 + 3*x^16 + 2*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12
numerator: 4*x^20 + 3*x^18 + 3*x^16 + 3*x^14 + 4*x^12 + x^10 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8
numerator: 3*x^18 + x^16 + 3*x^14 + 2*x^10 + 2*x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8 + 2*x^6
numerator: x^16 + 2*x^10 + 2*x^8 + 3*x^6 + 2*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8 + 2*x^6 + x^4
numerator: 2*x^10 + 2*x^6 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8 + 2*x^6 + x^4 + 4*x^2
numerator 2*x^10 + 2*x^6 + x^2 + 2
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [134], in <cell line: 1>()
----> 1 int(A.diffn().regular_form())
 
Input In [133], in int(self)
34 if a < Integer(0):
35 print('numerator', numerator)
---> 36 W += Rx(numerator/f.derivative())
37 numerator = Rx(Integer(0))
38 result = result + superelliptic_function(C, y*W)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
1329 normalize(x._numer, x._denom, self.p)
1330 if nmod_poly_degree(x._denom) != 0:
-> 1331 raise ValueError("not integral")
1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:
 
ValueError: not integral
....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())
....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)
....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.
....: ^IW = Rx(0)
....: ^Iwhile(numerator != 0):
....: ^I^Iprint('numerator: ', numerator)
....: ^I^Iprint('W: ', W)
....: ^I^IW1 = superelliptic_function(C, W)
....: ^I^In1 = superelliptic_form(C, numerator/y)
....: ^I^Iprint(self == (C.y*W1).diffn() + n1)
....: ^I^Id = numerator.degree()
....: ^I^Ir = f.degree()
....: ^I^In_lead = numerator.leading_coefficient()
....: ^I^If_lead = Rx(f).leading_coefficient()
....: ^I^Ia = d - (r-1)
....: ^I^Iif a >= 0:
....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))
....: ^I^I^IW += W_coeff*Rx(x^a)
....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()
....: ^I^I^Inumerator = Rx(numerator)
....: ^I^Iif a < 0:
....: ^I^I^Iprint('numerator', numerator)
....: ^I^I^IW += Rx(numerator/f.derivative())
....: ^I^I^Inumerator = Rx(0)
....: ^Iresult = result + superelliptic_function(C, y*W)
....: ^Ireturn result
....:
sage: int(A.diffn().regular_form())
numerator: 2*x^140 + 4*x^136 + x^132 + 2*x^130 + 3*x^128 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: 0
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [136], in <cell line: 1>()
----> 1 int(A.diffn().regular_form())
 
Input In [135], in int(self)
24 W1 = superelliptic_function(C, W)
25 n1 = superelliptic_form(C, numerator/y)
---> 26 print(self == (C.y*W1).diffn() + n1)
27 d = numerator.degree()
28 r = f.degree()
 
File <string>:12, in __eq__(self, other)
 
AttributeError: 'superelliptic_regular_form' object has no attribute 'reduce'
....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())
....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)
....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.
....: ^IW = Rx(0)
....: ^Iwhile(numerator != 0):
....: ^I^Iprint('numerator: ', numerator)
....: ^I^Iprint('W: ', W)
....: ^I^IW1 = superelliptic_function(C, W)
....: ^I^In1 = superelliptic_form(C, numerator/y)
....: ^I^Iprint(self.form() == (C.y*W1).diffn() + n1)
....: ^I^Id = numerator.degree()
....: ^I^Ir = f.degree()
....: ^I^In_lead = numerator.leading_coefficient()
....: ^I^If_lead = Rx(f).leading_coefficient()
....: ^I^Ia = d - (r-1)
....: ^I^Iif a >= 0:
....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))
....: ^I^I^IW += W_coeff*Rx(x^a)
....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()
....: ^I^I^Inumerator = Rx(numerator)
....: ^I^Iif a < 0:
....: ^I^I^Iprint('numerator', numerator)
....: ^I^I^IW += Rx(numerator/f.derivative())
....: ^I^I^Inumerator = Rx(0)
....: ^Iresult = result + superelliptic_function(C, y*W)
....: ^Ireturn result
....:
[6nsage: int(A.diffn().regular_form())
numerator: 2*x^140 + 4*x^136 + x^132 + 2*x^130 + 3*x^128 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: 0
False
numerator: 3*x^136 + 4*x^132 + 3*x^128 + 3*x^126 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126
False
numerator: 4*x^132 + 2*x^128 + 2*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122
False
numerator: x^128 + x^124 + 3*x^122 + 4*x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118
False
numerator: 3*x^122 + 3*x^118 + 4*x^116 + 3*x^114 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114
False
numerator: x^118 + 4*x^116 + x^114 + 4*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108
False
numerator: 4*x^116 + 3*x^108 + x^106 + 3*x^104 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104
False
numerator: 2*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102
False
numerator: 3*x^102 + x^98 + x^96 + x^94 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92
False
numerator: 4*x^98 + x^96 + 4*x^94 + x^92 + 3*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88
False
numerator: x^96 + x^92 + 4*x^88 + 3*x^86 + 4*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84
False
numerator: x^92 + 2*x^88 + 2*x^86 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82
False
numerator: 3*x^88 + 2*x^86 + 3*x^84 + x^82 + 4*x^80 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78
False
numerator: 2*x^86 + x^82 + 4*x^80 + 2*x^78 + 4*x^76 + 2*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74
False
numerator: x^82 + 4*x^80 + 3*x^78 + 2*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72
False
numerator: 4*x^80 + 4*x^78 + 2*x^76 + 4*x^74 + 4*x^72 + x^70 + x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68
False
numerator: 4*x^78 + 4*x^74 + 2*x^70 + x^68 + 3*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66
False
numerator: 2*x^70 + 2*x^68 + x^66 + 2*x^64 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64
False
numerator: 2*x^68 + 2*x^64 + 3*x^62 + 4*x^60 + 3*x^58 + 2*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56
False
numerator: 3*x^62 + 4*x^60 + x^58 + x^56 + x^54 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54
False
numerator: 4*x^60 + 4*x^58 + x^56 + 4*x^54 + 2*x^52 + 3*x^50 + 2*x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [138], in <cell line: 1>()
----> 1 int(A.diffn().regular_form())
 
Input In [137], in int(self)
24 W1 = superelliptic_function(C, W)
25 n1 = superelliptic_form(C, numerator/y)
---> 26 print(self.form() == (C.y*W1).diffn() + n1)
27 d = numerator.degree()
28 r = f.degree()
 
File <string>:95, in diffn(self)
 
File <string>:7, in __init__(self, C, g)
 
File <string>:296, in reduction_form(C, g)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
636 ring_one = self.ring().one()
637 try:
--> 638 return self._element_class(self, x, ring_one, coerce=coerce)
639 except (TypeError, ValueError):
640 pass
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
112 FieldElement.__init__(self, parent)
113 if coerce:
--> 114 self.__numerator = parent.ring()(numerator)
115 self.__denominator = parent.ring()(denominator)
116 else:
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
1001
1002 try:
-> 1003 return self(str(element))
1004 except TypeError:
1005 pass
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())
....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)
....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.
....: ^IW = Rx(0)
....: ^Iwhile(numerator != 0):
....: ^I^Iprint('numerator: ', numerator)
....: ^I^Iprint('W: ', W)
....: ^I^IW1 = superelliptic_function(C, W)
....: ^I^In1 = superelliptic_form(C, numerator/y)
....: ^I^Iprint(self.form(), (C.y*W1).diffn() + n1)
....: ^I^Id = numerator.degree()
....: ^I^Ir = f.degree()
....: ^I^In_lead = numerator.leading_coefficient()
....: ^I^If_lead = Rx(f).leading_coefficient()
....: ^I^Ia = d - (r-1)
....: ^I^Iif a >= 0:
....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))
....: ^I^I^IW += W_coeff*Rx(x^a)
....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()
....: ^I^I^Inumerator = Rx(numerator)
....: ^I^Iif a < 0:
....: ^I^I^Iprint('numerator', numerator)
....: ^I^I^IW += Rx(numerator/f.derivative())
....: ^I^I^Inumerator = Rx(0)
....: ^Iresult = result + superelliptic_function(C, y*W)
....: ^Ireturn result
....:
[6nsage: int(A.diffn().regular_form())
numerator: 2*x^140 + 4*x^136 + x^132 + 2*x^130 + 3*x^128 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: 0
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((2*x^140 - x^136 + x^132 + 2*x^130 - 2*x^128 - 2*x^124 + 2*x^122 - x^120 + x^118 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator: 3*x^136 + 4*x^132 + 3*x^128 + 3*x^126 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + x^136 + x^130 - 2*x^128 - x^126 - 2*x^124 + 2*x^122 - x^120 + x^118 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator: 4*x^132 + 2*x^128 + 2*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 + x^130 + 2*x^122 - x^120 + x^118 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator: x^128 + x^124 + 3*x^122 + 4*x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 + 2*x^128 + 2*x^124 + 2*x^120 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator: 3*x^122 + 3*x^118 + 4*x^116 + 3*x^114 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + 2*x^120 + 2*x^118 - 2*x^116 - x^114 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator: x^118 + 4*x^116 + x^114 + 4*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 + x^118 - 2*x^116 - 2*x^114 - x^112 - x^110 + x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator: 4*x^116 + 3*x^108 + x^106 + 3*x^104 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 - 2*x^116 - x^112 - x^110 - 2*x^108 - x^104 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator: 2*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 - 2*x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator: 3*x^102 + x^98 + x^96 + x^94 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - 2*x^102 - 2*x^98 + 2*x^96 - 2*x^94 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator: 4*x^98 + x^96 + 4*x^94 + x^92 + 3*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 + 2*x^98 + 2*x^96 + 2*x^94 - x^90 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator: x^96 + x^92 + 4*x^88 + 3*x^86 + 4*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 + 2*x^96 - x^90 - 2*x^88 - x^86 - 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator: x^92 + 2*x^88 + 2*x^86 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 - x^90 + 2*x^88 + x^86 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator: 3*x^88 + 2*x^86 + 3*x^84 + x^82 + 4*x^80 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^86 - x^82 + 2*x^80 - x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator: 2*x^86 + x^82 + 4*x^80 + 2*x^78 + 4*x^76 + 2*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^86 + x^84 - x^82 + 2*x^80 + x^76 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator: x^82 + 4*x^80 + 3*x^78 + 2*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 - x^82 + 2*x^80 - 2*x^78 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator: 4*x^80 + 4*x^78 + 2*x^76 + 4*x^74 + 4*x^72 + x^70 + x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 + 2*x^80 + x^78 + x^74 + 2*x^72 - x^70 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator: 4*x^78 + 4*x^74 + 2*x^70 + x^68 + 3*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 + x^78 - x^76 + x^74 + 2*x^70 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator: 2*x^70 + 2*x^68 + x^66 + 2*x^64 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + 2*x^70 - 2*x^68 - x^66 + x^64 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator: 2*x^68 + 2*x^64 + 3*x^62 + 4*x^60 + 3*x^58 + 2*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 - 2*x^68 + x^66 + x^64 - x^62 - 2*x^58 - 2*x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator: 3*x^62 + 4*x^60 + x^58 + x^56 + x^54 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - x^62 + 2*x^58 - 2*x^54 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator: 4*x^60 + 4*x^58 + x^56 + 4*x^54 + 2*x^52 + 3*x^50 + 2*x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 + x^58 + 2*x^54 + x^52 + 2*x^50 - x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator: 4*x^58 + 4*x^56 + 4*x^54 + 3*x^52 + 4*x^50 + 2*x^48 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 + x^58 - x^56 + 2*x^54 - x^52 - x^48 + 2*x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator: 4*x^56 + 3*x^52 + 4*x^50 + 3*x^48 + 3*x^46 + 3*x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 - x^56 - x^52 + 2*x^48 + x^46 + 2*x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator: 3*x^52 + 4*x^50 + 4*x^46 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [140], in <cell line: 1>()
----> 1 int(A.diffn().regular_form())
 
Input In [139], in int(self)
24 W1 = superelliptic_function(C, W)
25 n1 = superelliptic_form(C, numerator/y)
---> 26 print(self.form(), (C.y*W1).diffn() + n1)
27 d = numerator.degree()
28 r = f.degree()
 
File <string>:17, in form(self)
 
File <string>:95, in diffn(self)
 
File <string>:7, in __init__(self, C, g)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
636 ring_one = self.ring().one()
637 try:
--> 638 return self._element_class(self, x, ring_one, coerce=coerce)
639 except (TypeError, ValueError):
640 pass
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
112 FieldElement.__init__(self, parent)
113 if coerce:
--> 114 self.__numerator = parent.ring()(numerator)
115 self.__denominator = parent.ring()(denominator)
116 else:
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
1001
1002 try:
-> 1003 return self(str(element))
1004 except TypeError:
1005 pass
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:988, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
986 try:
987 if '/' in element:
--> 988 element = sage_eval(element,d)
989 else:
990 element = element.replace("^","**")
 
File /ext/sage/9.7/src/sage/misc/sage_eval.py:192, in sage_eval(source, locals, cmds, preparse)
190 else:
191 if preparse:
--> 192 source = preparser.preparse(source)
194 if cmds:
195 exec(cmd_seq, sage.all.__dict__, locals)
 
File /ext/sage/9.7/src/sage/repl/preparse.py:1816, in preparse(line, reset, do_time, ignore_prompts, numeric_literals)
1811 L = implicit_mul(L, level = implicit_mul_level)
1813 if numeric_literals:
1814 # Wrapping
1815 # 1 + 0.5 -> Integer(1) + RealNumber('0.5')
-> 1816 L = preparse_numeric_literals(L, quotes=quote_state.safe_delimiter())
1818 # Generators
1819 # R.0 -> R.gen(0)
1820 L = re.sub(r'(\b[^\W\d]\w*|[)\]])\.(\d+)', r'\1.gen(\2)', L)
 
File /ext/sage/9.7/src/sage/repl/preparse.py:1286, in preparse_numeric_literals(code, extract, quotes)
1283 all_num_regex = re.compile(all_num, re.I)
1285 for m in all_num_regex.finditer(code):
-> 1286 start, end = m.start(), m.end()
1287 num = m.group(1)
1288 postfix = m.groups()[-1].upper()
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())
....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)
....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.
....: ^IW = Rx(0)
....: ^Iwhile(numerator != 0):
....: ^I^Iprint('numerator: ', numerator)
....: ^I^Iprint('W: ', W)
....: ^I^IW1 = superelliptic_function(C, W)
....: ^I^In1 = superelliptic_form(C, numerator/y)
....: ^I^Iprint(self.form() == (2*C.y*W1).diffn() + n1)
....: ^I^Id = numerator.degree()
....: ^I^Ir = f.degree()
....: ^I^In_lead = numerator.leading_coefficient()
....: ^I^If_lead = Rx(f).leading_coefficient()
....: ^I^Ia = d - (r-1)
....: ^I^Iif a >= 0:
....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))
....: ^I^I^IW += W_coeff*Rx(x^a)
....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()
....: ^I^I^Inumerator = Rx(numerator)
....: ^I^Iif a < 0:
....: ^I^I^Iprint('numerator', numerator)
....: ^I^I^IW += Rx(numerator/f.derivative())
....: ^I^I^Inumerator = Rx(0)
....: ^Iresult = result + superelliptic_function(C, y*W)
....: ^Ireturn result
....:
sage: int(A.diffn().regular_form())
numerator: 2*x^140 + 4*x^136 + x^132 + 2*x^130 + 3*x^128 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: 0
False
numerator: 3*x^136 + 4*x^132 + 3*x^128 + 3*x^126 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126
False
numerator: 4*x^132 + 2*x^128 + 2*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122
False
numerator: x^128 + x^124 + 3*x^122 + 4*x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118
False
numerator: 3*x^122 + 3*x^118 + 4*x^116 + 3*x^114 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114
False
numerator: x^118 + 4*x^116 + x^114 + 4*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108
False
numerator: 4*x^116 + 3*x^108 + x^106 + 3*x^104 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104
False
numerator: 2*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102
False
numerator: 3*x^102 + x^98 + x^96 + x^94 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92
False
numerator: 4*x^98 + x^96 + 4*x^94 + x^92 + 3*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88
False
numerator: x^96 + x^92 + 4*x^88 + 3*x^86 + 4*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84
False
numerator: x^92 + 2*x^88 + 2*x^86 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82
False
numerator: 3*x^88 + 2*x^86 + 3*x^84 + x^82 + 4*x^80 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78
False
numerator: 2*x^86 + x^82 + 4*x^80 + 2*x^78 + 4*x^76 + 2*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74
False
numerator: x^82 + 4*x^80 + 3*x^78 + 2*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [142], in <cell line: 1>()
----> 1 int(A.diffn().regular_form())
 
Input In [141], in int(self)
23 print('W: ', W)
24 W1 = superelliptic_function(C, W)
---> 25 n1 = superelliptic_form(C, numerator/y)
26 print(self.form() == (Integer(2)*C.y*W1).diffn() + n1)
27 d = numerator.degree()
 
File <string>:7, in __init__(self, C, g)
 
File <string>:296, in reduction_form(C, g)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
636 ring_one = self.ring().one()
637 try:
--> 638 return self._element_class(self, x, ring_one, coerce=coerce)
639 except (TypeError, ValueError):
640 pass
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
112 FieldElement.__init__(self, parent)
113 if coerce:
--> 114 self.__numerator = parent.ring()(numerator)
115 self.__denominator = parent.ring()(denominator)
116 else:
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1009, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
1007 try:
1008 # now try calling the base ring's __call__ methods
-> 1009 element = self.base_ring()(element)
1010 _p = p_NSet(sa2si(element,_ring), _ring)
1011 return new_MP(self,_p)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x)
1143 """
1144 TESTS::
1145
(...)
1182 True
1183 """
1184 try:
-> 1185 return integer_mod.IntegerMod(self, x)
1186 except (NotImplementedError, PariError):
1187 raise TypeError("error coercing to finite field")
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod()
199 return a
200 t = modulus.element_class()
--> 201 return t(parent, value)
202
203
 
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:380, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
378 else:
379 try:
--> 380 z = integer_ring.Z(value)
381 except (TypeError, ValueError):
382 from sage.structure.element import Expression
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
285 raise TypeError("Cannot coerce {} to {}".format(x, C))
286 cdef Map m
--> 287 cdef Element e = method(C)
288 if e is None:
289 raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x)))
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:831, in sage.rings.fraction_field_element.FractionFieldElement._conversion()
829 return R(self.__numerator)
830 else:
--> 831 self.reduce()
832 num = R(self.__numerator)
833 inv_den = R(self.__denominator).inverse_of_unit()
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:1239, in sage.rings.fraction_field_element.FractionFieldElement_1poly_field.reduce()
1237 if self._is_reduced:
1238 return
-> 1239 super(self.__class__, self).reduce()
1240 self.normalize_leading_coefficients()
1241
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:164, in sage.rings.fraction_field_element.FractionFieldElement.reduce()
162 return codomain.coerce(nnum/nden)
163
--> 164 cpdef reduce(self):
165 """
166 Reduce this fraction.
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:197, in sage.rings.fraction_field_element.FractionFieldElement.reduce()
195 return
196 try:
--> 197 g = self.__numerator.gcd(self.__denominator)
198 if not g.is_unit():
199 self.__numerator //= g
 
File /ext/sage/9.7/src/sage/structure/element.pyx:4494, in sage.structure.element.coerce_binop.new_method()
4492 def new_method(self, other, *args, **kwargs):
4493 if have_same_parent(self, other):
-> 4494 return method(self, other, *args, **kwargs)
4495 else:
4496 a, b = coercion_model.canonical_coercion(self, other)
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:4913, in sage.rings.polynomial.polynomial_element.Polynomial.gcd()
4911 raise NotImplementedError("%s does not provide a gcd implementation for univariate polynomials"%self._parent._base)
4912 else:
-> 4913 return doit(self, other)
4914
4915 @coerce_binop
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:946, in FractionField_generic._gcd_univariate_polynomial(self, f, g)
944 f1 = Num(f.numerator())
945 g1 = Num(g.numerator())
--> 946 return Pol(f1.gcd(g1)).monic()
 
File /ext/sage/9.7/src/sage/structure/element.pyx:4494, in sage.structure.element.coerce_binop.new_method()
4492 def new_method(self, other, *args, **kwargs):
4493 if have_same_parent(self, other):
-> 4494 return method(self, other, *args, **kwargs)
4495 else:
4496 a, b = coercion_model.canonical_coercion(self, other)
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:4906, in sage.rings.polynomial.polynomial_element.Polynomial.gcd()
4904 tgt = flatten.codomain()
4905 if tgt.ngens() > 1 and tgt._has_singular:
-> 4906 g = flatten(self).gcd(flatten(other))
4907 return flatten.section()(g)
4908 try:
 
File /ext/sage/9.7/src/sage/categories/map.pyx:769, in sage.categories.map.Map.__call__()
767 if P is D: # we certainly want to call _call_/with_args
768 if not args and not kwds:
--> 769 return self._call_(x)
770 return self._call_with_args(x, args, kwds)
771 # Is there coercion?
 
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
786 return self._call_with_args(x, args, kwds)
787
--> 788 cpdef Element _call_(self, x):
789 """
790 Call method with a single argument, not implemented in the base class.
 
File /ext/sage/9.7/src/sage/rings/polynomial/flatten.py:220, in FlatteningMorphism._call_(self, p)
218 for mon, pp in p.items():
219 assert pp.parent() is ring
--> 220 for i, j in pp.dict().items():
221 new_p[(i,)+(mon)] = j
222 elif is_MPolynomialRing(ring):
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)
....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.
....: ^IW = Rx(0)
....: ^Iwhile(numerator != 0):
....: ^I^Iprint('numerator: ', numerator)
....: ^I^Iprint('W: ', W)
....: ^I^IW1 = superelliptic_function(C, W)
....: ^I^In1 = superelliptic_form(C, numerator/y)
....: ^I^Iprint(self.form() == (2*C.y*W1).diffn() + n1 + result)
....: ^I^Iprint(self.form(), (2*C.y*W1).diffn() + n1 + result)
....: ^I^Id = numerator.degree()
....: ^I^Ir = f.degree()
....: ^I^In_lead = numerator.leading_coefficient()
....: ^I^If_lead = Rx(f).leading_coefficient()
....: ^I^Ia = d - (r-1)
....: ^I^Iif a >= 0:
....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))
....: ^I^I^IW += W_coeff*Rx(x^a)
....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()
....: ^I^I^Inumerator = Rx(numerator)
....: ^I^Iif a < 0:
....: ^I^I^Iprint('numerator', numerator)
....: ^I^I^IW += Rx(numerator/f.derivative())
....: ^I^I^Inumerator = Rx(0)
....: ^Iresult = result + superelliptic_function(C, y*W)
....: ^Ireturn result
....:
[6nsage: int(A.diffn().regular_form())
numerator: 2*x^140 + 4*x^136 + x^132 + 2*x^130 + 3*x^128 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: 0
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [144], in <cell line: 1>()
----> 1 int(A.diffn().regular_form())
 
Input In [143], in int(self)
24 W1 = superelliptic_function(C, W)
25 n1 = superelliptic_form(C, numerator/y)
---> 26 print(self.form() == (Integer(2)*C.y*W1).diffn() + n1 + result)
27 print(self.form(), (Integer(2)*C.y*W1).diffn() + n1 + result)
28 d = numerator.degree()
 
File <string>:19, in __add__(self, other)
 
AttributeError: 'superelliptic_function' object has no attribute 'form'
....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)
....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.
....: ^IW = Rx(0)
....: ^Iwhile(numerator != 0):
....: ^I^Iprint('numerator: ', numerator)
....: ^I^Iprint('W: ', W)
....: ^I^IW1 = superelliptic_function(C, W)
....: ^I^In1 = superelliptic_form(C, numerator/y)
....: ^I^Iprint(self.form() == (2*C.y*W1).diffn() + n1 + result.diffn())
....: ^I^Iprint(self.form(), (2*C.y*W1).diffn() + n1 + result.diffn())
....: ^I^Id = numerator.degree()
....: ^I^Ir = f.degree()
....: ^I^In_lead = numerator.leading_coefficient()
....: ^I^If_lead = Rx(f).leading_coefficient()
....: ^I^Ia = d - (r-1)
....: ^I^Iif a >= 0:
....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))
....: ^I^I^IW += W_coeff*Rx(x^a)
....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()
....: ^I^I^Inumerator = Rx(numerator)
....: ^I^Iif a < 0:
....: ^I^I^Iprint('numerator', numerator)
....: ^I^I^IW += Rx(numerator/f.derivative())
....: ^I^I^Inumerator = Rx(0)
....: ^Iresult = result + superelliptic_function(C, y*W)
....: ^Ireturn result
....:
ssage: int(A.diffn().regular_form())
numerator: 2*x^140 + 4*x^136 + x^132 + 2*x^130 + 3*x^128 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: 0
False
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((2*x^140 - x^136 + x^132 + 2*x^130 - 2*x^128 - 2*x^124 + 2*x^122 - x^120 + x^118 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator: 3*x^136 + 4*x^132 + 3*x^128 + 3*x^126 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126
False
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((2*x^140 - x^136 + x^132 + 2*x^130 - 2*x^128 - 2*x^124 + 2*x^122 - x^120 + x^118 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator: 4*x^132 + 2*x^128 + 2*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122
False
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((2*x^140 - x^136 + x^132 + 2*x^130 - 2*x^128 - 2*x^124 + 2*x^122 - x^120 + x^118 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator: x^128 + x^124 + 3*x^122 + 4*x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118
False
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((2*x^140 - x^136 + x^132 + 2*x^130 - 2*x^128 - 2*x^124 + 2*x^122 - x^120 + x^118 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator: 3*x^122 + 3*x^118 + 4*x^116 + 3*x^114 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114
False
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((2*x^140 - x^136 + x^132 + 2*x^130 - 2*x^128 - 2*x^124 + 2*x^122 - x^120 + x^118 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator: x^118 + 4*x^116 + x^114 + 4*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108
False
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [146], in <cell line: 1>()
----> 1 int(A.diffn().regular_form())
 
Input In [145], in int(self)
25 n1 = superelliptic_form(C, numerator/y)
26 print(self.form() == (Integer(2)*C.y*W1).diffn() + n1 + result.diffn())
---> 27 print(self.form(), (Integer(2)*C.y*W1).diffn() + n1 + result.diffn())
28 d = numerator.degree()
29 r = f.degree()
 
File <string>:95, in diffn(self)
 
File <string>:7, in __init__(self, C, g)
 
File <string>:282, in reduction_form(C, g)
 
File <string>:263, in reduction(C, g)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:974, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
972 if isinstance(element, (SingularElement, cypari2.gen.Gen)):
973 element = str(element)
--> 974 elif is_Macaulay2Element(element):
975 element = element.external_string()
976
 
File /ext/sage/9.7/src/sage/interfaces/macaulay2.py:1835, in is_Macaulay2Element(x)
1823 """
1824 EXAMPLES::
1825
(...)
1828 -- code for method: resolution(Matrix)...
1829 """
1830 return self._obj.parent().eval(
1831 'code select(methods %s, m->instance(%s, m#1))'
1832 % (self._name, self._obj._name))
-> 1835 def is_Macaulay2Element(x):
1836 """
1837 EXAMPLES::
1838
(...)
1843 True
1844 """
1845 return isinstance(x, Macaulay2Element)
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)
....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.
....: ^IW = Rx(0)
....: ^Iwhile(numerator != 0):
....: ^I^Iprint('numerator: ', numerator)
....: ^I^Iprint('W: ', W)
....: ^I^IW1 = superelliptic_function(C, W)
....: ^I^In1 = superelliptic_form(C, numerator/y)
....: ^I^Iprint(self.form() == (C.y*W1).diffn() + n1 + result.diffn())
....: ^I^Iprint(self.form(), (C.y*W1).diffn() + n1 + result.diffn())
....: ^I^Id = numerator.degree()
....: ^I^Ir = f.degree()
....: ^I^In_lead = numerator.leading_coefficient()
....: ^I^If_lead = Rx(f).leading_coefficient()
....: ^I^Ia = d - (r-1)
....: ^I^Iif a >= 0:
....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))
....: ^I^I^IW += W_coeff*Rx(x^a)
....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()
....: ^I^I^Inumerator = Rx(numerator)
....: ^I^Iif a < 0:
....: ^I^I^Iprint('numerator', numerator)
....: ^I^I^IW += Rx(numerator/f.derivative())
....: ^I^I^Inumerator = Rx(0)
....: ^Iresult = result + superelliptic_function(C, y*W)
....: ^Ireturn result
....:
sage: int(A.diffn().regular_form())
numerator: 2*x^140 + 4*x^136 + x^132 + 2*x^130 + 3*x^128 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: 0
False
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((2*x^140 - x^136 + x^132 + 2*x^130 - 2*x^128 - 2*x^124 + 2*x^122 - x^120 + x^118 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator: 3*x^136 + 4*x^132 + 3*x^128 + 3*x^126 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126
False
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + x^136 + x^130 - 2*x^128 - x^126 - 2*x^124 + 2*x^122 - x^120 + x^118 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator: 4*x^132 + 2*x^128 + 2*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122
False
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 + x^130 + 2*x^122 - x^120 + x^118 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator: x^128 + x^124 + 3*x^122 + 4*x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118
False
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 + 2*x^128 + 2*x^124 + 2*x^120 + 2*x^116 - 2*x^112 - 2*x^110 - 2*x^108 - x^106 - 2*x^102 - 2*x^96 - x^92 - 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 - 2*x^78 - 2*x^76 - 2*x^74 + 2*x^70 - x^68 + 2*x^66 + x^60 - 2*x^58 - x^56 + x^50 + x^48 - x^46 + x^44 + 2*x^42 - 2*x^40 + x^38 + x^36 + 2*x^32 + x^30 - 2*x^28 + 2*x^26 - 2*x^24 + 2*x^22 - x^18 - x^14 + 2*x^10 - 2*x^8 + x^6 - 2*x^4 + x^2 + 2)/y) dx
numerator: 3*x^122 + 3*x^118 + 4*x^116 + 3*x^114 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114
False
^C---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
File <string>:58, in __mul__(self, other)
 
AttributeError: 'superelliptic_form' object has no attribute 'function'
 
During handling of the above exception, another exception occurred:
 
KeyboardInterrupt Traceback (most recent call last)
Input In [148], in <cell line: 1>()
----> 1 int(A.diffn().regular_form())
 
Input In [147], in int(self)
25 n1 = superelliptic_form(C, numerator/y)
26 print(self.form() == (C.y*W1).diffn() + n1 + result.diffn())
---> 27 print(self.form(), (C.y*W1).diffn() + n1 + result.diffn())
28 d = numerator.degree()
29 r = f.degree()
 
File <string>:17, in form(self)
 
File <string>:65, in __mul__(self, other)
 
File <string>:7, in __init__(self, C, g)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
636 ring_one = self.ring().one()
637 try:
--> 638 return self._element_class(self, x, ring_one, coerce=coerce)
639 except (TypeError, ValueError):
640 pass
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
112 FieldElement.__init__(self, parent)
113 if coerce:
--> 114 self.__numerator = parent.ring()(numerator)
115 self.__denominator = parent.ring()(denominator)
116 else:
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
1001
1002 try:
-> 1003 return self(str(element))
1004 except TypeError:
1005 pass
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:988, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
986 try:
987 if '/' in element:
--> 988 element = sage_eval(element,d)
989 else:
990 element = element.replace("^","**")
 
File /ext/sage/9.7/src/sage/misc/sage_eval.py:186, in sage_eval(source, locals, cmds, preparse)
183 locals = {}
185 import sage.all
--> 186 if cmds:
187 cmd_seq = cmds + '\n_sage_eval_returnval_ = ' + source
188 if preparse:
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)
....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.
....: ^IW = Rx(0)
....: ^Iwhile(numerator != 0):
....: ^I^Iprint('numerator: ', numerator)
....: ^I^Iprint('W: ', W)
....: ^I^IW1 = superelliptic_function(C, W)
....: ^I^In1 = superelliptic_form(C, numerator/(2*y))
....: ^I^Iprint(self.form() == (C.y*W1).diffn() + n1 + result.diffn())
....: ^I^Iprint(self.form(), (C.y*W1).diffn() + n1 + result.diffn())
....: ^I^Id = numerator.degree()
....: ^I^Ir = f.degree()
....: ^I^In_lead = numerator.leading_coefficient()
....: ^I^If_lead = Rx(f).leading_coefficient()
....: ^I^Ia = d - (r-1)
....: ^I^Iif a >= 0:
....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))
....: ^I^I^IW += W_coeff*Rx(x^a)
....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()
....: ^I^I^Inumerator = Rx(numerator)
....: ^I^Iif a < 0:
....: ^I^I^Iprint('numerator', numerator)
....: ^I^I^IW += Rx(numerator/f.derivative())
....: ^I^I^Inumerator = Rx(0)
....: ^Iresult = result + superelliptic_function(C, y*W)
....: ^Ireturn result
....:
[6nsage: int(A.diffn().regular_form())
numerator: 2*x^140 + 4*x^136 + x^132 + 2*x^130 + 3*x^128 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: 0
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: 3*x^136 + 4*x^132 + 3*x^128 + 3*x^126 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: 4*x^132 + 2*x^128 + 2*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: x^128 + x^124 + 3*x^122 + 4*x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: 3*x^122 + 3*x^118 + 4*x^116 + 3*x^114 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: x^118 + 4*x^116 + x^114 + 4*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: 4*x^116 + 3*x^108 + x^106 + 3*x^104 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: 2*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: 3*x^102 + x^98 + x^96 + x^94 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: 4*x^98 + x^96 + 4*x^94 + x^92 + 3*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: x^96 + x^92 + 4*x^88 + 3*x^86 + 4*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: x^92 + 2*x^88 + 2*x^86 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: 3*x^88 + 2*x^86 + 3*x^84 + x^82 + 4*x^80 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: 2*x^86 + x^82 + 4*x^80 + 2*x^78 + 4*x^76 + 2*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: x^82 + 4*x^80 + 3*x^78 + 2*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: 4*x^80 + 4*x^78 + 2*x^76 + 4*x^74 + 4*x^72 + x^70 + x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: 4*x^78 + 4*x^74 + 2*x^70 + x^68 + 3*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: 2*x^70 + 2*x^68 + x^66 + 2*x^64 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: 2*x^68 + 2*x^64 + 3*x^62 + 4*x^60 + 3*x^58 + 2*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: 3*x^62 + 4*x^60 + x^58 + x^56 + x^54 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: 4*x^60 + 4*x^58 + x^56 + 4*x^54 + 2*x^52 + 3*x^50 + 2*x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: 4*x^58 + 4*x^56 + 4*x^54 + 3*x^52 + 4*x^50 + 2*x^48 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: 4*x^56 + 3*x^52 + 4*x^50 + 3*x^48 + 3*x^46 + 3*x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: 3*x^52 + 4*x^50 + 4*x^46 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: 4*x^50 + 3*x^48 + 4*x^46 + 3*x^44 + 4*x^42 + 2*x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: 3*x^48 + 2*x^46 + 3*x^44 + x^40 + 2*x^38 + 2*x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: 2*x^46 + x^40 + 4*x^38 + 3*x^36 + 4*x^34 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: x^40 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: 3*x^36 + x^32 + 3*x^28 + x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: x^32 + 2*x^28 + 3*x^26 + 2*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: 3*x^28 + 3*x^26 + 3*x^24 + x^22 + 4*x^20 + x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: 3*x^26 + x^22 + 4*x^20 + 3*x^18 + x^16 + 3*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: x^22 + 4*x^20 + 2*x^18 + 3*x^16 + 2*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: 4*x^20 + 3*x^18 + 3*x^16 + 3*x^14 + 4*x^12 + x^10 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: 3*x^18 + x^16 + 3*x^14 + 2*x^10 + 2*x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8 + 2*x^6
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: x^16 + 2*x^10 + 2*x^8 + 3*x^6 + 2*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8 + 2*x^6 + x^4
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator: 2*x^10 + 2*x^6 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8 + 2*x^6 + x^4 + 4*x^2
True
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx ((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 + x^10 - x^8 - 2*x^6 - x^4 - 2*x^2 + 1)/y) dx
numerator 2*x^10 + 2*x^6 + x^2 + 2
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [150], in <cell line: 1>()
----> 1 int(A.diffn().regular_form())
 
Input In [149], in int(self)
38 if a < Integer(0):
39 print('numerator', numerator)
---> 40 W += Rx(numerator/f.derivative())
41 numerator = Rx(Integer(0))
42 result = result + superelliptic_function(C, y*W)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
1329 normalize(x._numer, x._denom, self.p)
1330 if nmod_poly_degree(x._denom) != 0:
-> 1331 raise ValueError("not integral")
1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:
 
ValueError: not integral
....: ^Iresult = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())
....: ^Inumerator = Rx(2*f*Py + f.derivative()*Qx)
....: ^I# Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.
....: ^IW = Rx(0)
....: ^Iwhile(numerator != 0):
....: ^I^Iprint('numerator: ', numerator)
....: ^I^Iprint('W: ', W)
....: ^I^IW1 = superelliptic_function(C, W)
....: ^I^In1 = superelliptic_form(C, numerator/(2*y))
....: ^I^Iprint((C.y*W1).diffn())
....: ^I^Id = numerator.degree()
....: ^I^Ir = f.degree()
....: ^I^In_lead = numerator.leading_coefficient()
....: ^I^If_lead = Rx(f).leading_coefficient()
....: ^I^Ia = d - (r-1)
....: ^I^Iif a >= 0:
....: ^I^I^IW_coeff = F(n_lead/f_lead)*F((2*a + r)^(-1))
....: ^I^I^IW += W_coeff*Rx(x^a)
....: ^I^I^Inumerator -= 2*f*(W_coeff*Rx(x^a)).derivative() + (W_coeff*Rx(x^a))*f.derivative()
....: ^I^I^Inumerator = Rx(numerator)
....: ^I^Iif a < 0:
....: ^I^I^Iprint('numerator', numerator)
....: ^I^I^IW += Rx(numerator/f.derivative())
....: ^I^I^Inumerator = Rx(0)
....: ^Iresult = result + superelliptic_function(C, y*W)
....: ^Ireturn result
....:
[6nsage: int(A.diffn().regular_form())
numerator: 2*x^140 + 4*x^136 + x^132 + 2*x^130 + 3*x^128 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: 0
0 dx
numerator: 3*x^136 + 4*x^132 + 3*x^128 + 3*x^126 + 3*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126
((x^140 - 2*x^136 + x^132 + x^130 + x^126)/y) dx
numerator: 4*x^132 + 2*x^128 + 2*x^124 + 2*x^122 + 4*x^120 + x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122
((x^140 + 2*x^136 + x^132 + x^130 - 2*x^128 - 2*x^124)/y) dx
numerator: x^128 + x^124 + 3*x^122 + 4*x^118 + 2*x^116 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118
((x^140 + 2*x^136 - 2*x^132 + x^130 + x^128 + x^124 + 2*x^122 + 2*x^120 + x^118)/y) dx
numerator: 3*x^122 + 3*x^118 + 4*x^116 + 3*x^114 + 3*x^112 + 3*x^110 + 3*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + 2*x^122 + 2*x^120 - x^118 - x^116 + x^114)/y) dx
numerator: x^118 + 4*x^116 + x^114 + 4*x^108 + 4*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - x^116 + 2*x^114 - x^112 - x^110 + 2*x^108)/y) dx
numerator: 4*x^116 + 3*x^108 + x^106 + 3*x^104 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 - x^116 - x^112 - x^110 - x^106 + x^104)/y) dx
numerator: 2*x^106 + 3*x^102 + 3*x^96 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + x^106)/y) dx
numerator: 3*x^102 + x^98 + x^96 + x^94 + 4*x^92 + 3*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 + 2*x^98 + x^96 + 2*x^94)/y) dx
numerator: 4*x^98 + x^96 + 4*x^94 + x^92 + 3*x^88 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - 2*x^98 + x^96 - 2*x^94 - x^92 - x^90 + 2*x^88)/y) dx
numerator: x^96 + x^92 + 4*x^88 + 3*x^86 + 4*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 + x^96 - x^92 - x^90 - x^88 + x^86 - x^84)/y) dx
numerator: x^92 + 2*x^88 + 2*x^86 + 2*x^84 + 2*x^82 + 3*x^78 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 - x^92 - x^90 - x^86)/y) dx
numerator: 3*x^88 + 2*x^86 + 3*x^84 + x^82 + 4*x^80 + 3*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + 2*x^88 - x^86 + 2*x^84 - 2*x^82 - 2*x^80 - x^78)/y) dx
numerator: 2*x^86 + x^82 + 4*x^80 + 2*x^78 + 4*x^76 + 2*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 - x^86 + x^84 - 2*x^82 - 2*x^80 - 2*x^78 + 2*x^76 - 2*x^74)/y) dx
numerator: x^82 + 4*x^80 + 3*x^78 + 2*x^76 + 3*x^74 + 2*x^70 + 4*x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 - 2*x^82 - 2*x^80 - 2*x^76)/y) dx
numerator: 4*x^80 + 4*x^78 + 2*x^76 + 4*x^74 + 4*x^72 + x^70 + x^68 + 2*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - 2*x^80 + 2*x^78 - 2*x^76 + 2*x^74 - 2*x^72 - 2*x^70 - x^68)/y) dx
numerator: 4*x^78 + 4*x^74 + 2*x^70 + x^68 + 3*x^66 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 + 2*x^78 - x^76 + 2*x^74 - x^68 + 2*x^66)/y) dx
numerator: 2*x^70 + 2*x^68 + x^66 + 2*x^64 + x^60 + 3*x^58 + 4*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^68 - 2*x^66 - x^64)/y) dx
numerator: 2*x^68 + 2*x^64 + 3*x^62 + 4*x^60 + 3*x^58 + 2*x^56 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + x^68 + x^66 - x^64 + x^62 + x^60 + x^56)/y) dx
numerator: 3*x^62 + 4*x^60 + x^58 + x^56 + x^54 + x^50 + x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 + x^62 + x^60 + x^58 - x^56 + 2*x^54)/y) dx
numerator: 4*x^60 + 4*x^58 + x^56 + 4*x^54 + 2*x^52 + 3*x^50 + 2*x^48 + 4*x^46 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 + x^60 + 2*x^58 - x^56 - 2*x^54 - x^52 - x^50 + 2*x^48)/y) dx
numerator: 4*x^58 + 4*x^56 + 4*x^54 + 3*x^52 + 4*x^50 + 2*x^48 + x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 + 2*x^58 - 2*x^54 + x^52 + x^50 + 2*x^48 + 2*x^46)/y) dx
numerator: 4*x^56 + 3*x^52 + 4*x^50 + 3*x^48 + 3*x^46 + 3*x^44 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + x^52 + x^50 - x^48 - 2*x^46 - x^44)/y) dx
numerator: 3*x^52 + 4*x^50 + 4*x^46 + 2*x^42 + 3*x^40 + x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 + x^52 + x^50 - 2*x^48 - 2*x^44)/y) dx
numerator: 4*x^50 + 3*x^48 + 4*x^46 + 3*x^44 + 4*x^42 + 2*x^38 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 + x^50 - x^48 - x^44 - x^42 - x^40 + 2*x^38)/y) dx
numerator: 3*x^48 + 2*x^46 + 3*x^44 + x^40 + 2*x^38 + 2*x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - x^48 + x^46 - x^44 + x^42 + x^40 + 2*x^38 + 2*x^36)/y) dx
numerator: 2*x^46 + x^40 + 4*x^38 + 3*x^36 + 4*x^34 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + x^46 - 2*x^44 + x^42 + x^40 + x^38 - x^36 - 2*x^34)/y) dx
numerator: x^40 + x^36 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 + x^40 - 2*x^38)/y) dx
numerator: 3*x^36 + x^32 + 3*x^28 + x^26 + 3*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - x^36 - 2*x^32 - 2*x^30 - 2*x^26)/y) dx
numerator: x^32 + 2*x^28 + 3*x^26 + 2*x^24 + 2*x^22 + 4*x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 - 2*x^32 - 2*x^30 - 2*x^28 + 2*x^26 - 2*x^24)/y) dx
numerator: 3*x^28 + 3*x^26 + 3*x^24 + x^22 + 4*x^20 + x^18 + 4*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 + 2*x^26 - 2*x^22 - 2*x^20 - x^18)/y) dx
numerator: 3*x^26 + x^22 + 4*x^20 + 3*x^18 + x^16 + 3*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + 2*x^26 - x^24 - 2*x^22 - 2*x^20 - 2*x^18 + 2*x^16 - 2*x^14)/y) dx
numerator: x^22 + 4*x^20 + 2*x^18 + 3*x^16 + 2*x^14 + 2*x^10 + 3*x^8 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 - 2*x^22 - 2*x^20 + x^18 + x^16 + x^14)/y) dx
numerator: 4*x^20 + 3*x^18 + 3*x^16 + 3*x^14 + 4*x^12 + x^10 + x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 - 2*x^20 - 2*x^18 + x^16 - 2*x^14 - 2*x^12 - 2*x^10 - x^8)/y) dx
numerator: 3*x^18 + x^16 + 3*x^14 + 2*x^10 + 2*x^6 + 3*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8 + 2*x^6
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 - 2*x^18 + 2*x^16 - 2*x^14 - x^8 + 2*x^6)/y) dx
numerator: x^16 + 2*x^10 + 2*x^8 + 3*x^6 + 2*x^4 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8 + 2*x^6 + x^4
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^16 + 2*x^14 - 2*x^8 - x^6 - 2*x^4)/y) dx
numerator: 2*x^10 + 2*x^6 + x^2 + 2
W: x^126 + 2*x^122 + 4*x^118 + 2*x^114 + 3*x^108 + 2*x^104 + x^102 + 3*x^92 + 3*x^88 + 3*x^84 + 4*x^82 + x^78 + x^74 + 3*x^72 + x^68 + 2*x^66 + 3*x^64 + x^56 + 4*x^54 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 3*x^38 + 2*x^36 + x^34 + 3*x^32 + 3*x^26 + 2*x^22 + x^18 + x^14 + 2*x^12 + x^8 + 2*x^6 + x^4 + 4*x^2
((x^140 + 2*x^136 - 2*x^132 + x^130 - x^128 - x^124 + x^122 + 2*x^120 - 2*x^118 + x^116 - x^112 - x^110 - x^108 + 2*x^106 - x^102 - x^96 + 2*x^92 - x^90 + x^88 + x^84 + x^82 - x^78 - x^76 - x^74 + x^70 + 2*x^68 + x^66 - 2*x^60 - x^58 + 2*x^56 - 2*x^50 - 2*x^48 + 2*x^46 - 2*x^44 + x^42 - x^40 - 2*x^38 - 2*x^36 + x^32 - 2*x^30 - x^28 + x^26 - x^24 + x^22 + 2*x^18 + 2*x^14 - x^8 + 2*x^6 - x^4)/y) dx
numerator 2*x^10 + 2*x^6 + x^2 + 2
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [152], in <cell line: 1>()
----> 1 int(A.diffn().regular_form())
 
Input In [151], in int(self)
37 if a < Integer(0):
38 print('numerator', numerator)
---> 39 W += Rx(numerator/f.derivative())
40 numerator = Rx(Integer(0))
41 result = result + superelliptic_function(C, y*W)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
1329 normalize(x._numer, x._denom, self.p)
1330 if nmod_poly_degree(x._denom) != 0:
-> 1331 raise ValueError("not integral")
1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:
 
ValueError: not integral
sage: A1 = C1.x^126 + 2*C1.x^122 + 4*C1.x^118 + 2*C1.x^114 + 3*C1.x^108 + 2*C1.x^104 + C1.x^102 + 3*C1.x^92 + 3*C1.x^88 + 3*C1.4^84 + 4*C1.x^82 + C1.x^78 + C1.x^7
....: + 3*C1.x^72 + C1.x^68 + 2*C1.x^66 + 3*C1.x^64 + C1.x^56 + 4*C1.x^54 + 3*C1.x^48 + 2*C1.x^46 + 3*C1.x^44 + C1.x^42 + 3*C1xx^38 + 2*C1.x^36 + C1.x^34 + 3*C1.
....: ^32 + 3*C1.x^26 + 2*C1.x^22 + C1.x^18 + C1.x^14 + 2*C1.x^12 + C1.x^8 + 2*C1.x^6 + C1.x^4 + 4*C1.x^2
sage: A1 = A1 * C1.y
sage: (A - A1).diffn()
((x^10 + x^6 - 2*x^2 + 1)/y) dx
[6nsage: A - A1
((x^146 + 2*x^144 + x^142 + 4*x^136 + 3*x^134 + 4*x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 3*x^106 + x^104 + 3*x^102 + 3*x^96 + x^94 + 3*x^92 + x^86 + 2*x^84 + x^82 + 4*x^76 + 3*x^74 + 4*x^72 + 3*x^66 + x^64 + 3*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 2*x^46 + 4*x^44 + 2*x^42 + x^32 + 2*x^30 + x^28 + 2*x^26 + 3*x^24 + 2*x^22 + x^20 + 2*x^18 + 2*x^16 + 2*x^14 + 3*x^12 + 3*x^10 + 3*x^8 + 4*x^6 + 3*x^2 + 2)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y
[6nsage: C1.polynomial.derivative()
2*x^10 + x^6 + 2*x^2 + 4
[6nsage: (A - A1 - C.y/2).diffn()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [158], in <cell line: 1>()
----> 1 (A - A1 - C.y/Integer(2)).diffn()
 
File <string>:75, in __truediv__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
493 """
--> 494 return self.getattr_from_category(name)
495
496 cdef getattr_from_category(self, name):
 
File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
505 else:
506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
508
509 def __dir__(self):
 
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
359 dummy_error_message.cls = type(self)
360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
362 attribute = <object>attr
363 # Check for a descriptor (__get__ in Python)
 
AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function'
[6nsage: (A - A1 - 1/2*C.y).diffn()
((-2*x^10 + 2*x^6)/y) dx
[6nsage: (A - A1 - C.y).diffn()
((-2*x^6 + 2*x^2 - 1)/y) dx
[6nsage: (A - A1 - C.y)
((x^146 + 2*x^144 + x^142 + 4*x^136 + 3*x^134 + 4*x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 3*x^106 + x^104 + 3*x^102 + 3*x^96 + x^94 + 3*x^92 + x^86 + 2*x^84 + x^82 + 4*x^76 + 3*x^74 + 4*x^72 + 3*x^66 + x^64 + 3*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 2*x^46 + 4*x^44 + 2*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^28 + 3*x^26 + 2*x^24 + 3*x^20 + 2*x^16 + x^14 + 4*x^12 + 3*x^10 + 2*x^8 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y
[6nsage: A2 = (A - A1 - C.y)/C.y
[6nsage: A2
(x^146 + 2*x^144 + x^142 + 4*x^136 + 3*x^134 + 4*x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 3*x^106 + x^104 + 3*x^102 + 3*x^96 + x^94 + 3*x^92 + x^86 + 2*x^84 + x^82 + 4*x^76 + 3*x^74 + 4*x^72 + 3*x^66 + x^64 + 3*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 2*x^46 + 4*x^44 + 2*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^28 + 3*x^26 + 2*x^24 + 3*x^20 + 2*x^16 + x^14 + 4*x^12 + 3*x^10 + 2*x^8 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4)
[6nsage: A2.function.numerator().quo_rem(A2.function.denominator())
((x^146 + 2*x^144 + x^142 + 4*x^136 + 3*x^134 + 4*x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 3*x^106 + x^104 + 3*x^102 + 3*x^96 + x^94 + 3*x^92 + x^86 + 2*x^84 + x^82 + 4*x^76 + 3*x^74 + 4*x^72 + 3*x^66 + x^64 + 3*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 2*x^46 + 4*x^44 + 2*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^28 + 3*x^26 + 2*x^24 + 3*x^20 + 2*x^16 + x^14 + 4*x^12 + 3*x^10 + 2*x^8 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4),
0)
[6nsage: A2.function.numerator()
x^146 + 2*x^144 + x^142 + 4*x^136 + 3*x^134 + 4*x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 3*x^106 + x^104 + 3*x^102 + 3*x^96 + x^94 + 3*x^92 + x^86 + 2*x^84 + x^82 + 4*x^76 + 3*x^74 + 4*x^72 + 3*x^66 + x^64 + 3*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 2*x^46 + 4*x^44 + 2*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^28 + 3*x^26 + 2*x^24 + 3*x^20 + 2*x^16 + x^14 + 4*x^12 + 3*x^10 + 2*x^8 + 3*x^6 + 2*x^4 + 3*x^2 + 3
[6nsage: (A2.function.numerator()).quo_rem(A2.function.denominator())
((x^146 + 2*x^144 + x^142 + 4*x^136 + 3*x^134 + 4*x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 3*x^106 + x^104 + 3*x^102 + 3*x^96 + x^94 + 3*x^92 + x^86 + 2*x^84 + x^82 + 4*x^76 + 3*x^74 + 4*x^72 + 3*x^66 + x^64 + 3*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 2*x^46 + 4*x^44 + 2*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^28 + 3*x^26 + 2*x^24 + 3*x^20 + 2*x^16 + x^14 + 4*x^12 + 3*x^10 + 2*x^8 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4),
0)
[6nssage: Fxy, Rxy, x, y=C.fct_field
[6nsage: Fxy, Rxy, x, y=C1.fct_field
[6nsage: Rxy(A2.function.numerator()).quo_rem(Rxy(A2.function.denominator()))
(x^110 - x^106 + 2*x^100 + 2*x^96 + 2*x^92 - x^90 + 2*x^88 + 2*x^84 + x^82 + x^76 - 2*x^72 + x^70 - 2*x^68 - 2*x^66 - 2*x^64 - 2*x^62 - x^58 + x^56 - x^54 + x^52 + x^50 - x^48 + x^46 - x^44 - x^42 + 2*x^40 + 2*x^38 - 2*x^36 + 2*x^34 - x^32 - 2*x^30 - 2*x^28 - x^26 - 2*x^24 + 2*x^22 - 2*x^18 + x^16 - 2*x^14 - x^12 + 2*x^10 - 2*x^6 + 2,
x^32 + 2*x^30 + 2*x^22 - x^20 + 2*x^18 - x^16 - 2*x^14 + 2*x^12 + x^10 - x^6 + x^4 - 2*x^2)
[6nsage: omega1
((2*x^10 + 2*x^6 + x^2 + 2)/y) dx
[6nsage: C1.y.diffn()
((x^10 - 2*x^6 + x^2 + 2)/y) dx
[6nsage: omega2 = omega1 - 2*C1.y.diffn()
[6nsage: omega2
((x^6 - x^2 - 2)/y) dx
[6nsage: omega2.regular_form()
((3*x^11 + 4*x^7 + 4*x^5 + 3*x^3 + x)*y) dx + (2*x^16 + 4*x^12 + x^10 + x^8 + x^6 + 3*x^4 + 3*x^2 + 4) dy
[6nsage: omega2.int()
((3*x^28 + 4*x^26 + 4*x^24 + x^22 + 4*x^20 + 4*x^16 + x^14 + 2*x^12 + 2*x^10 + 4*x^8 + 3*x^6 + 4*x^4 + 2*x^2 + 4)/(x^36 + 3*x^34 + 2*x^32 + 3*x^30 + 2*x^28 + 2*x^26 + 4*x^24 + 2*x^22 + 2*x^20 + 2*x^18 + 4*x^16 + 3*x^14 + 3*x^12 + 4*x^10 + 4*x^6 + x^2 + 1))*y
[6nsage: C1
Superelliptic curve with the equation y^2 = x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x over Finite Field of size 5
[6nsage: C1.is_smooth()
1
[6nsagesage: A2 = (A - A1 - C.y)/C.y
[6nsasage: (A - A1 - C.y).diffn()
((-2*x^6 + 2*x^2 - 1)/y) dx
[6nsage: A - A1 - C.y
((x^146 + 2*x^144 + x^142 + 4*x^136 + 3*x^134 + 4*x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 3*x^106 + x^104 + 3*x^102 + 3*x^96 + x^94 + 3*x^92 + x^86 + 2*x^84 + x^82 + 4*x^76 + 3*x^74 + 4*x^72 + 3*x^66 + x^64 + 3*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 2*x^46 + 4*x^44 + 2*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^28 + 3*x^26 + 2*x^24 + 3*x^20 + 2*x^16 + x^14 + 4*x^12 + 3*x^10 + 2*x^8 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y
[6nsage: Rx
Univariate Polynomial Ring in x over Finite Field of size 5
[6nsage: (x^36 +sage: (x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4).factor()
(x - 1)^3 * (x + 1)^3 * (x^5 - x + 2)^3 * (x^5 - x - 2)^3
[6nsage: (sage: (A - A1 - C1.y).diffn()
((-2*x^6 + 2*x^2 - 1)/y) dx
[6nsage: A - A1 - C.y
((x^146 + 2*x^144 + x^142 + 4*x^136 + 3*x^134 + 4*x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 3*x^106 + x^104 + 3*x^102 + 3*x^96 + x^94 + 3*x^92 + x^86 + 2*x^84 + x^82 + 4*x^76 + 3*x^74 + 4*x^72 + 3*x^66 + x^64 + 3*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 2*x^46 + 4*x^44 + 2*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^28 + 3*x^26 + 2*x^24 + 3*x^20 + 2*x^16 + x^14 + 4*x^12 + 3*x^10 + 2*x^8 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y
sage: p = 5
....: m = 2
....: F = GF(p)
....: Rx.<x> = PolynomialRing(F)
....: #f = (x^3 - x)^3 + x^3 - x
....: f = x^3 + x
....: f1 = f(x = x^5 - x)
....: C = superelliptic(f, m)
....: C1 = superelliptic(f1, m, prec = 500)
....: A = ((C1.x^146 + 2*C1.x^144 + C1.x^142 + 4*C1.x^136 + 3*C1.x^134 + 4*C1.x^132 + 2*C1.x^126 + 4*C1.x^124 + 2*C1.x^122 + 3*31.x^106 + C1.x^104 + 3*C1.x^102 +
....: *C1.x^96 + C1.x^94 + 3*C1.x^92 + C1.x^86 + 2*C1.x^84 + C1.x^82 + 4*C1.x^76 + 3*C1.x^74 + 4*C1.x^72 + 3*C1.x^66 + C1.x^64 + 3*C1.x^62 + 4*C1.x^56 + 3*C1.x^54
....: + 4*C1.x^52 + 2*C1.x^46 + 4*C1.x^44 + 2*C1.x^42 + 4*C1.x^36 + 3*C1.x^34 + 4*C1.x^32 + 4*C1.x^28 + 3*C1.x^26 + 2*C1.x^24 +43*C1.x^20 + 2*C1.x^16 + C1.x^14 +
....: *C1.x^12 + 3*C1.x^10 + 2*C1.x^8 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 3*C1.one)/(C1.x^36 + 2*C1.x^34 + 2*C1.x^32 + 2*C1.x^30++ 2*C1.x^28 + 4*C1.x^26 + C1.x^24
....: 2*C1.x^22 + 3*C1.x^20 + 2*C1.x^18 + C1.x^14 + 4*C1.x^12 + C1.x^8 + C1.x^6 + 3*C1.x^4 + 4*C1.one))*C1.y
....: print(A.diffn())
....: print(A.diffn().is_regular_on_U0())
((-2*x^6 + 2*x^2 - 1)/y) dx
True
[6nsage:
sage: A.expansion_at_infty()
t^-235 + 3*t^-195 + 2*t^-175 + 2*t^-155 + 3*t^-95 + 3*t^-55 + 3*t^-35 + 4*t + 2*t^9 + 4*t^13 + 4*t^25 + 4*t^29 + 2*t^33 + 4*t^37 + 2*t^41 + 3*t^49 + 2*t^65 + t^69 + 3*t^73 + 4*t^77 + 4*t^81 + t^85 + 4*t^93 + 4*t^97 + 2*t^105 + t^109 + 3*t^117 + 3*t^125 + 2*t^129 + t^137 + t^145 + 4*t^149 + 2*t^165 + 4*t^173 + 4*t^177 + 2*t^181 + 3*t^185 + t^197 + 2*t^201 + 3*t^205 + t^209 + 2*t^213 + 3*t^217 + 3*t^221 + 2*t^225 + 2*t^229 + 4*t^237 + t^245 + 4*t^249 + O(t^265)
sage: decomposition_g0_pth_power(A)
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [187], in <cell line: 1>()
----> 1 decomposition_g0_pth_power(A)
 
File <string>:5, in decomposition_g0_pth_power(fct)
 
File <string>:51, in int(self)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
1329 normalize(x._numer, x._denom, self.p)
1330 if nmod_poly_degree(x._denom) != 0:
-> 1331 raise ValueError("not integral")
1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:
 
ValueError: not integral
[6nsage: A
((x^146 + 2*x^144 + x^142 + 4*x^136 + 3*x^134 + 4*x^132 + 2*x^126 + 4*x^124 + 2*x^122 + 3*x^106 + x^104 + 3*x^102 + 3*x^96 + x^94 + 3*x^92 + x^86 + 2*x^84 + x^82 + 4*x^76 + 3*x^74 + 4*x^72 + 3*x^66 + x^64 + 3*x^62 + 4*x^56 + 3*x^54 + 4*x^52 + 2*x^46 + 4*x^44 + 2*x^42 + 4*x^36 + 3*x^34 + 4*x^32 + 4*x^28 + 3*x^26 + 2*x^24 + 3*x^20 + 2*x^16 + x^14 + 4*x^12 + 3*x^10 + 2*x^8 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/(x^36 + 2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4))*y
[6nsage: A.diffn()
((-2*x^6 + 2*x^2 - 1)/y) dx
sage: import itertools
....: p = 5
....: m = 2
....: F = GF(p)
....: Rx.<x> = PolynomialRing(F)
....: #f = (x^3 - x)^3 + x^3 - x
....: f = x^3 + x
....: f1 = f(x = x^5 - x)
....: C = superelliptic(f, m)
....: C1 = superelliptic(f1, m, prec = 500)
....: om1 = ((-2*C1.x^6 + 2*C1.x^2 - C1.one)/C1.y)* C1.dx
....: N = 5
....: lista = [GF(p) for _ in range(N)]
....: for a in itertools.product(*lista):
....: polynom = sum(a[i] * x^i for i in range(N))
....: ^Ipolynom = superelliptic_function(C1, polynom)
....: ^Iif polynom.diffn() == om1:
....: ^I print(polynom)
Input In [190]
polynom = superelliptic_function(C1, polynom)
^
TabError: inconsistent use of tabs and spaces in indentation
 
sage: import itertools
....: p = 5
....: m = 2
....: F = GF(p)
....: Rx.<x> = PolynomialRing(F)
....: #f = (x^3 - x)^3 + x^3 - x
....: f = x^3 + x
....: f1 = f(x = x^5 - x)
....: C = superelliptic(f, m)
....: C1 = superelliptic(f1, m, prec = 500)
....: om1 = ((-2*C1.x^6 + 2*C1.x^2 - C1.one)/C1.y)* C1.dx
....: N = 5
....: lista = [GF(p) for _ in range(N)]
....: for a in itertools.product(*lista):
....: polynom = sum(a[i] * x^i for i in range(N))
....: ^Ipolynom = superelliptic_function(C1, polynom)
....: ^Iif polynom.diffn() == om1:
....: ^I^Iprint(polynom)
Input In [191]
polynom = superelliptic_function(C1, polynom)
^
TabError: inconsistent use of tabs and spaces in indentation
 
sage: import itertools
....: p = 5
....: m = 2
....: F = GF(p)
....: Rx.<x> = PolynomialRing(F)
....: #f = (x^3 - x)^3 + x^3 - x
....: f = x^3 + x
....: f1 = f(x = x^5 - x)
....: C = superelliptic(f, m)
....: C1 = superelliptic(f1, m, prec = 500)
....: om1 = ((-2*C1.x^6 + 2*C1.x^2 - C1.one)/C1.y)* C1.dx
....: N = 5
....: lista = [GF(p) for _ in range(N)]
....: for a in itertools.product(*lista):
....: ^Ipolynom = sum(a[i] * x^i for i in range(N))
....: ^Ipolynom = superelliptic_function(C1, polynom)
....: ^Iif polynom.diffn() == om1:
....: ^I^Iprint(polynom)
....:
sage: import itertools
....: p = 5
....: m = 2
....: F = GF(p)
....: Rx.<x> = PolynomialRing(F)
....: #f = (x^3 - x)^3 + x^3 - x
....: f = x^3 + x
....: f1 = f(x = x^5 - x)
....: C = superelliptic(f, m)
....: C1 = superelliptic(f1, m, prec = 500)
....: om1 = ((-2*C1.x^6 + 2*C1.x^2 - C1.one)/C1.y)* C1.dx
....: N = 7
....: lista = [GF(p) for _ in range(N)]
....: for a in itertools.product(*lista):
....: ^Ipolynom = sum(a[i] * x^i for i in range(N))
....: ^Ipolynom = superelliptic_function(C1, polynom)
....: ^Iif polynom.diffn() == om1:
....: ^I^Iprint(polynom)
....:
^C---------------------------------------------------------------------------
KeyError Traceback (most recent call last)
File /ext/sage/9.7/src/sage/structure/category_object.pyx:839, in sage.structure.category_object.CategoryObject.getattr_from_category()
838 try:
--> 839 return self.__cached_methods[name]
840 except KeyError:
 
KeyError: '_mpoly_base_ring'
 
During handling of the above exception, another exception occurred:
 
AttributeError Traceback (most recent call last)
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:1114, in PolynomialRing_general._mpoly_base_ring(self, variables)
1113 try:
-> 1114 return self.base_ring()._mpoly_base_ring(variables[:variables.index(var)])
1115 except AttributeError:
 
File /ext/sage/9.7/src/sage/structure/category_object.pyx:833, in sage.structure.category_object.CategoryObject.__getattr__()
832 """
--> 833 return self.getattr_from_category(name)
834
 
File /ext/sage/9.7/src/sage/structure/category_object.pyx:848, in sage.structure.category_object.CategoryObject.getattr_from_category()
847
--> 848 attr = getattr_from_other_class(self, cls, name)
849 self.__cached_methods[name] = attr
 
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:356, in sage.cpython.getattr.getattr_from_other_class()
355 dummy_error_message.name = name
--> 356 raise AttributeError(dummy_error_message)
357 cdef PyObject* attr = instance_getattr(cls, name)
 
AttributeError: 'FpT_with_category' object has no attribute '_mpoly_base_ring'
 
During handling of the above exception, another exception occurred:
 
KeyboardInterrupt Traceback (most recent call last)
Input In [193], in <cell line: 14>()
15 polynom = sum(a[i] * x**i for i in range(N))
16 polynom = superelliptic_function(C1, polynom)
---> 17 if polynom.diffn() == om1:
18 print(polynom)
 
File <string>:12, in __eq__(self, other)
 
File <string>:161, in reduce(self)
 
File <string>:263, in reduction(C, g)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:921, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
919
920 elif isinstance(element, polynomial_element.Polynomial):
--> 921 if base_ring.has_coerce_map_from(element.parent()._mpoly_base_ring(self.variable_names())):
922 return self(element._mpoly_dict_recursive(self.variable_names(), base_ring))
923
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:1114, in PolynomialRing_general._mpoly_base_ring(self, variables)
1112 else:
1113 try:
-> 1114 return self.base_ring()._mpoly_base_ring(variables[:variables.index(var)])
1115 except AttributeError:
1116 return self.base_ring()
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
sage: import itertools
....: p = 5
....: m = 2
....: F = GF(p)
....: Rx.<x> = PolynomialRing(F)
....: #f = (x^3 - x)^3 + x^3 - x
....: f = x^3 + x
....: f1 = f(x = x^5 - x)
....: C = superelliptic(f, m)
....: C1 = superelliptic(f1, m, prec = 500)
....: om1 = ((-2*C1.x^6 + 2*C1.x^2 - C1.one)/C1.y)* C1.dx
....: N = 7
....: lista = [GF(p) for _ in range(N)]
....: for a in itertools.product(*lista):
....: ^Ipolynom = sum(a[i] * x^i for i in range(N))
....: ^Ipolynom = C1.y*superelliptic_function(C1, polynom)
....: ^Iif polynom.diffn() == om1:
....: ^I^Iprint(polynom)
....:
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [194], in <cell line: 14>()
15 polynom = sum(a[i] * x**i for i in range(N))
16 polynom = C1.y*superelliptic_function(C1, polynom)
---> 17 if polynom.diffn() == om1:
18 print(polynom)
 
File <string>:12, in __eq__(self, other)
 
File <string>:162, in reduce(self)
 
File <string>:7, in __init__(self, C, g)
 
File <string>:296, in reduction_form(C, g)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
1514 return (<Element>left)._mul_(right)
1515 if BOTH_ARE_ELEMENT(cl):
-> 1516 return coercion_model.bin_op(left, right, mul)
1517
1518 cdef long value
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1200, in sage.structure.coerce.CoercionModel.bin_op()
1198 # Now coerce to a common parent and do the operation there
1199 try:
-> 1200 xy = self.canonical_coercion(x, y)
1201 except TypeError:
1202 self._record_exception()
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1315, in sage.structure.coerce.CoercionModel.canonical_coercion()
1313 x_elt = x
1314 if y_map is not None:
-> 1315 y_elt = (<Map>y_map)._call_(y)
1316 else:
1317 y_elt = y
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:432, in sage.structure.coerce_maps.CallableConvertMap._call_()
430 y = self._func(C, x)
431 else:
--> 432 y = self._func(x)
433 except Exception:
434 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:324, in FractionField_generic._coerce_map_from_.<locals>.wrapper(x)
323 def wrapper(x):
--> 324 return self._element_class(self, x.numerator(), x.denominator())
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:1167, in sage.rings.fraction_field_element.FractionFieldElement_1poly_field.__init__()
1165 1/2/x
1166 """
-> 1167 FractionFieldElement.__init__(self, parent, numerator, denominator,
1168 coerce, reduce)
1169 if not reduce:
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:121, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
119 if reduce and parent.is_exact():
120 try:
--> 121 self.reduce()
122 except ArithmeticError:
123 pass
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:1239, in sage.rings.fraction_field_element.FractionFieldElement_1poly_field.reduce()
1237 if self._is_reduced:
1238 return
-> 1239 super(self.__class__, self).reduce()
1240 self.normalize_leading_coefficients()
1241
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:164, in sage.rings.fraction_field_element.FractionFieldElement.reduce()
162 return codomain.coerce(nnum/nden)
163
--> 164 cpdef reduce(self):
165 """
166 Reduce this fraction.
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:197, in sage.rings.fraction_field_element.FractionFieldElement.reduce()
195 return
196 try:
--> 197 g = self.__numerator.gcd(self.__denominator)
198 if not g.is_unit():
199 self.__numerator //= g
 
File /ext/sage/9.7/src/sage/structure/element.pyx:4494, in sage.structure.element.coerce_binop.new_method()
4492 def new_method(self, other, *args, **kwargs):
4493 if have_same_parent(self, other):
-> 4494 return method(self, other, *args, **kwargs)
4495 else:
4496 a, b = coercion_model.canonical_coercion(self, other)
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:4913, in sage.rings.polynomial.polynomial_element.Polynomial.gcd()
4911 raise NotImplementedError("%s does not provide a gcd implementation for univariate polynomials"%self._parent._base)
4912 else:
-> 4913 return doit(self, other)
4914
4915 @coerce_binop
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:946, in FractionField_generic._gcd_univariate_polynomial(self, f, g)
944 f1 = Num(f.numerator())
945 g1 = Num(g.numerator())
--> 946 return Pol(f1.gcd(g1)).monic()
 
File /ext/sage/9.7/src/sage/structure/element.pyx:4494, in sage.structure.element.coerce_binop.new_method()
4492 def new_method(self, other, *args, **kwargs):
4493 if have_same_parent(self, other):
-> 4494 return method(self, other, *args, **kwargs)
4495 else:
4496 a, b = coercion_model.canonical_coercion(self, other)
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:4907, in sage.rings.polynomial.polynomial_element.Polynomial.gcd()
4905 if tgt.ngens() > 1 and tgt._has_singular:
4906 g = flatten(self).gcd(flatten(other))
-> 4907 return flatten.section()(g)
4908 try:
4909 doit = self._parent._base._gcd_univariate_polynomial
 
File /ext/sage/9.7/src/sage/categories/map.pyx:769, in sage.categories.map.Map.__call__()
767 if P is D: # we certainly want to call _call_/with_args
768 if not args and not kwds:
--> 769 return self._call_(x)
770 return self._call_with_args(x, args, kwds)
771 # Is there coercion?
 
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
786 return self._call_with_args(x, args, kwds)
787
--> 788 cpdef Element _call_(self, x):
789 """
790 Call method with a single argument, not implemented in the base class.
 
File /ext/sage/9.7/src/sage/rings/polynomial/flatten.py:362, in UnflatteningMorphism._call_(self, p)
359 Morphism.__init__(self, hom)
360 self._repr_type_str = 'Unflattening'
--> 362 def _call_(self, p):
363 """
364 Evaluate an unflattening morphism.
365
(...)
377 ....: assert z == g(f(z))
378 """
379 index = [0]
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: om1
((-2*x^6 + 2*x^2 - 1)/y) dx
[6nsage: om1.cartier()
0 dx
[6nsage: om1.int()
((4*x^28 + 2*x^26 + 2*x^24 + 3*x^22 + 2*x^20 + 2*x^16 + 3*x^14 + x^12 + x^10 + 2*x^8 + 4*x^6 + 2*x^4 + x^2 + 2)/(x^36 + 3*x^34 + 2*x^32 + 3*x^30 + 2*x^28 + 2*x^26 + 4*x^24 + 2*x^22 + 2*x^20 + 2*x^18 + 4*x^16 + 3*x^14 + 3*x^12 + 4*x^10 + 4*x^6 + x^2 + 1))*y
[6nsage: om1.curve
Superelliptic curve with the equation y^2 = x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x over Finite Field of size 5
[6nsage: C1.genus()
7
[6nsage: load('init.sage')
Computing 0. basis element
Computing 1. basis element
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [200], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:32, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:11, in <module>
 
File <string>:44, in crystalline_cohomology_basis(self, prec, info)
 
File <string>:26, in de_rham_witt_lift(cech_class, prec)
 
File <string>:90, in diffn(self, dy_w)
 
File <string>:99, in diffn(self, dy_w)
 
File <string>:73, in diffn(self, dy_w)
 
File <string>:177, in dy_w(C)
 
File <string>:149, in auxilliary_derivative(P)
 
File <string>:55, in __rmul__(self, other)
 
File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
1962 return y
1963
-> 1964 return coercion_model.bin_op(left, right, operator.mul)
1965
1966 cpdef _mul_(self, right):
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:55, in __rmul__(self, other)
 
File <string>:84, in __add__(self, other)
 
File <string>:65, in __mul__(self, other)
 
File <string>:94, in diffn(self)
 
File /ext/sage/9.7/src/sage/categories/quotient_fields.py:610, in QuotientFields.ElementMethods.derivative(self, *args)
580 r"""
581 The derivative of this rational function, with respect to variables
582 supplied in args.
(...)
607 2/(x^3 + 3*x^2*y + 3*x*y^2 + y^3)
608 """
609 from sage.misc.derivative import multi_derivative
--> 610 return multi_derivative(self, args)
 
File /ext/sage/9.7/src/sage/misc/derivative.pyx:222, in sage.misc.derivative.multi_derivative()
220
221 for arg in derivative_parse(args):
--> 222 F = F._derivative(arg)
223 return F
224
 
File /ext/sage/9.7/src/sage/categories/quotient_fields.py:671, in QuotientFields.ElementMethods._derivative(self, var)
613 r"""
614 Returns the derivative of this rational function with respect to the
615 variable ``var``.
(...)
668 (-t + 1)/(t^3 + 3*t^2 + 3*t + 1)
669 """
670 R = self.parent()
--> 671 if var in R.gens():
672 var = R.ring()(var)
674 num = self.numerator()
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1112, in sage.structure.element.Element.__richcmp__()
1110 return (<Element>self)._richcmp_(other, op)
1111 else:
-> 1112 return coercion_model.richcmp(self, other, op)
1113
1114 cpdef _richcmp_(left, right, int op):
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1973, in sage.structure.coerce.CoercionModel.richcmp()
1971 # Coerce to a common parent
1972 try:
-> 1973 x, y = self.canonical_coercion(x, y)
1974 except (TypeError, NotImplementedError):
1975 pass
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1315, in sage.structure.coerce.CoercionModel.canonical_coercion()
1313 x_elt = x
1314 if y_map is not None:
-> 1315 y_elt = (<Map>y_map)._call_(y)
1316 else:
1317 y_elt = y
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
636 ring_one = self.ring().one()
637 try:
--> 638 return self._element_class(self, x, ring_one, coerce=coerce)
639 except (TypeError, ValueError):
640 pass
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: load('init.sage')
Computing 0. basis element
Computing 1. basis element
[6nsage: B
[([(1/(x^3 + x))*y] d[x] + V(((-x^2 + 2)/(x^4*y + 2*x^2*y + y)) dx) + dV([((4*x^18 + 4*x^16 + 4*x^14 + x^8 + x^6 + x^4)/(x^4 + 2*x^2 + 1))*y]), V((4*x^14 + x^12 + 3*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 4)*y), [(1/(x^3 + x))*y] d[x] + V(((-x^2 + 2)/(x^4*y + 2*x^2*y + y)) dx) + dV([((4*x^2 + 1)/(x^4 + 2*x^2 + 1))*y])),
([(1/(x^2 + 1))*y] d[x] + V(((-2*x^7 - 2*x^5 - 2*x^3 + x)/(x^4*y + 2*x^2*y + y)) dx) + dV([((4*x^23 + 4*x^21 + 4*x^19 + x^13 + x^11 + x^9)/(x^4 + 2*x^2 + 1))*y]), [2/x*y] + V(((4*x^20 + x^18 + 3*x^16 + 3*x^14 + x^12 + x^10 + 3*x^8 + 4*x^6 + 4*x^4 + 3*x^2 + 4)/x)*y), [(1/(x^4 + x^2))*y] d[x] + V(((-2*x^6 + x^4 - 2*x^2 - 2)/(x^7*y + 2*x^5*y + x^3*y)) dx) + dV([(3*x/(x^4 + 2*x^2 + 1))*y]))]
[6nsage: autom(B[0]).coordinates(basis=B)
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [203], in <cell line: 1>()
----> 1 autom(B[Integer(0)]).coordinates(basis=B)
 
File <string>:109, in coordinates(self, basis, prec, info)
 
File <string>:59, in coordinates(self)
 
File <string>:93, in coordinates(self, basis)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
786 return self._call_with_args(x, args, kwds)
787
--> 788 cpdef Element _call_(self, x):
789 """
790 Call method with a single argument, not implemented in the base class.
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
1249 return num
1250 if check and not den.is_unit():
1251 # This should probably be a ValueError.
1252 # However, too much existing code is expecting this to throw a
1253 # TypeError, so we decided to keep it for the time being.
-> 1254 raise TypeError("fraction must have unit denominator")
1255 return num * den.inverse_of_unit()
 
TypeError: fraction must have unit denominator
[6nsage: C
Superelliptic curve with the equation y^2 = x^3 + x over Finite Field of size 5
[6nsage: load('init.sage')
Computing 0. basis element
Computing 1. basis element
[6nsage: autom(B[0]).coordinates(basis=B)
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [206], in <cell line: 1>()
----> 1 autom(B[Integer(0)]).coordinates(basis=B)
 
File <string>:117, in coordinates(self, basis, prec, info)
 
File <string>:88, in div_by_p(self, info)
 
TypeError: cannot unpack non-iterable superelliptic_function object
[6nsage: load('init.sage')
Computing 0. basis element
Computing 1. basis element
[6nsage: autom(B[0]).coordinates(basis=B)
[4, 6]
[6nsage: load('init.sage')
Computing 0. basis element
Computing 1. basis element
Computing 2. basis element
Computing 3. basis element
Computing 4. basis element
Computing 5. basis element
Computing 6. basis element
Computing 7. basis element
Computing 8. basis element
Computing 9. basis element
Computing 10. basis element
Computing 11. basis element
Computing 12. basis element
Computing 13. basis element
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [209], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:32, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:13, in <module>
 
File <string>:91, in regular_drw_cech(cocycle)
 
File <string>:83, in regular_drw_form(omega)
 
AttributeError: 'superelliptic_drw_form' object has no attribute 'omega0'
sage: def regular_drw_form(omega):
....: C = omega.curve
....: omega_aux = omega.r()
....: omega_aux = omega_aux.regular_form()
....: aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()
....: aux.omega, fct = decomposition_omega0_hpdh(aux.omega)
....: aux.h2 += fct^p
....: aux.h2, A = decomposition_g0_pth_power(aux.h2)
....: aux.omega += (A.diffn()).inv_cartier()
....: result = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2)
....: return result
....:
[6nsage: regular_drw_form(B[0].omega0)
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
File <string>:59, in __mul__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
1515 if BOTH_ARE_ELEMENT(cl):
-> 1516 return coercion_model.bin_op(left, right, mul)
1517
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op()
1247 # This causes so much headache.
-> 1248 raise bin_op_exception(op, x, y)
1249
 
TypeError: unsupported operand parent(s) for *: 'Univariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 3' and 'Univariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 5'
 
During handling of the above exception, another exception occurred:
 
AttributeError Traceback (most recent call last)
Input In [211], in <cell line: 1>()
----> 1 regular_drw_form(B[Integer(0)].omega0)
 
Input In [210], in regular_drw_form(omega)
3 omega_aux = omega.r()
4 omega_aux = omega_aux.regular_form()
----> 5 aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()
6 aux.omega, fct = decomposition_omega0_hpdh(aux.omega)
7 aux.h2 += fct**p
 
File <string>:73, in diffn(self, dy_w)
 
File <string>:177, in dy_w(C)
 
File /ext/sage/9.7/src/sage/rings/rational.pyx:2414, in sage.rings.rational.Rational.__mul__()
2412 return x
2413
-> 2414 return coercion_model.bin_op(left, right, operator.mul)
2415
2416 cpdef _mul_(self, right):
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:48, in __rmul__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
1526 if not err:
1527 return (<Element>right)._mul_long(value)
-> 1528 return coercion_model.bin_op(left, right, mul)
1529 except TypeError:
1530 return NotImplemented
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:43, in __rmul__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
1526 if not err:
1527 return (<Element>right)._mul_long(value)
-> 1528 return coercion_model.bin_op(left, right, mul)
1529 except TypeError:
1530 return NotImplemented
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:43, in __rmul__(self, other)
 
[... skipping similar frames: __rmul__ at line 43 (2 times), sage.structure.coerce.CoercionModel.bin_op at line 1242 (2 times), sage.structure.element.Element.__mul__ at line 1528 (2 times)]
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
1526 if not err:
1527 return (<Element>right)._mul_long(value)
-> 1528 return coercion_model.bin_op(left, right, mul)
1529 except TypeError:
1530 return NotImplemented
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:43, in __rmul__(self, other)
 
File <string>:31, in __add__(self, other)
 
File <string>:63, in __mul__(self, other)
 
AttributeError: 'superelliptic_function' object has no attribute 'form'
[6nsage: B[0]
([(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), V(((x^2 + 1)/x)*y), [(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
[6nsage: B[0].omega0
[(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
sage: def regular_drw_form(omega):
....: C = omega.curve
....: p = C.characteristic
....: omega_aux = omega.r()
....: omega_aux = omega_aux.regular_form()
....: aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()
....: aux.omega, fct = decomposition_omega0_hpdh(aux.omega)
....: aux.h2 += fct^p
....: aux.h2, A = decomposition_g0_pth_power(aux.h2)
....: aux.omega += (A.diffn()).inv_cartier()
....: result = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2)
....: return result
....:
sage: regular_drw_form(B[0].omega0)
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
File <string>:59, in __mul__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
1515 if BOTH_ARE_ELEMENT(cl):
-> 1516 return coercion_model.bin_op(left, right, mul)
1517
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op()
1247 # This causes so much headache.
-> 1248 raise bin_op_exception(op, x, y)
1249
 
TypeError: unsupported operand parent(s) for *: 'Univariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 3' and 'Univariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 5'
 
During handling of the above exception, another exception occurred:
 
AttributeError Traceback (most recent call last)
Input In [215], in <cell line: 1>()
----> 1 regular_drw_form(B[Integer(0)].omega0)
 
Input In [214], in regular_drw_form(omega)
4 omega_aux = omega.r()
5 omega_aux = omega_aux.regular_form()
----> 6 aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()
7 aux.omega, fct = decomposition_omega0_hpdh(aux.omega)
8 aux.h2 += fct**p
 
File <string>:73, in diffn(self, dy_w)
 
File <string>:177, in dy_w(C)
 
File /ext/sage/9.7/src/sage/rings/rational.pyx:2414, in sage.rings.rational.Rational.__mul__()
2412 return x
2413
-> 2414 return coercion_model.bin_op(left, right, operator.mul)
2415
2416 cpdef _mul_(self, right):
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:48, in __rmul__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
1526 if not err:
1527 return (<Element>right)._mul_long(value)
-> 1528 return coercion_model.bin_op(left, right, mul)
1529 except TypeError:
1530 return NotImplemented
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:43, in __rmul__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
1526 if not err:
1527 return (<Element>right)._mul_long(value)
-> 1528 return coercion_model.bin_op(left, right, mul)
1529 except TypeError:
1530 return NotImplemented
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:43, in __rmul__(self, other)
 
[... skipping similar frames: __rmul__ at line 43 (2 times), sage.structure.coerce.CoercionModel.bin_op at line 1242 (2 times), sage.structure.element.Element.__mul__ at line 1528 (2 times)]
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
1526 if not err:
1527 return (<Element>right)._mul_long(value)
-> 1528 return coercion_model.bin_op(left, right, mul)
1529 except TypeError:
1530 return NotImplemented
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:43, in __rmul__(self, other)
 
File <string>:31, in __add__(self, other)
 
File <string>:63, in __mul__(self, other)
 
AttributeError: 'superelliptic_function' object has no attribute 'form'
[6nssage: C.x.teichmuller().diffn()
[1] d[x]
[6nsage: omega = B[0].omega0
[6nsage: omega_aux = omega.r()
[6nsage: omega_aux = omega_aux.regular_form()
[6nsage: aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
File <string>:58, in __mul__(self, other)
 
AttributeError: 'superelliptic_form' object has no attribute 'function'
 
During handling of the above exception, another exception occurred:
 
TypeError Traceback (most recent call last)
Input In [220], in <cell line: 1>()
----> 1 aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()
 
File <string>:65, in __mul__(self, other)
 
File <string>:64, in __mul__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
1514 return (<Element>left)._mul_(right)
1515 if BOTH_ARE_ELEMENT(cl):
-> 1516 return coercion_model.bin_op(left, right, mul)
1517
1518 cdef long value
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op()
1246 # We should really include the underlying error.
1247 # This causes so much headache.
-> 1248 raise bin_op_exception(op, x, y)
1249
1250 cpdef canonical_coercion(self, x, y):
 
TypeError: unsupported operand parent(s) for *: 'Univariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 3' and 'Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 5'
[6nsage: sage: omega_aux.dx.teichmuller()*C.x.teichmuller().diffn()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
File <string>:58, in __mul__(self, other)
 
AttributeError: 'superelliptic_form' object has no attribute 'function'
 
During handling of the above exception, another exception occurred:
 
TypeError Traceback (most recent call last)
Input In [221], in <cell line: 1>()
----> 1 omega_aux.dx.teichmuller()*C.x.teichmuller().diffn()
 
File <string>:65, in __mul__(self, other)
 
File <string>:64, in __mul__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
1514 return (<Element>left)._mul_(right)
1515 if BOTH_ARE_ELEMENT(cl):
-> 1516 return coercion_model.bin_op(left, right, mul)
1517
1518 cdef long value
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op()
1246 # We should really include the underlying error.
1247 # This causes so much headache.
-> 1248 raise bin_op_exception(op, x, y)
1249
1250 cpdef canonical_coercion(self, x, y):
 
TypeError: unsupported operand parent(s) for *: 'Univariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 3' and 'Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 5'
[6nsage: omega_aux.dx.teichmuller()
[0]
[6nsage: parent(omega_aux.dx.teichmuller())
<class '__main__.superelliptic_witt'>
[6nsage: parent(omega_aux.dx.teichmuller().t.function)
Univariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 3
[6nsage: omega
[(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[6nsage: sage: aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
File <string>:58, in __mul__(self, other)
 
AttributeError: 'superelliptic_form' object has no attribute 'function'
 
During handling of the above exception, another exception occurred:
 
TypeError Traceback (most recent call last)
Input In [226], in <cell line: 1>()
----> 1 aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()
 
File <string>:65, in __mul__(self, other)
 
File <string>:64, in __mul__(self, other)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
1514 return (<Element>left)._mul_(right)
1515 if BOTH_ARE_ELEMENT(cl):
-> 1516 return coercion_model.bin_op(left, right, mul)
1517
1518 cdef long value
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op()
1246 # We should really include the underlying error.
1247 # This causes so much headache.
-> 1248 raise bin_op_exception(op, x, y)
1249
1250 cpdef canonical_coercion(self, x, y):
 
TypeError: unsupported operand parent(s) for *: 'Univariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 3' and 'Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 5'
[6nsage: omega_aux = omega_aux.regular_form()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [227], in <cell line: 1>()
----> 1 omega_aux = omega_aux.regular_form()
 
AttributeError: 'superelliptic_regular_form' object has no attribute 'regular_form'
[6nsage: omega_aux = omega.r()
[6nsage: parent(omega_aux.function)
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [229], in <cell line: 1>()
----> 1 parent(omega_aux.function)
 
AttributeError: 'superelliptic_form' object has no attribute 'function'
[6nsage: parent(omega_aux.form)
Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3
[6nsage: omega.curve
Superelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
[6nsage: C.de_rham_basis()
[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, (1/(x*y)) dx)]
[6nsage: C
Superelliptic curve with the equation y^2 = x^3 + x over Finite Field of size 5
sage: A = C.de_rham_basis[0]
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [234], in <cell line: 1>()
----> 1 A = C.de_rham_basis[Integer(0)]
 
TypeError: 'method' object is not subscriptable
[6nsage: A = C.de_rham_basis()[0]
[6nsage: A = A.omega0
[6nsage: parent(A.form)
Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 5
[6nsage: parent(B[0].omega0.omega.form)
Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3
sage: de_rham_witt_lift_form0(C.dx)
[1] d[x]
sage: A = de_rham_witt_lift_form0(C.dx)
sage: parent(A.omega.form)
Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 5
[6nsage: parent(A.h1.function)
Univariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 5
[6nsage: parent(A.h2.function)
Univariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 5
[6nsasage: quit()
[23;0t
~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
[22;0t[6nsage: load('init.sage')
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [1], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:32, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:12, in <module>
 
NameError: name 'C1' is not defined
[6nsage: load('init.sage')
Computing 0. basis element
Computing 1. basis element
Computing 2. basis element
Computing 3. basis element
Computing 4. basis element
Computing 5. basis element
Computing 6. basis element
Computing 7. basis element
Computing 8. basis element
Computing 9. basis element
Computing 10. basis element
Computing 11. basis element
Computing 12. basis element
Computing 13. basis element
( [(3*x^5 + 2*x)*y] d[x] + [2*x^10 + x^6 + 2*x^2 + 3] d[y] + V(((2*x^215 + 2*x^211 + 2*x^207 + 3*x^205 + 2*x^203 + 4*x^201 + 3*x^197 + 4*x^189 + 3*x^185 + x^181 + 4*x^179 + 4*x^177 + 2*x^175 + 2*x^173 + 4*x^171 + 2*x^169 + x^167 + 4*x^165 + 2*x^163 + 3*x^161 + x^159 + x^155 + 2*x^151 + 4*x^149 + 3*x^147 + 4*x^145 + 3*x^143 + 2*x^141 + 3*x^137 + 4*x^135 + 4*x^133 + 2*x^131 + 4*x^129 + x^127 + x^125 + 4*x^123 + 2*x^121 + x^117 + 4*x^115 + x^113 + 2*x^111 + x^109 + 2*x^105 + x^103 + 2*x^99 + 3*x^97 + 2*x^95 + 4*x^93 + 4*x^91 + 2*x^89 + x^87 + x^85 + x^83 + x^81 + x^79 + 3*x^77 + 4*x^75 + 4*x^71 + 3*x^69 + x^67 + 2*x^63 + 3*x^61 + x^59 + x^57 + x^55 + 3*x^51 + 3*x^47 + x^43 + x^41 + 4*x^37 + 4*x^33 + 4*x^31 + 4*x^29 + 4*x^25 + 2*x^23 + 2*x^21 + x^19 + 4*x^17 + 3*x^13 + 3*x^11 + x^9 + 3*x^7 + 2*x^3)*y) dx + (3*x^220 + 4*x^210 + 3*x^206 + 2*x^204 + 2*x^202 + 3*x^200 + x^198 + 2*x^196 + 4*x^194 + 4*x^190 + 4*x^180 + x^176 + 2*x^174 + 2*x^170 + 3*x^168 + 4*x^166 + 2*x^164 + 2*x^162 + x^158 + 2*x^156 + 3*x^154 + 2*x^152 + 3*x^150 + 3*x^148 + 2*x^146 + 2*x^142 + 2*x^140 + x^134 + 2*x^132 + 3*x^130 + 2*x^128 + x^126 + 3*x^124 + 4*x^122 + x^120 + 2*x^118 + 4*x^116 + 2*x^114 + 3*x^108 + 4*x^104 + 2*x^100 + 3*x^98 + 3*x^94 + 3*x^92 + 4*x^90 + 4*x^88 + 2*x^86 + x^84 + x^82 + 4*x^80 + 2*x^78 + 3*x^76 + 2*x^74 + 4*x^72 + 2*x^70 + x^62 + 4*x^60 + 2*x^58 + 2*x^54 + 3*x^52 + 3*x^50 + 4*x^44 + x^42 + 3*x^40 + 2*x^32 + x^26 + 2*x^24 + 2*x^22 + x^20 + 2*x^18 + 4*x^16 + 4*x^14 + x^12 + 3*x^10 + 2*x^4 + 3*x^2) dy) + dV(0), V(((2*x^80 + 4*x^76 + x^74 + 3*x^72 + 4*x^68 + 2*x^66 + 4*x^64 + 2*x^60 + x^58 + 3*x^56 + x^54 + 3*x^52 + x^50 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 4*x^38 + 3*x^36 + x^34 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 4*x^20 + x^18 + 2*x^16 + 4*x^14 + x^12 + x^10 + 4*x^8 + 2*x^6 + 4*x^4 + 3)/x^4)*y) )
[6nsage:
~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
[22;0t[6nsage: load('init.sage')
Computing 0. basis element
Computing 1. basis element
Computing 0. basis element
Computing 1. basis element
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [1], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:32, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:12, in <module>
 
File <string>:44, in crystalline_cohomology_basis(self, prec, info)
 
File <string>:25, in de_rham_witt_lift(cech_class, prec)
 
File <string>:15, in de_rham_witt_lift_form8(omega)
 
File <string>:90, in diffn(self, dy_w)
 
File <string>:73, in diffn(self, dy_w)
 
File <string>:177, in dy_w(C)
 
File <string>:149, in auxilliary_derivative(P)
 
File <string>:149, in auxilliary_derivative(P)
 
[... skipping similar frames: auxilliary_derivative at line 149 (1 times)]
 
File <string>:149, in auxilliary_derivative(P)
 
File <string>:55, in __rmul__(self, other)
 
File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
1962 return y
1963
-> 1964 return coercion_model.bin_op(left, right, operator.mul)
1965
1966 cpdef _mul_(self, right):
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:55, in __rmul__(self, other)
 
File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
1962 return y
1963
-> 1964 return coercion_model.bin_op(left, right, operator.mul)
1965
1966 cpdef _mul_(self, right):
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
[... skipping similar frames: __rmul__ at line 55 (2 times), sage.rings.integer.Integer.__mul__ at line 1964 (2 times), sage.structure.coerce.CoercionModel.bin_op at line 1242 (2 times)]
 
File <string>:55, in __rmul__(self, other)
 
File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
1962 return y
1963
-> 1964 return coercion_model.bin_op(left, right, operator.mul)
1965
1966 cpdef _mul_(self, right):
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:53, in __rmul__(self, other)
 
File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
1962 return y
1963
-> 1964 return coercion_model.bin_op(left, right, operator.mul)
1965
1966 cpdef _mul_(self, right):
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:44, in __rmul__(self, constant)
 
File <string>:7, in __init__(self, C, g)
 
File <string>:296, in reduction_form(C, g)
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
1514 return (<Element>left)._mul_(right)
1515 if BOTH_ARE_ELEMENT(cl):
-> 1516 return coercion_model.bin_op(left, right, mul)
1517
1518 cdef long value
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
1202 self._record_exception()
1203 else:
-> 1204 return PyObject_CallObject(op, xy)
1205
1206 if op is mul:
 
File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__()
1512 cdef int cl = classify_elements(left, right)
1513 if HAVE_SAME_PARENT(cl):
-> 1514 return (<Element>left)._mul_(right)
1515 if BOTH_ARE_ELEMENT(cl):
1516 return coercion_model.bin_op(left, right, mul)
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:669, in sage.rings.fraction_field_element.FractionFieldElement._mul_()
667 try:
668 d1 = rnum.gcd(sden)
--> 669 d2 = snum.gcd(rden)
670 if not d1.is_unit():
671 rnum = rnum // d1
 
File /ext/sage/9.7/src/sage/structure/element.pyx:4494, in sage.structure.element.coerce_binop.new_method()
4492 def new_method(self, other, *args, **kwargs):
4493 if have_same_parent(self, other):
-> 4494 return method(self, other, *args, **kwargs)
4495 else:
4496 a, b = coercion_model.canonical_coercion(self, other)
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:4913, in sage.rings.polynomial.polynomial_element.Polynomial.gcd()
4911 raise NotImplementedError("%s does not provide a gcd implementation for univariate polynomials"%self._parent._base)
4912 else:
-> 4913 return doit(self, other)
4914
4915 @coerce_binop
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:946, in FractionField_generic._gcd_univariate_polynomial(self, f, g)
944 f1 = Num(f.numerator())
945 g1 = Num(g.numerator())
--> 946 return Pol(f1.gcd(g1)).monic()
 
File /ext/sage/9.7/src/sage/structure/element.pyx:4494, in sage.structure.element.coerce_binop.new_method()
4492 def new_method(self, other, *args, **kwargs):
4493 if have_same_parent(self, other):
-> 4494 return method(self, other, *args, **kwargs)
4495 else:
4496 a, b = coercion_model.canonical_coercion(self, other)
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:4907, in sage.rings.polynomial.polynomial_element.Polynomial.gcd()
4905 if tgt.ngens() > 1 and tgt._has_singular:
4906 g = flatten(self).gcd(flatten(other))
-> 4907 return flatten.section()(g)
4908 try:
4909 doit = self._parent._base._gcd_univariate_polynomial
 
File /ext/sage/9.7/src/sage/categories/map.pyx:769, in sage.categories.map.Map.__call__()
767 if P is D: # we certainly want to call _call_/with_args
768 if not args and not kwds:
--> 769 return self._call_(x)
770 return self._call_with_args(x, args, kwds)
771 # Is there coercion?
 
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
786 return self._call_with_args(x, args, kwds)
787
--> 788 cpdef Element _call_(self, x):
789 """
790 Call method with a single argument, not implemented in the base class.
 
File /ext/sage/9.7/src/sage/rings/polynomial/flatten.py:380, in UnflatteningMorphism._call_(self, p)
363 """
364 Evaluate an unflattening morphism.
365
(...)
377 ....: assert z == g(f(z))
378 """
379 index = [0]
--> 380 for R, _ in reversed(self._intermediate_rings):
381 index.append(index[-1] + len(R.gens()))
382 newpol = [{} for _ in self._intermediate_rings]
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: load('init.sage')
Computing 0. basis element
Computing 1. basis element
Computing 0. basis element
Computing 1. basis element
Computing 2. basis element
Computing 3. basis element
Computing 4. basis element
Computing 5. basis element
Computing 6. basis element
Computing 7. basis element
Computing 8. basis element
Computing 9. basis element
Computing 10. basis element
Computing 11. basis element
Computing 12. basis element
Computing 13. basis element
( [3*x*y] d[x] + [3*x^2 + 2] d[y] + V(((x^37 + 2*x^35 + x^33 + 4*x^29 + 4*x^27 + x^25 + x^23 + 2*x^19 + 4*x^17 + 2*x^15 + 4*x^9 + x^7 + 3*x^3)*y) dx + (x^38 + x^36 + 4*x^34 + 4*x^32 + 4*x^30 + 2*x^26 + 4*x^22 + 2*x^20 + 2*x^18 + 3*x^16 + 3*x^14 + 4*x^10 + 2*x^8 + 4*x^6 + 3*x^4 + 2*x^2) dy) + dV(0), V((4*x^14 + x^12 + 3*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 4)*y) )
( [3*x^2*y] d[x] + [3*x^3 + 2*x] d[y] + V(((x^42 + 2*x^40 + x^38 + 4*x^34 + 4*x^32 + x^30 + x^28 + 2*x^24 + 3*x^22 + 4*x^18)*y) dx + (x^43 + x^41 + 4*x^39 + 4*x^37 + 4*x^35 + 2*x^31 + 4*x^27 + 2*x^25 + x^23 + 2*x^21 + 4*x^19 + x^17) dy) + dV(0), [2/x*y] + V(((4*x^20 + x^18 + 3*x^16 + 3*x^14 + x^12 + x^10 + 3*x^8 + 4*x^6 + 4*x^4 + 3*x^2 + 4)/x)*y) )
( [(3*x^5 + 2*x)*y] d[x] + [2*x^10 + x^6 + 2*x^2 + 3] d[y] + V(((2*x^215 + 2*x^211 + 2*x^207 + 3*x^205 + 2*x^203 + 4*x^201 + 3*x^197 + 4*x^189 + 3*x^185 + x^181 + 4*x^179 + 4*x^177 + 2*x^175 + 2*x^173 + 4*x^171 + 2*x^169 + x^167 + 4*x^165 + 2*x^163 + 3*x^161 + x^159 + x^155 + 2*x^151 + 4*x^149 + 3*x^147 + 4*x^145 + 3*x^143 + 2*x^141 + 3*x^137 + 4*x^135 + 4*x^133 + 2*x^131 + 4*x^129 + x^127 + x^125 + 4*x^123 + 2*x^121 + x^117 + 4*x^115 + x^113 + 2*x^111 + x^109 + 2*x^105 + x^103 + 2*x^99 + 3*x^97 + 2*x^95 + 4*x^93 + 4*x^91 + 2*x^89 + x^87 + x^85 + x^83 + x^81 + x^79 + 3*x^77 + 4*x^75 + 4*x^71 + 3*x^69 + x^67 + 2*x^63 + 3*x^61 + x^59 + x^57 + x^55 + 3*x^51 + 3*x^47 + x^43 + x^41 + 4*x^37 + 4*x^33 + 4*x^31 + 4*x^29 + 4*x^25 + 2*x^23 + 2*x^21 + x^19 + 4*x^17 + 3*x^13 + 3*x^11 + x^9 + 3*x^7 + 2*x^3)*y) dx + (3*x^220 + 4*x^210 + 3*x^206 + 2*x^204 + 2*x^202 + 3*x^200 + x^198 + 2*x^196 + 4*x^194 + 4*x^190 + 4*x^180 + x^176 + 2*x^174 + 2*x^170 + 3*x^168 + 4*x^166 + 2*x^164 + 2*x^162 + x^158 + 2*x^156 + 3*x^154 + 2*x^152 + 3*x^150 + 3*x^148 + 2*x^146 + 2*x^142 + 2*x^140 + x^134 + 2*x^132 + 3*x^130 + 2*x^128 + x^126 + 3*x^124 + 4*x^122 + x^120 + 2*x^118 + 4*x^116 + 2*x^114 + 3*x^108 + 4*x^104 + 2*x^100 + 3*x^98 + 3*x^94 + 3*x^92 + 4*x^90 + 4*x^88 + 2*x^86 + x^84 + x^82 + 4*x^80 + 2*x^78 + 3*x^76 + 2*x^74 + 4*x^72 + 2*x^70 + x^62 + 4*x^60 + 2*x^58 + 2*x^54 + 3*x^52 + 3*x^50 + 4*x^44 + x^42 + 3*x^40 + 2*x^32 + x^26 + 2*x^24 + 2*x^22 + x^20 + 2*x^18 + 4*x^16 + 4*x^14 + x^12 + 3*x^10 + 2*x^4 + 3*x^2) dy) + dV(0), V(((2*x^80 + 4*x^76 + x^74 + 3*x^72 + 4*x^68 + 2*x^66 + 4*x^64 + 2*x^60 + x^58 + 3*x^56 + x^54 + 3*x^52 + x^50 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 4*x^38 + 3*x^36 + x^34 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 4*x^20 + x^18 + 2*x^16 + 4*x^14 + x^12 + x^10 + 4*x^8 + 2*x^6 + 4*x^4 + 3)/x^4)*y) )
( [(3*x^6 + 2*x^2)*y] d[x] + [2*x^11 + x^7 + 2*x^3 + 3*x] d[y] + V(((2*x^220 + 2*x^216 + 2*x^212 + 4*x^210 + 2*x^208 + 4*x^202 + 4*x^200 + x^198 + 2*x^196 + 4*x^194 + 4*x^192 + 3*x^190 + x^186 + x^184 + 4*x^182 + 2*x^180 + 2*x^178 + 3*x^176 + 4*x^174 + 4*x^172 + 2*x^170 + 4*x^168 + 2*x^164 + x^160 + 4*x^158 + 3*x^156 + 4*x^154 + x^152 + 2*x^150 + 4*x^148 + x^138 + x^136 + 3*x^134 + 3*x^128 + 3*x^126 + 4*x^124 + 3*x^122 + x^120 + 3*x^118 + 3*x^116 + 3*x^114 + 2*x^110 + 3*x^108 + 4*x^106 + 4*x^104 + 2*x^102 + 4*x^98 + 2*x^94 + 4*x^90 + 2*x^88 + 4*x^86 + 2*x^84 + 2*x^82 + 2*x^80 + 3*x^78 + x^76 + 4*x^74 + 2*x^72 + x^70 + 3*x^68 + 3*x^66 + 2*x^64 + 3*x^58 + x^56 + 2*x^50 + x^48 + 2*x^46 + x^44 + 4*x^42 + 2*x^40 + x^38 + 4*x^36 + x^32 + 4*x^30 + 2*x^28 + x^26 + 4*x^24 + 3*x^22 + 4*x^18 + 3*x^16 + x^14 + 3*x^12 + 2*x^8)*y) dx + (3*x^225 + 3*x^215 + 3*x^211 + 2*x^209 + 2*x^207 + x^203 + x^201 + x^197 + 3*x^195 + 3*x^193 + x^191 + 2*x^189 + x^181 + 2*x^179 + 3*x^175 + 3*x^173 + x^171 + 4*x^169 + 3*x^167 + 3*x^163 + 2*x^161 + 4*x^159 + x^157 + 2*x^155 + x^149 + 4*x^147 + 4*x^145 + 2*x^143 + 3*x^141 + x^139 + x^135 + 2*x^133 + x^131 + 2*x^129 + 4*x^127 + x^125 + 2*x^123 + 4*x^121 + x^119 + 2*x^117 + 3*x^115 + 4*x^113 + 3*x^111 + 4*x^109 + 2*x^107 + x^105 + x^103 + x^101 + 4*x^99 + 3*x^97 + 2*x^91 + 4*x^89 + 4*x^87 + 3*x^85 + 3*x^83 + 3*x^81 + 3*x^77 + x^75 + x^73 + 2*x^71 + 2*x^69 + 4*x^67 + 4*x^65 + x^63 + 4*x^61 + 4*x^59 + x^57 + 4*x^55 + 2*x^53 + 2*x^51 + 3*x^49 + 4*x^45 + x^43 + 4*x^37 + 2*x^35 + x^33 + 3*x^31 + 4*x^27 + 2*x^23 + 4*x^21 + 3*x^15 + 2*x^9 + 3*x^7) dy) + dV(0), V(((2*x^88 + 4*x^84 + x^82 + 3*x^80 + 4*x^76 + 2*x^74 + 4*x^72 + 2*x^68 + x^66 + 3*x^64 + x^62 + 3*x^60 + x^58 + 3*x^56 + 2*x^54 + 3*x^52 + x^50 + 4*x^46 + 3*x^44 + x^42 + 2*x^40 + x^38 + 3*x^36 + 2*x^34 + 4*x^28 + x^26 + 2*x^24 + 4*x^22 + x^20 + x^18 + 4*x^16 + 2*x^14 + 4*x^12 + 3*x^8 + 3*x^4 + 4*x^2 + 3)/x^7)*y) )
( [(3*x^7 + 2*x^3)*y] d[x] + [2*x^12 + x^8 + 2*x^4 + 3*x^2] d[y] + V(((2*x^225 + 2*x^221 + 2*x^217 + 2*x^213 + x^211 + 3*x^205 + 2*x^203 + 4*x^201 + 4*x^199 + 3*x^197 + 3*x^195 + x^191 + 3*x^189 + 4*x^187 + 2*x^185 + 2*x^183 + 2*x^181 + x^179 + 2*x^177 + x^173 + 2*x^171 + 3*x^169 + x^165 + 3*x^163 + 4*x^161 + 4*x^159 + 4*x^157 + 3*x^151 + 2*x^147 + x^145 + 3*x^143 + 2*x^139 + 4*x^137 + 4*x^135 + 2*x^133 + 4*x^131 + 3*x^129 + 4*x^125 + x^117 + x^115 + x^113 + x^109 + 2*x^105 + 4*x^103 + 4*x^99 + 3*x^97 + 2*x^95 + 2*x^93 + 3*x^91 + 4*x^87 + 2*x^85 + 2*x^83 + x^81 + 4*x^79 + 2*x^77 + 4*x^75 + x^73 + x^71 + 4*x^69 + x^67 + 2*x^65 + 4*x^61 + 3*x^59 + 4*x^57 + 2*x^55 + x^49 + 4*x^47 + x^45 + x^43 + 3*x^41 + 4*x^39 + x^37 + 4*x^35 + 3*x^33 + x^31 + 2*x^29 + x^27 + 2*x^25 + 2*x^23 + 4*x^21 + 4*x^19 + x^13 + 4*x^11 + 3*x^9 + 4*x^7 + x^3)*y) dx + (3*x^230 + 2*x^220 + 3*x^216 + 2*x^214 + 2*x^212 + 2*x^210 + x^208 + x^204 + 2*x^202 + 2*x^200 + x^198 + 2*x^196 + 4*x^194 + x^190 + x^186 + 2*x^184 + 4*x^180 + 3*x^178 + 3*x^176 + x^174 + 4*x^172 + 2*x^166 + x^160 + 2*x^158 + 3*x^156 + 2*x^154 + x^152 + x^150 + 4*x^148 + x^146 + x^144 + 3*x^142 + 4*x^140 + 2*x^138 + x^136 + x^134 + 4*x^132 + 2*x^128 + 4*x^126 + 4*x^122 + 3*x^120 + 2*x^108 + 3*x^106 + 2*x^104 + 3*x^102 + x^100 + x^98 + 3*x^96 + x^94 + x^92 + 4*x^90 + x^88 + 2*x^84 + 2*x^82 + x^80 + x^78 + x^74 + 4*x^72 + x^68 + 2*x^66 + x^64 + 2*x^60 + 4*x^58 + 2*x^56 + 2*x^54 + 2*x^48 + 3*x^46 + 2*x^44 + x^42 + x^40 + 3*x^38 + 2*x^36 + 3*x^30 + 2*x^28 + 2*x^26 + 3*x^24 + 4*x^22 + x^20 + x^18 + 2*x^16 + 4*x^14 + x^12 + 4*x^10 + x^4 + 4*x^2) dy) + dV(0), V(((2*x^92 + 4*x^88 + x^86 + 3*x^84 + 4*x^80 + 2*x^78 + 4*x^76 + 2*x^72 + x^70 + 3*x^68 + x^66 + 3*x^64 + x^62 + 3*x^60 + 2*x^58 + 3*x^56 + x^54 + 4*x^50 + 3*x^48 + x^46 + 2*x^44 + x^42 + 3*x^40 + 2*x^38 + 4*x^32 + x^30 + 2*x^28 + 4*x^26 + x^24 + x^22 + 4*x^20 + 2*x^18 + 4*x^16 + 3*x^12 + 3*x^8 + 4*x^6 + 3*x^4 + 3)/x^6)*y) )
( [(3*x^8 + 2*x^4)*y] d[x] + [2*x^13 + x^9 + 2*x^5 + 3*x^3] d[y] + V(((2*x^230 + 2*x^226 + 2*x^222 + x^220 + 2*x^218 + 2*x^216 + x^212 + 2*x^210 + 3*x^208 + x^206 + 4*x^204 + 2*x^202 + 3*x^200 + x^196 + 4*x^192 + 2*x^190 + 2*x^188 + x^186 + 3*x^184 + 3*x^180 + 3*x^178 + 4*x^176 + 4*x^174 + x^170 + 2*x^168 + 4*x^164 + 2*x^162 + 3*x^160 + x^158 + x^156 + 4*x^152 + 2*x^150 + 4*x^146 + x^144 + 3*x^142 + 3*x^140 + x^138 + 2*x^134 + 2*x^132 + 3*x^130 + 2*x^128 + 3*x^126 + 2*x^124 + 3*x^122 + x^120 + 3*x^114 + 4*x^112 + 4*x^110 + x^108 + x^106 + 3*x^104 + x^102 + 4*x^100 + 4*x^98 + x^96 + 4*x^94 + 3*x^92 + 4*x^88 + 4*x^86 + 3*x^84 + 3*x^82 + 4*x^80 + 3*x^78 + x^76 + 4*x^74 + 2*x^72 + 3*x^70 + 2*x^68 + x^66 + 2*x^64 + 4*x^62 + 2*x^54 + 4*x^52 + x^50 + 2*x^48 + 4*x^46 + 4*x^44 + 3*x^40 + 3*x^38 + 4*x^36 + 4*x^34 + 3*x^30 + 3*x^28 + 4*x^24 + 4*x^22 + x^16 + 2*x^14 + x^12 + 4*x^8)*y) dx + (3*x^235 + x^225 + 3*x^221 + 2*x^219 + 2*x^217 + 4*x^215 + x^213 + 4*x^211 + 2*x^209 + 3*x^207 + x^205 + 4*x^203 + 3*x^201 + x^199 + 2*x^195 + x^191 + 2*x^189 + 3*x^183 + 3*x^179 + 2*x^173 + 2*x^171 + x^169 + 4*x^167 + 4*x^163 + x^161 + 3*x^159 + 3*x^157 + 3*x^155 + x^153 + 4*x^151 + x^149 + x^147 + 2*x^145 + 2*x^143 + x^141 + 4*x^137 + 3*x^135 + 2*x^133 + 4*x^131 + 4*x^129 + x^127 + 3*x^125 + x^123 + x^121 + 2*x^119 + 4*x^117 + x^113 + 4*x^111 + 4*x^109 + 4*x^105 + 3*x^103 + 4*x^101 + 4*x^99 + 2*x^95 + x^89 + 3*x^87 + 4*x^85 + x^83 + 2*x^81 + 3*x^79 + x^77 + 4*x^75 + x^71 + 4*x^69 + 3*x^67 + 4*x^65 + 2*x^63 + 3*x^61 + 3*x^59 + 3*x^57 + x^55 + 4*x^53 + 2*x^51 + 2*x^49 + 3*x^47 + x^45 + 3*x^43 + 3*x^41 + 4*x^39 + 3*x^37 + 4*x^35 + 4*x^33 + 3*x^27 + 3*x^25 + 4*x^23 + 3*x^21 + 2*x^19 + 3*x^17 + x^15 + 4*x^9 + x^7) dy) + dV(0), V(((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 4)/x^7)*y) )
( [(3*x^9 + 2*x^5)*y] d[x] + [2*x^14 + x^10 + 2*x^6 + 3*x^4] d[y] + V(((2*x^235 + 2*x^231 + 2*x^227 + 2*x^225 + 2*x^223 + 3*x^221 + 2*x^217 + x^215 + 4*x^213 + 3*x^211 + 4*x^209 + x^207 + 3*x^205 + x^201 + 2*x^199 + 4*x^197 + 2*x^195 + 2*x^193 + 3*x^187 + x^185 + x^181 + x^175 + x^173 + x^171 + 4*x^169 + x^165 + 2*x^163 + 4*x^161 + x^157 + 3*x^155 + 2*x^153 + 3*x^151 + 2*x^147 + 2*x^145 + x^141 + x^139 + 4*x^137 + 2*x^135 + 4*x^133 + x^131 + 4*x^129 + 4*x^123 + 4*x^121 + 2*x^117 + x^115 + 2*x^113 + 4*x^111 + 2*x^109 + 4*x^107 + 4*x^105 + 4*x^101 + x^99 + 2*x^95 + 3*x^93 + 3*x^91 + 3*x^89 + 3*x^85 + 4*x^83 + 2*x^77 + 4*x^75 + x^73 + x^69 + x^65 + 2*x^61 + 3*x^59 + 2*x^57 + 4*x^55 + x^53 + x^51 + 4*x^49 + 2*x^47 + x^45 + 4*x^43 + 3*x^41 + 2*x^37 + x^35 + x^33 + x^31 + 4*x^29 + 3*x^27 + x^25 + 3*x^23 + 3*x^19 + 3*x^17 + 2*x^11 + 4*x^9 + 2*x^7 + 3*x^3)*y) dx + (3*x^240 + 3*x^226 + 2*x^224 + 2*x^222 + x^220 + x^218 + 3*x^216 + 3*x^214 + 4*x^212 + 2*x^208 + 4*x^206 + 3*x^204 + 3*x^200 + x^196 + 2*x^194 + x^190 + 3*x^188 + 2*x^186 + x^182 + 4*x^178 + 2*x^176 + 2*x^174 + 3*x^172 + 4*x^170 + x^168 + 4*x^166 + 4*x^164 + 3*x^158 + 2*x^156 + x^154 + 4*x^152 + 2*x^148 + x^146 + 4*x^144 + 4*x^142 + x^140 + 2*x^138 + 4*x^136 + 3*x^134 + 3*x^132 + 4*x^130 + 2*x^128 + 2*x^126 + 4*x^124 + 3*x^122 + 4*x^120 + x^116 + x^112 + 4*x^110 + 2*x^108 + 4*x^104 + 3*x^102 + 3*x^100 + x^98 + 2*x^96 + x^92 + 2*x^90 + 2*x^88 + 3*x^86 + 3*x^84 + 3*x^82 + 3*x^80 + x^76 + 4*x^74 + 4*x^72 + 3*x^70 + 2*x^66 + 3*x^64 + 3*x^62 + x^60 + 4*x^58 + 2*x^56 + 3*x^54 + 3*x^50 + 4*x^46 + 4*x^42 + x^40 + 3*x^38 + 4*x^34 + x^30 + 3*x^28 + 2*x^24 + 4*x^22 + x^20 + 3*x^18 + x^16 + 4*x^14 + x^12 + 2*x^10 + 3*x^4 + 2*x^2) dy) + dV(0), V(((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 4)/x^2)*y) )
( [(3*x^10 + 2*x^6)*y] d[x] + [2*x^15 + x^11 + 2*x^7 + 3*x^5] d[y] + V(((2*x^240 + 2*x^236 + 2*x^232 + 3*x^230 + 2*x^228 + 4*x^226 + 3*x^222 + 4*x^214 + 3*x^210 + x^206 + 4*x^204 + 4*x^202 + 2*x^200 + 2*x^198 + 4*x^196 + 2*x^194 + x^192 + 4*x^190 + 2*x^188 + 3*x^186 + x^184 + x^180 + 2*x^176 + 4*x^174 + 3*x^172 + 4*x^170 + 3*x^168 + 2*x^166 + 3*x^162 + 4*x^160 + 4*x^158 + 2*x^156 + 4*x^154 + x^152 + x^150 + 4*x^148 + 2*x^146 + x^142 + x^140 + x^138 + 4*x^136 + x^134 + 2*x^132 + 4*x^130 + 3*x^128 + 3*x^126 + 2*x^124 + 4*x^120 + 3*x^118 + 3*x^116 + x^114 + 3*x^112 + x^110 + 2*x^108 + 2*x^106 + 3*x^104 + 4*x^102 + 4*x^100 + x^96 + 2*x^92 + x^90 + 3*x^88 + x^86 + 4*x^84 + 4*x^82 + 4*x^78 + x^76 + 3*x^74 + 2*x^72 + 2*x^70 + 4*x^68 + x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^58 + 4*x^54 + 3*x^52 + 3*x^50 + 3*x^48 + 2*x^46 + 3*x^42 + 3*x^38 + 2*x^36 + 3*x^34 + x^32 + x^30 + 2*x^28 + 3*x^26 + 4*x^24 + x^22 + 2*x^18 + 2*x^16 + 4*x^14 + 2*x^12 + 3*x^8)*y) dx + (3*x^245 + 4*x^235 + 3*x^231 + 2*x^229 + 2*x^227 + 3*x^225 + x^223 + 2*x^221 + 4*x^219 + 4*x^215 + 4*x^205 + x^201 + 2*x^199 + 2*x^195 + 3*x^193 + 4*x^191 + 2*x^189 + 2*x^187 + x^183 + 2*x^181 + 3*x^179 + 2*x^177 + 3*x^175 + 3*x^173 + 2*x^171 + 2*x^167 + 2*x^165 + x^159 + 2*x^157 + 3*x^155 + 2*x^153 + x^151 + 3*x^149 + 4*x^147 + 4*x^145 + 2*x^143 + 4*x^141 + 2*x^139 + 3*x^133 + 3*x^131 + x^129 + 2*x^127 + 2*x^125 + 4*x^123 + 3*x^121 + x^119 + 2*x^117 + 3*x^115 + x^113 + 2*x^107 + x^105 + 2*x^101 + 4*x^99 + 2*x^97 + 2*x^95 + 2*x^93 + 4*x^91 + 2*x^89 + 3*x^87 + 3*x^85 + 4*x^83 + 4*x^81 + 4*x^79 + 3*x^77 + 4*x^75 + x^73 + 3*x^69 + 4*x^67 + 4*x^65 + 4*x^63 + 2*x^59 + 4*x^57 + 4*x^55 + x^53 + 4*x^51 + 3*x^49 + 3*x^45 + 4*x^43 + 3*x^41 + 4*x^39 + 4*x^37 + x^35 + 4*x^31 + 2*x^29 + 4*x^27 + 4*x^25 + 3*x^23 + x^21 + x^19 + 4*x^17 + 2*x^15 + 3*x^9 + 2*x^7) dy) + dV(0), V(((2*x^106 + 4*x^102 + x^100 + 3*x^98 + 4*x^94 + 2*x^92 + 4*x^90 + 2*x^86 + x^84 + 3*x^82 + x^80 + 3*x^78 + x^76 + 3*x^74 + 2*x^72 + 3*x^70 + x^68 + 4*x^64 + 3*x^62 + x^60 + 2*x^58 + x^56 + 3*x^54 + 2*x^52 + 4*x^46 + x^44 + 2*x^42 + 4*x^40 + x^38 + x^36 + 4*x^34 + 2*x^32 + 4*x^30 + 3*x^26 + 3*x^22 + 4*x^20 + 3*x^18 + 3*x^14 + 2*x^12 + 3*x^10 + 4*x^8 + 3*x^2 + 3)/x^5)*y) )
( [(3*x^11 + 2*x^7)*y] d[x] + [2*x^16 + x^12 + 2*x^8 + 3*x^6] d[y] + V(((2*x^245 + 2*x^241 + 2*x^237 + 4*x^235 + 2*x^233 + 4*x^227 + 4*x^225 + x^223 + 2*x^221 + 4*x^219 + 4*x^217 + 3*x^215 + x^211 + x^209 + 4*x^207 + 2*x^205 + 2*x^203 + 3*x^201 + 4*x^199 + 4*x^197 + 2*x^195 + 4*x^193 + 2*x^189 + x^185 + 4*x^183 + 3*x^181 + 4*x^179 + x^177 + 2*x^175 + 4*x^173 + x^163 + x^161 + 3*x^159 + 3*x^153 + 3*x^151 + 4*x^149 + 3*x^147 + 3*x^143 + 2*x^141 + 3*x^139 + 4*x^137 + 3*x^135 + 2*x^133 + 2*x^131 + 4*x^129 + 3*x^127 + 2*x^125 + 4*x^123 + 2*x^121 + 2*x^117 + 4*x^115 + 4*x^113 + x^111 + 4*x^107 + x^105 + 3*x^103 + 2*x^101 + 2*x^99 + 4*x^97 + 3*x^95 + 3*x^93 + 4*x^91 + 4*x^85 + 2*x^83 + 4*x^81 + 4*x^79 + 4*x^75 + 3*x^73 + 3*x^71 + 4*x^69 + 4*x^65 + 4*x^63 + 3*x^61 + x^59 + x^53 + x^51 + 3*x^49 + x^45 + 2*x^41 + 4*x^39 + 2*x^37 + 2*x^35 + x^33 + 4*x^29 + 4*x^27 + 2*x^25 + 3*x^23 + x^19 + x^17 + 4*x^11 + 3*x^9 + 4*x^7 + x^3)*y) dx + (3*x^250 + 3*x^240 + 3*x^236 + 2*x^234 + 2*x^232 + x^228 + x^226 + x^222 + 3*x^220 + 3*x^218 + x^216 + 2*x^214 + x^206 + 2*x^204 + 3*x^200 + 3*x^198 + x^196 + 4*x^194 + 3*x^192 + 3*x^188 + 2*x^186 + 4*x^184 + x^182 + 2*x^180 + x^174 + 4*x^172 + 4*x^170 + 2*x^168 + 3*x^166 + x^164 + x^160 + 2*x^158 + x^156 + 2*x^154 + 4*x^152 + 2*x^150 + 2*x^148 + 4*x^146 + x^144 + 2*x^142 + x^140 + 4*x^138 + 4*x^136 + 3*x^134 + x^132 + 3*x^128 + 2*x^124 + 3*x^122 + x^120 + x^114 + x^112 + 4*x^108 + x^106 + 4*x^104 + 4*x^102 + 3*x^100 + 4*x^94 + 4*x^92 + x^88 + 3*x^86 + x^84 + 2*x^82 + 2*x^80 + 2*x^78 + 2*x^76 + 3*x^74 + 4*x^72 + 3*x^70 + 2*x^66 + x^64 + 4*x^62 + 3*x^60 + 4*x^58 + 4*x^56 + 4*x^54 + x^52 + 3*x^50 + x^48 + x^46 + 2*x^42 + 2*x^40 + 3*x^38 + 4*x^36 + 3*x^34 + x^28 + x^24 + x^22 + 2*x^20 + x^18 + 2*x^16 + 3*x^14 + 2*x^12 + 4*x^10 + x^4 + 4*x^2) dy) + dV(0), V(((2*x^112 + 4*x^108 + x^106 + 3*x^104 + 4*x^100 + 2*x^98 + 4*x^96 + 2*x^92 + x^90 + 3*x^88 + x^86 + 3*x^84 + x^82 + 3*x^80 + 2*x^78 + 3*x^76 + x^74 + 4*x^70 + 3*x^68 + x^66 + 2*x^64 + x^62 + 3*x^60 + 2*x^58 + 4*x^52 + x^50 + 2*x^48 + 4*x^46 + x^44 + x^42 + 4*x^40 + 2*x^38 + 4*x^36 + 3*x^32 + 3*x^28 + 4*x^26 + 3*x^24 + 3*x^20 + 2*x^18 + 3*x^16 + 4*x^14 + 3*x^8 + 3*x^6 + 4*x^2 + 3)/x^6)*y) )
( [(4*x^18 + x^10 + 4*x^8 + 2*x^6 + x^4 + 3*x^2)*y] d[x] + [x^23 + 4*x^19 + 4*x^15 + 4*x^11 + 2*x^9 + 4*x^7 + x^5 + 2*x^3 + 2*x] d[y] + V(((x^280 + x^276 + x^272 + 3*x^270 + x^268 + x^266 + 3*x^262 + x^260 + 4*x^258 + 3*x^256 + 2*x^254 + x^252 + 3*x^250 + 2*x^246 + x^242 + 4*x^236 + 4*x^234 + 4*x^232 + x^230 + 2*x^228 + 3*x^226 + 2*x^222 + 3*x^220 + x^218 + x^216 + x^214 + 3*x^212 + 4*x^210 + x^208 + x^206 + 4*x^202 + x^196 + x^194 + x^192 + 3*x^190 + 2*x^188 + x^186 + 2*x^184 + x^180 + 2*x^178 + 4*x^174 + 4*x^172 + 2*x^170 + 2*x^168 + 2*x^166 + x^164 + 2*x^162 + 3*x^160 + x^158 + x^156 + x^150 + 3*x^148 + 4*x^144 + x^142 + x^138 + 4*x^136 + 4*x^132 + 4*x^130 + 2*x^128 + x^126 + x^124 + x^122 + 3*x^120 + 3*x^118 + x^116 + 2*x^112 + 3*x^110 + x^108 + 2*x^106 + 4*x^104 + 2*x^102 + 3*x^100 + 4*x^98 + 4*x^96 + 2*x^92 + x^88 + 3*x^86 + 2*x^84 + x^82 + x^80 + 4*x^78 + 3*x^74 + 3*x^70 + 3*x^68 + 2*x^66 + 4*x^64 + 3*x^62 + 4*x^60 + 4*x^58 + x^56 + 3*x^54 + x^48 + 3*x^46 + 2*x^44 + 4*x^42 + 3*x^40 + 4*x^38 + x^36 + 4*x^34 + 3*x^32 + 2*x^30 + 2*x^28 + 2*x^26 + 3*x^22 + 3*x^18 + 4*x^16 + 3*x^14 + 4*x^12 + x^8)*y) dx + (4*x^285 + 3*x^275 + 4*x^271 + x^269 + x^267 + 2*x^265 + 3*x^263 + 2*x^261 + x^259 + 4*x^257 + 4*x^255 + 2*x^253 + 4*x^251 + 3*x^249 + x^245 + 4*x^241 + 4*x^237 + 2*x^235 + x^233 + x^231 + 3*x^227 + x^225 + 4*x^221 + 4*x^219 + 2*x^217 + 4*x^215 + 2*x^213 + x^211 + 2*x^209 + 3*x^207 + x^203 + x^199 + 4*x^193 + x^189 + 4*x^183 + x^181 + x^179 + x^177 + x^175 + 4*x^173 + 4*x^171 + 2*x^169 + 3*x^167 + x^165 + x^163 + 2*x^161 + 2*x^159 + 3*x^157 + 3*x^155 + x^151 + 2*x^149 + 4*x^147 + 3*x^145 + 3*x^143 + 3*x^139 + 3*x^135 + 3*x^133 + 4*x^131 + 2*x^129 + 3*x^125 + 3*x^121 + x^119 + x^117 + 3*x^115 + x^113 + 3*x^111 + 2*x^109 + 4*x^107 + 4*x^105 + 3*x^103 + 4*x^101 + 3*x^99 + 4*x^97 + 2*x^95 + 2*x^93 + 3*x^91 + 2*x^85 + x^83 + 2*x^79 + 2*x^75 + x^73 + 3*x^71 + x^69 + x^67 + 4*x^63 + x^57 + x^55 + 3*x^53 + x^51 + x^49 + 3*x^47 + x^45 + 2*x^41 + 2*x^39 + 2*x^37 + 2*x^35 + 4*x^33 + x^31 + 4*x^29 + 3*x^27 + 4*x^25 + x^23 + 2*x^21 + x^19 + 4*x^17 + 4*x^15 + x^9 + 4*x^7) dy) + dV(0), [2/x*y] + V(((x^146 + 2*x^142 + 3*x^140 + 4*x^138 + 2*x^134 + x^132 + 2*x^130 + 2*x^126 + 3*x^124 + x^122 + x^120 + 3*x^118 + 3*x^116 + x^114 + 2*x^112 + x^110 + 3*x^108 + x^106 + 3*x^102 + x^100 + 2*x^96 + 3*x^94 + 4*x^92 + 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + x^80 + x^78 + 2*x^76 + 4*x^72 + x^70 + 4*x^68 + 2*x^66 + x^64 + 3*x^62 + 2*x^60 + 2*x^58 + 2*x^56 + 4*x^52 + x^50 + 2*x^48 + 2*x^46 + x^42 + 2*x^38 + 3*x^36 + 3*x^34 + 2*x^32 + 4*x^30 + 3*x^28 + x^26 + x^24 + 3*x^18 + 4*x^14 + x^12 + 4*x^10 + 2*x^8 + 3*x^6 + 4*x^4 + 3*x^2 + 1)/x^5)*y) )
( [(3*x^17 + 4*x^13 + 3*x^7 + x^5 + 2*x^3 + 2*x)*y] d[x] + [2*x^22 + 4*x^18 + 4*x^14 + 4*x^10 + 3*x^8 + 4*x^6 + 4*x^4 + 3] d[y] + V(((2*x^275 + 2*x^271 + 2*x^267 + 2*x^263 + x^261 + 4*x^255 + 2*x^253 + 4*x^249 + 4*x^247 + 2*x^245 + x^243 + 3*x^241 + 3*x^239 + 3*x^237 + x^235 + 2*x^233 + x^231 + 3*x^229 + x^227 + 2*x^225 + x^215 + x^213 + x^211 + 3*x^209 + x^207 + 2*x^205 + 2*x^203 + x^201 + 4*x^197 + 3*x^195 + 2*x^193 + 2*x^191 + 4*x^189 + x^187 + 4*x^185 + 4*x^183 + 3*x^181 + 4*x^179 + x^177 + 3*x^175 + x^173 + 3*x^171 + x^169 + 3*x^167 + x^165 + x^163 + 3*x^161 + 4*x^159 + 4*x^157 + 4*x^153 + 2*x^151 + 3*x^149 + 3*x^143 + 2*x^139 + 4*x^135 + 3*x^133 + 2*x^131 + 3*x^129 + 3*x^127 + x^123 + 4*x^121 + 2*x^119 + 4*x^117 + 2*x^115 + 4*x^111 + 4*x^109 + 4*x^107 + 4*x^105 + 3*x^103 + x^101 + 2*x^99 + 4*x^97 + 2*x^95 + 3*x^89 + x^87 + 2*x^85 + 4*x^79 + 2*x^77 + 4*x^75 + 2*x^73 + 4*x^71 + x^67 + 4*x^65 + x^61 + 4*x^59 + x^57 + 3*x^53 + 4*x^49 + 2*x^45 + 2*x^43 + 4*x^39 + 4*x^37 + 3*x^31 + 2*x^29 + 4*x^27 + 4*x^25 + 3*x^23 + 2*x^21 + x^19 + 4*x^17 + 3*x^13 + 3*x^11 + x^9 + 3*x^7 + 2*x^3)*y) dx + (3*x^280 + 2*x^270 + 3*x^266 + 2*x^264 + 2*x^262 + x^260 + x^258 + x^254 + 2*x^252 + 4*x^250 + x^248 + x^246 + x^242 + x^240 + 3*x^238 + 2*x^236 + 4*x^234 + 2*x^230 + 3*x^228 + 4*x^226 + 3*x^222 + x^220 + 2*x^218 + 2*x^216 + x^214 + 2*x^212 + 2*x^208 + x^206 + 3*x^204 + 3*x^202 + x^194 + 4*x^192 + x^190 + 2*x^188 + 4*x^186 + 4*x^184 + x^182 + 4*x^180 + 3*x^178 + x^176 + 2*x^174 + 2*x^172 + x^166 + x^164 + 4*x^160 + 2*x^158 + x^156 + 2*x^154 + 4*x^152 + 4*x^150 + 3*x^148 + 3*x^146 + 3*x^142 + 2*x^140 + 3*x^138 + x^136 + 3*x^134 + 3*x^132 + 4*x^128 + 4*x^124 + 2*x^122 + 2*x^118 + 2*x^116 + x^114 + 3*x^112 + 2*x^110 + 4*x^108 + 4*x^106 + 3*x^104 + 2*x^102 + x^100 + 2*x^98 + 4*x^96 + 2*x^94 + 3*x^90 + 2*x^88 + 4*x^86 + x^82 + x^80 + 3*x^78 + x^76 + 4*x^74 + x^72 + 2*x^70 + x^68 + 3*x^66 + x^64 + x^62 + 3*x^60 + 4*x^58 + 4*x^54 + x^52 + 2*x^50 + 2*x^48 + 2*x^46 + x^44 + x^42 + 4*x^40 + x^38 + 2*x^36 + 4*x^34 + 3*x^32 + 4*x^30 + x^26 + 3*x^24 + x^22 + x^20 + 2*x^18 + 4*x^16 + 4*x^14 + x^12 + 3*x^10 + 2*x^4 + 3*x^2) dy) + dV(0), [2/x^2*y] + V(((2*x^142 + 4*x^138 + x^136 + 3*x^134 + 4*x^130 + 2*x^128 + 4*x^126 + x^120 + 4*x^118 + x^112 + 4*x^110 + 4*x^106 + x^104 + x^102 + 3*x^100 + x^98 + 4*x^96 + x^94 + 2*x^92 + x^90 + 2*x^88 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + 2*x^76 + 4*x^74 + x^72 + 3*x^70 + 3*x^68 + x^66 + 2*x^64 + 2*x^62 + 4*x^60 + 3*x^58 + 3*x^56 + 4*x^54 + 4*x^52 + 3*x^50 + 3*x^48 + 3*x^46 + 2*x^44 + 4*x^42 + x^40 + 3*x^38 + x^36 + 3*x^34 + 3*x^32 + 4*x^28 + 3*x^26 + 3*x^24 + 3*x^22 + x^18 + 3*x^16 + 4*x^14 + 4*x^6 + 3*x^4 + 4)/x^6)*y) )
( [(2*x^16 + 3*x^12 + 4*x^8 + 2*x^6 + x^4 + 3*x^2)*y] d[x] + [3*x^21 + 4*x^17 + 4*x^13 + 3*x^9 + 4*x^7 + x^5 + 2*x^3 + 2*x] d[y] + V(((3*x^270 + 3*x^266 + 3*x^262 + x^260 + 3*x^258 + x^252 + x^250 + 4*x^248 + 3*x^246 + x^244 + x^242 + x^240 + 3*x^236 + 4*x^234 + 4*x^230 + 2*x^228 + x^224 + 2*x^222 + 3*x^220 + x^218 + x^214 + x^208 + 4*x^206 + 4*x^204 + 2*x^202 + 3*x^200 + 4*x^196 + 4*x^194 + 3*x^192 + x^190 + 4*x^188 + x^186 + 4*x^184 + 3*x^182 + 4*x^180 + x^178 + x^174 + 4*x^170 + 4*x^168 + 2*x^164 + x^162 + 4*x^160 + 2*x^156 + 2*x^152 + 3*x^150 + 4*x^148 + 2*x^142 + x^138 + 2*x^136 + 3*x^134 + x^132 + 4*x^130 + 2*x^128 + 2*x^124 + 3*x^122 + 3*x^120 + 3*x^118 + 3*x^116 + 3*x^114 + 2*x^112 + 4*x^106 + 4*x^104 + 3*x^102 + 2*x^96 + x^94 + 3*x^92 + 3*x^90 + 3*x^86 + 4*x^84 + 3*x^82 + 3*x^80 + 3*x^76 + 4*x^74 + 2*x^72 + 2*x^70 + 2*x^68 + x^66 + 4*x^64 + 4*x^62 + x^60 + 3*x^58 + x^56 + 3*x^54 + x^50 + 4*x^44 + 4*x^42 + 3*x^40 + 2*x^38 + 3*x^36 + 3*x^34 + 2*x^30 + 2*x^26 + 3*x^22 + 3*x^18 + 4*x^16 + 3*x^14 + 4*x^12 + x^8)*y) dx + (2*x^275 + 2*x^265 + 2*x^261 + 3*x^259 + 3*x^257 + 4*x^253 + 4*x^251 + 4*x^247 + 3*x^245 + 2*x^243 + 4*x^241 + 3*x^239 + 3*x^235 + 2*x^229 + 4*x^227 + 3*x^225 + 4*x^223 + 3*x^221 + 4*x^219 + 2*x^217 + 3*x^215 + 2*x^213 + 3*x^211 + x^209 + 4*x^207 + 2*x^201 + 3*x^199 + x^197 + 3*x^195 + 4*x^193 + 4*x^191 + 4*x^189 + 3*x^183 + 4*x^177 + x^175 + x^173 + 3*x^171 + 3*x^169 + 3*x^167 + 3*x^165 + 4*x^163 + 2*x^161 + x^157 + x^155 + 4*x^153 + 4*x^151 + x^147 + 4*x^145 + 3*x^143 + 2*x^141 + 2*x^137 + x^135 + x^133 + 3*x^131 + 2*x^127 + 3*x^125 + 2*x^123 + 4*x^121 + 4*x^119 + 3*x^117 + 2*x^113 + x^111 + 4*x^109 + 3*x^107 + 2*x^105 + 4*x^97 + 4*x^95 + 3*x^93 + 3*x^91 + 2*x^89 + x^87 + 4*x^83 + 2*x^81 + x^79 + x^77 + 2*x^71 + 2*x^69 + 4*x^65 + x^63 + 2*x^61 + 4*x^59 + 2*x^57 + 2*x^55 + 4*x^53 + 2*x^51 + 3*x^49 + 2*x^47 + 4*x^45 + 3*x^43 + 3*x^41 + 4*x^39 + 4*x^35 + 4*x^33 + x^31 + 2*x^29 + 4*x^25 + x^23 + 2*x^21 + x^19 + 4*x^17 + 4*x^15 + x^9 + 4*x^7) dy) + dV(0), [2/x^3*y] + V(((3*x^138 + x^134 + 4*x^132 + 2*x^130 + x^126 + 3*x^124 + x^122 + 3*x^118 + 4*x^116 + 2*x^114 + 4*x^112 + 2*x^110 + 4*x^108 + 2*x^106 + 3*x^104 + 2*x^102 + 4*x^100 + x^98 + x^96 + 4*x^94 + 2*x^92 + 2*x^90 + 2*x^88 + 4*x^86 + x^82 + 2*x^80 + 2*x^78 + 3*x^76 + 3*x^70 + 4*x^66 + x^64 + 4*x^62 + x^58 + 4*x^56 + 4*x^54 + x^52 + 2*x^50 + 3*x^48 + 2*x^46 + x^44 + x^42 + 4*x^40 + x^38 + x^34 + 4*x^32 + 3*x^30 + 3*x^26 + 2*x^22 + 3*x^20 + 3*x^18 + x^16 + x^14 + 4*x^12 + 2*x^10 + 2*x^8 + 4*x^6 + 3*x^4 + 2*x^2 + 4)/x^7)*y) )
( [(x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x)*y] d[x] + [4*x^20 + 4*x^16 + 4*x^12 + 4*x^8 + 4*x^4 + 1] d[y] + V(((4*x^265 + 4*x^261 + 4*x^257 + x^255 + 4*x^253 + 3*x^251 + x^247 + 2*x^245 + 2*x^241 + 3*x^239 + 2*x^237 + 3*x^235 + 2*x^233 + 3*x^229 + 3*x^223 + x^221 + 3*x^219 + 3*x^217 + x^215 + 4*x^213 + 2*x^211 + 4*x^209 + 4*x^207 + 2*x^205 + 2*x^203 + 2*x^201 + 3*x^199 + 2*x^197 + 3*x^195 + 4*x^193 + 3*x^191 + x^185 + x^183 + 3*x^181 + 3*x^179 + 4*x^177 + x^175 + 4*x^173 + x^165 + 2*x^163 + 3*x^161 + 2*x^159 + 4*x^157 + x^153 + x^151 + 4*x^149 + 4*x^147 + x^145 + 2*x^143 + 3*x^141 + 2*x^139 + 4*x^137 + 4*x^133 + 2*x^131 + 4*x^129 + 3*x^127 + 4*x^123 + 2*x^121 + 3*x^119 + 3*x^117 + x^115 + x^113 + 4*x^111 + 4*x^103 + 4*x^101 + x^99 + 2*x^97 + x^95 + 3*x^93 + x^91 + x^89 + 3*x^87 + 3*x^85 + 2*x^81 + 2*x^77 + 3*x^75 + 3*x^73 + 3*x^71 + 3*x^67 + 2*x^65 + 3*x^61 + 2*x^59 + 3*x^57 + 2*x^55 + 4*x^53 + x^51 + 3*x^47 + 3*x^45 + 2*x^43 + 2*x^41 + 2*x^39 + 3*x^35 + x^31 + 4*x^27 + x^25 + 3*x^23 + 4*x^21 + x^19 + 2*x^17 + x^13 + 2*x^11 + 4*x^9 + 2*x^7 + 3*x^3)*y) dx + (x^270 + 3*x^260 + x^256 + 4*x^254 + 4*x^252 + 4*x^250 + 2*x^248 + 4*x^246 + 3*x^244 + 3*x^240 + 3*x^236 + 2*x^234 + 2*x^232 + 4*x^230 + x^228 + 2*x^224 + 4*x^222 + 4*x^220 + 3*x^218 + 2*x^216 + 2*x^214 + 4*x^212 + 2*x^208 + 3*x^204 + 4*x^202 + x^200 + 4*x^198 + 3*x^196 + 3*x^194 + 3*x^192 + x^190 + 3*x^188 + 3*x^186 + 2*x^184 + 4*x^182 + 2*x^180 + x^178 + 4*x^176 + 3*x^174 + 2*x^172 + 4*x^170 + 4*x^168 + 3*x^166 + x^164 + 4*x^162 + 4*x^160 + 4*x^156 + x^154 + x^152 + 2*x^150 + 2*x^148 + 3*x^146 + 4*x^144 + 3*x^142 + 2*x^140 + x^138 + x^136 + 3*x^134 + x^132 + 2*x^130 + 3*x^126 + x^124 + 2*x^122 + 2*x^120 + 4*x^118 + 4*x^116 + x^114 + 4*x^112 + x^110 + 2*x^108 + x^106 + 4*x^104 + 2*x^102 + x^100 + 3*x^98 + 2*x^94 + 4*x^90 + 3*x^88 + 3*x^86 + x^84 + x^80 + 4*x^78 + x^76 + 3*x^74 + 3*x^72 + x^70 + 4*x^68 + 4*x^64 + 4*x^62 + 3*x^60 + 3*x^58 + 2*x^56 + 2*x^52 + 4*x^48 + 3*x^44 + 4*x^42 + 4*x^38 + x^34 + 3*x^30 + 4*x^28 + 2*x^26 + x^22 + 3*x^18 + x^16 + 2*x^10 + 3*x^4 + 2*x^2) dy) + dV(0), [2/x^4*y] + V(((4*x^132 + 3*x^128 + 2*x^126 + x^124 + 3*x^120 + 4*x^118 + 3*x^116 + x^112 + 2*x^110 + 3*x^106 + 4*x^104 + 2*x^102 + x^98 + 2*x^94 + x^92 + 4*x^90 + 2*x^88 + 3*x^84 + 2*x^82 + 2*x^80 + 3*x^78 + 3*x^76 + 2*x^74 + 2*x^72 + x^70 + 2*x^68 + 4*x^66 + 4*x^62 + 4*x^60 + x^58 + x^56 + 3*x^54 + 2*x^52 + 3*x^48 + 3*x^44 + 3*x^42 + 4*x^40 + x^38 + 2*x^36 + 2*x^34 + 3*x^32 + 3*x^30 + 2*x^28 + 3*x^26 + 3*x^22 + 4*x^20 + 3*x^18 + x^16 + 3*x^14 + 2*x^12 + 3*x^10 + 3*x^8 + 4*x^6 + x^4 + 2)/x^6)*y) )
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [2], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:32, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:28, in <module>
 
File <string>:92, in regular_drw_cech(cocycle)
 
File <string>:81, in regular_drw_form(omega)
 
File <string>:73, in diffn(self, dy_w)
 
File <string>:177, in dy_w(C)
 
File <string>:149, in auxilliary_derivative(P)
 
File <string>:55, in __rmul__(self, other)
 
File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
1962 return y
1963
-> 1964 return coercion_model.bin_op(left, right, operator.mul)
1965
1966 cpdef _mul_(self, right):
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:55, in __rmul__(self, other)
 
File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
1962 return y
1963
-> 1964 return coercion_model.bin_op(left, right, operator.mul)
1965
1966 cpdef _mul_(self, right):
 
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:55, in __rmul__(self, other)
 
File <string>:84, in __add__(self, other)
 
File <string>:65, in __mul__(self, other)
 
File <string>:95, in diffn(self)
 
File <string>:7, in __init__(self, C, g)
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
636 ring_one = self.ring().one()
637 try:
--> 638 return self._element_class(self, x, ring_one, coerce=coerce)
639 except (TypeError, ValueError):
640 pass
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
112 FieldElement.__init__(self, parent)
113 if coerce:
--> 114 self.__numerator = parent.ring()(numerator)
115 self.__denominator = parent.ring()(denominator)
116 else:
 
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
895 if mor is not None:
896 if no_extra_args:
--> 897 return mor._call_(x)
898 else:
899 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
1001
1002 try:
-> 1003 return self(str(element))
1004 except TypeError:
1005 pass
 
File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
192 except AttributeError:
193 return super().__repr__()
--> 194 result = reprfunc()
195 if isinstance(result, str):
196 return result
 
File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:482, in sage.rings.fraction_field_element.FractionFieldElement._repr_()
480 if self.is_zero():
481 return "0"
--> 482 s = "%s" % self.__numerator
483 if self.__denominator != 1:
484 denom_string = str( self.__denominator )
 
File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
192 except AttributeError:
193 return super().__repr__()
--> 194 result = reprfunc()
195 if isinstance(result, str):
196 return result
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_()
2688 NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3
2689 """
-> 2690 return self._repr()
2691
2692 def _latex_(self, name=None):
 
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2656, in sage.rings.polynomial.polynomial_element.Polynomial._repr()
2654 if n != m-1:
2655 s += " + "
-> 2656 x = y = repr(x)
2657 if y.find("-") == 0:
2658 y = y[1:]
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
[6nsage: load('init.sage')
Traceback (most recent call last):
 
File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
exec(code_obj, self.user_global_ns, self.user_ns)
 
Input In [3] in <cell line: 1>
load('init.sage')
 
File sage/misc/persist.pyx:175 in sage.misc.persist.load
sage.repl.load.load(filename, globals())
 
File /ext/sage/9.7/src/sage/repl/load.py:272 in load
exec(preparse_file(f.read()) + "\n", globals)
 
File <string>:21 in <module>
 
File sage/misc/persist.pyx:175 in sage.misc.persist.load
sage.repl.load.load(filename, globals())
 
File /ext/sage/9.7/src/sage/repl/load.py:272 in load
exec(preparse_file(f.read()) + "\n", globals)
 
File <string>:40
C = omega.curve
^
IndentationError: unexpected indent
 
[6nsage: load('init.sage')
Computing 0. basis element
Computing 1. basis element
Computing 0. basis element
Computing 1. basis element
Computing 2. basis element
Computing 3. basis element
Computing 4. basis element
Computing 5. basis element
Computing 6. basis element
Computing 7. basis element
Computing 8. basis element
Computing 9. basis element
Computing 10. basis element
Computing 11. basis element
Computing 12. basis element
Computing 13. basis element
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [4], in <cell line: 1>()
----> 1 load('init.sage')
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:32, in <module>
 
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:25, in <module>
 
File <string>:92, in regular_drw_cech(cocycle)
 
File <string>:84, in regular_drw_form(omega)
 
File <string>:5, in decomposition_g0_pth_power(fct)
 
AttributeError: 'superelliptic_function' object has no attribute 'fucntion'
[6nsage: load('superelliptic_drw/superelliptic_drw_auxilliaries.sage')
sage: for b in B:
....: print(b.regular_form())
....:
( [3*x*y] d[x] + [3*x^2 + 2] d[y] + V(((3*x^19 + 2*x^17 + x^15 + x^13 + 3*x^9 + 4*x^7 + x^5 + x^3 + x)*y) dx + (3*x^20 + 4*x^18 + 4*x^16 + 4*x^12 + 3*x^10 + x^8 + 2*x^6 + 4) dy) + dV(0), V((4*x^14 + x^12 + 3*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 4)*y) )
( [3*x^2*y] d[x] + [3*x^3 + 2*x] d[y] + V(((3*x^24 + 4*x^22 + x^20 + 3*x^18 + 3*x^16 + 3*x^10 + 2*x^8 + 3*x^4 + 3*x^2)*y) dx + (3*x^25 + x^23 + 2*x^21 + 2*x^19 + 2*x^15 + 3*x^11 + 4*x^9 + 3*x^7 + 3*x^5 + 2*x) dy) + dV(0), [2/x*y] + V(((4*x^20 + x^18 + 3*x^16 + 3*x^14 + x^12 + x^10 + 3*x^8 + 4*x^6 + 4*x^4 + 3*x^2 + 4)/x)*y) )
sage: for b in B1:
....: print(b.regular_form())
....:
( [(3*x^5 + 2*x)*y] d[x] + [2*x^10 + x^6 + 2*x^2 + 3] d[y] + V(((x^99 + 2*x^91 + 3*x^89 + 3*x^87 + 2*x^85 + 2*x^83 + 2*x^79 + x^77 + 4*x^75 + x^73 + 2*x^71 + 2*x^69 + 3*x^67 + 3*x^65 + x^63 + 3*x^61 + x^55 + 2*x^53 + 4*x^51 + x^49 + 2*x^47 + 4*x^45 + 4*x^43 + 3*x^35 + 2*x^33 + 2*x^31 + 2*x^29 + 3*x^25 + x^23 + 3*x^21 + 3*x^19 + 3*x^15 + x^13 + 4*x^11 + 2*x^7 + 4*x^5 + x^3 + 3*x)*y) dx + (4*x^104 + x^100 + 3*x^96 + 3*x^94 + 4*x^92 + 2*x^90 + x^88 + 3*x^84 + 3*x^80 + 3*x^78 + 2*x^76 + 4*x^74 + 3*x^70 + 4*x^68 + x^66 + 2*x^62 + x^60 + 3*x^58 + 2*x^56 + x^54 + 2*x^52 + 3*x^50 + 4*x^46 + 2*x^44 + 2*x^42 + 4*x^40 + 4*x^38 + 3*x^36 + x^34 + 4*x^32 + 3*x^30 + 3*x^28 + x^26 + 4*x^24 + 4*x^22 + 4*x^20 + x^18 + x^16 + x^14 + 4*x^12 + 4*x^10 + 4*x^8 + 3*x^6 + 4*x^4 + 2*x^2 + 2) dy) + dV(0), V(((2*x^80 + 4*x^76 + x^74 + 3*x^72 + 4*x^68 + 2*x^66 + 4*x^64 + 2*x^60 + x^58 + 3*x^56 + x^54 + 3*x^52 + x^50 + 3*x^48 + 2*x^46 + 3*x^44 + x^42 + 4*x^38 + 3*x^36 + x^34 + 2*x^32 + x^30 + 3*x^28 + 2*x^26 + 4*x^20 + x^18 + 2*x^16 + 4*x^14 + x^12 + x^10 + 4*x^8 + 2*x^6 + 4*x^4 + 3)/x^4)*y) )
( [(3*x^6 + 2*x^2)*y] d[x] + [2*x^11 + x^7 + 2*x^3 + 3*x] d[y] + V(((x^104 + x^100 + x^94 + x^90 + x^88 + 4*x^86 + x^84 + x^82 + 4*x^80 + 4*x^78 + 4*x^76 + x^74 + 4*x^72 + 2*x^70 + 2*x^66 + 4*x^64 + 2*x^60 + 4*x^58 + 3*x^56 + 3*x^54 + 4*x^52 + 2*x^50 + 4*x^48 + x^44 + 2*x^42 + 3*x^40 + 3*x^38 + 3*x^36 + 4*x^34 + x^32 + 3*x^30 + 3*x^28 + 4*x^26 + 4*x^24 + 2*x^22 + 2*x^20 + 4*x^18 + x^16 + 2*x^14 + 4*x^12 + 4*x^10 + 4*x^8 + x^4 + 2*x^2)*y) dx + (4*x^109 + x^101 + 2*x^95 + 4*x^93 + 4*x^91 + x^89 + 4*x^85 + x^81 + 2*x^79 + 2*x^77 + 2*x^75 + 2*x^71 + 3*x^69 + 3*x^67 + x^65 + 2*x^63 + x^59 + 3*x^55 + 2*x^51 + x^49 + 2*x^47 + 3*x^45 + 2*x^43 + 3*x^39 + 4*x^37 + 3*x^35 + 3*x^33 + 4*x^31 + 3*x^29 + 3*x^27 + 4*x^25 + 2*x^23 + 2*x^21 + 3*x^15 + 2*x^13 + 2*x^9 + 3*x^7 + 4*x^5 + x^3 + 3*x) dy) + dV(0), V(((2*x^88 + 4*x^84 + x^82 + 3*x^80 + 4*x^76 + 2*x^74 + 4*x^72 + 2*x^68 + x^66 + 3*x^64 + x^62 + 3*x^60 + x^58 + 3*x^56 + 2*x^54 + 3*x^52 + x^50 + 4*x^46 + 3*x^44 + x^42 + 2*x^40 + x^38 + 3*x^36 + 2*x^34 + 4*x^28 + x^26 + 2*x^24 + 4*x^22 + x^20 + x^18 + 4*x^16 + 2*x^14 + 4*x^12 + 3*x^8 + 3*x^4 + 4*x^2 + 3)/x^7)*y) )
( [(3*x^7 + 2*x^3)*y] d[x] + [2*x^12 + x^8 + 2*x^4 + 3*x^2] d[y] + V(((x^109 + 2*x^105 + 3*x^101 + 4*x^99 + 2*x^97 + 3*x^91 + x^87 + 4*x^85 + 2*x^83 + x^81 + x^75 + 4*x^73 + x^71 + 3*x^69 + 3*x^65 + x^63 + 2*x^61 + x^57 + 4*x^53 + 2*x^49 + 4*x^47 + 3*x^45 + 4*x^43 + 4*x^41 + x^39 + 2*x^37 + 3*x^35 + 4*x^27 + x^25 + 2*x^23 + 3*x^21 + 4*x^19 + x^17 + 4*x^15 + 3*x^13 + x^11 + 2*x^7 + 2*x^5 + 3*x^3 + 4*x)*y) dx + (4*x^114 + 4*x^110 + 4*x^106 + 2*x^104 + x^102 + 2*x^100 + 2*x^98 + 3*x^96 + 4*x^94 + 2*x^88 + 4*x^82 + x^80 + x^78 + 3*x^76 + x^74 + 4*x^72 + x^70 + x^68 + 3*x^66 + x^64 + 3*x^62 + 3*x^60 + 2*x^52 + 2*x^50 + 2*x^46 + 4*x^42 + 3*x^40 + 3*x^38 + 2*x^36 + 2*x^34 + 2*x^32 + 4*x^30 + 3*x^28 + 3*x^26 + 4*x^24 + x^22 + 2*x^20 + 4*x^18 + 3*x^16 + 3*x^14 + 2*x^10 + 3*x^8 + 3*x^6 + 2*x^4 + x^2 + 1) dy) + dV(0), V(((2*x^92 + 4*x^88 + x^86 + 3*x^84 + 4*x^80 + 2*x^78 + 4*x^76 + 2*x^72 + x^70 + 3*x^68 + x^66 + 3*x^64 + x^62 + 3*x^60 + 2*x^58 + 3*x^56 + x^54 + 4*x^50 + 3*x^48 + x^46 + 2*x^44 + x^42 + 3*x^40 + 2*x^38 + 4*x^32 + x^30 + 2*x^28 + 4*x^26 + x^24 + x^22 + 4*x^20 + 2*x^18 + 4*x^16 + 3*x^12 + 3*x^8 + 4*x^6 + 3*x^4 + 3)/x^6)*y) )
( [(3*x^8 + 2*x^4)*y] d[x] + [2*x^13 + x^9 + 2*x^5 + 3*x^3] d[y] + V(((x^114 + 3*x^110 + x^106 + 2*x^104 + 4*x^102 + 4*x^100 + 4*x^98 + 2*x^96 + 4*x^94 + x^92 + 4*x^90 + 3*x^86 + 4*x^84 + x^82 + 3*x^78 + 2*x^74 + 4*x^70 + 3*x^68 + x^66 + 2*x^64 + 3*x^62 + 3*x^60 + 4*x^58 + 3*x^54 + x^52 + 3*x^50 + 3*x^44 + 3*x^42 + 3*x^40 + 2*x^38 + x^36 + x^34 + x^32 + x^24 + 3*x^22 + 4*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + 2*x^12 + 4*x^10 + x^8 + x^6 + 4*x^2)*y) dx + (4*x^119 + 3*x^115 + 2*x^111 + 4*x^109 + 2*x^107 + 2*x^105 + 2*x^101 + 2*x^99 + x^95 + 4*x^93 + 4*x^91 + 3*x^89 + x^87 + 2*x^83 + 4*x^81 + 4*x^79 + x^75 + x^71 + x^69 + x^67 + 3*x^65 + 3*x^61 + 4*x^59 + 2*x^57 + x^55 + 3*x^53 + 4*x^51 + 2*x^49 + 4*x^47 + 3*x^45 + 3*x^43 + x^39 + x^37 + 4*x^35 + 4*x^33 + 4*x^31 + 3*x^29 + 2*x^27 + x^25 + x^23 + x^21 + x^19 + 2*x^17 + 3*x^15 + 2*x^9 + x^7 + 4*x^3 + x) dy) + dV(0), V(((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 4)/x^7)*y) )
( [(3*x^9 + 2*x^5)*y] d[x] + [2*x^14 + x^10 + 2*x^6 + 3*x^4] d[y] + V(((x^119 + 4*x^115 + 4*x^111 + x^107 + 3*x^105 + 3*x^103 + x^101 + 3*x^99 + x^97 + 4*x^95 + 3*x^93 + 3*x^89 + 2*x^87 + 4*x^85 + 2*x^83 + 4*x^81 + x^79 + 4*x^69 + x^65 + 4*x^63 + 4*x^59 + 3*x^57 + 3*x^55 + x^53 + x^51 + 4*x^47 + 3*x^45 + 4*x^43 + 2*x^41 + 2*x^39 + 3*x^37 + 4*x^35 + 3*x^33 + 2*x^31 + 3*x^29 + 4*x^25 + x^23 + 3*x^21 + 4*x^19 + 2*x^17 + x^15 + x^13 + 2*x^9 + x^7 + 2*x^5 + 4*x)*y) dx + (4*x^124 + 2*x^120 + x^114 + 3*x^112 + 2*x^110 + 3*x^108 + x^106 + 2*x^100 + x^98 + 3*x^96 + x^94 + 3*x^92 + 4*x^90 + 3*x^88 + 2*x^84 + x^82 + x^80 + 4*x^78 + 4*x^76 + x^74 + 4*x^72 + 3*x^70 + x^66 + 3*x^64 + 2*x^62 + x^58 + x^56 + 4*x^54 + 4*x^52 + 3*x^50 + 3*x^48 + 3*x^46 + 4*x^40 + 2*x^34 + 3*x^32 + 3*x^28 + 4*x^26 + 4*x^24 + 4*x^22 + 4*x^20 + 2*x^14 + 4*x^10 + 3*x^8 + 2*x^6 + 4*x^4 + 4*x^2 + 1) dy) + dV(0), V(((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 4)/x^2)*y) )
( [(3*x^10 + 2*x^6)*y] d[x] + [2*x^15 + x^11 + 2*x^7 + 3*x^5] d[y] + V(((x^124 + 2*x^116 + 3*x^114 + 3*x^112 + 2*x^110 + 2*x^108 + 2*x^104 + x^102 + 4*x^100 + x^98 + 2*x^96 + 2*x^94 + 3*x^92 + 3*x^90 + x^88 + 3*x^86 + x^80 + 2*x^78 + 4*x^76 + x^74 + 2*x^72 + 4*x^70 + 4*x^68 + 3*x^60 + 2*x^58 + 2*x^56 + 2*x^54 + 3*x^50 + x^48 + 3*x^46 + 3*x^44 + 3*x^40 + x^38 + 4*x^36 + 2*x^32 + 4*x^30 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + x^18 + 4*x^16 + 4*x^14 + 3*x^12 + 2*x^10 + 2*x^8 + 2*x^6 + 3*x^4 + 3*x^2)*y) dx + (4*x^129 + x^125 + 3*x^121 + 3*x^119 + 4*x^117 + 2*x^115 + x^113 + 3*x^109 + 3*x^105 + 3*x^103 + 2*x^101 + 4*x^99 + 3*x^95 + 4*x^93 + x^91 + 2*x^87 + x^85 + 3*x^83 + 2*x^81 + x^79 + 2*x^77 + 3*x^75 + 4*x^71 + 2*x^69 + 2*x^67 + 4*x^65 + 4*x^63 + 3*x^61 + x^59 + 4*x^57 + 3*x^55 + 3*x^53 + x^51 + 4*x^49 + 4*x^47 + 4*x^45 + x^43 + x^41 + x^39 + 4*x^37 + 4*x^35 + 2*x^31 + 2*x^29 + x^27 + 2*x^19 + 4*x^17 + 2*x^11 + 2*x^9 + 4*x^7 + 3*x^5 + 2*x) dy) + dV(0), V(((2*x^106 + 4*x^102 + x^100 + 3*x^98 + 4*x^94 + 2*x^92 + 4*x^90 + 2*x^86 + x^84 + 3*x^82 + x^80 + 3*x^78 + x^76 + 3*x^74 + 2*x^72 + 3*x^70 + x^68 + 4*x^64 + 3*x^62 + x^60 + 2*x^58 + x^56 + 3*x^54 + 2*x^52 + 4*x^46 + x^44 + 2*x^42 + 4*x^40 + x^38 + x^36 + 4*x^34 + 2*x^32 + 4*x^30 + 3*x^26 + 3*x^22 + 4*x^20 + 3*x^18 + 3*x^14 + 2*x^12 + 3*x^10 + 4*x^8 + 3*x^2 + 3)/x^5)*y) )
( [(3*x^11 + 2*x^7)*y] d[x] + [2*x^16 + x^12 + 2*x^8 + 3*x^6] d[y] + V(((x^129 + x^125 + x^119 + x^115 + x^113 + 4*x^111 + x^109 + x^107 + 4*x^105 + 4*x^103 + 4*x^101 + x^99 + 4*x^97 + 2*x^95 + 2*x^91 + 4*x^89 + 2*x^85 + 4*x^83 + 3*x^81 + 3*x^79 + 4*x^77 + 2*x^75 + 4*x^73 + x^69 + 2*x^67 + 3*x^65 + 3*x^63 + 3*x^61 + 4*x^59 + x^57 + 3*x^55 + 3*x^53 + 4*x^51 + 4*x^49 + 2*x^47 + 2*x^45 + 4*x^43 + x^41 + 2*x^39 + 4*x^37 + 4*x^35 + 4*x^33 + 3*x^29 + 2*x^27 + x^23 + 3*x^21 + x^19 + 2*x^15 + x^13 + x^9 + x^7 + 3*x)*y) dx + (4*x^134 + x^126 + 2*x^120 + 4*x^118 + 4*x^116 + x^114 + 4*x^110 + x^106 + 2*x^104 + 2*x^102 + 2*x^100 + 2*x^96 + 3*x^94 + 3*x^92 + x^90 + 2*x^88 + x^84 + 3*x^80 + 2*x^76 + x^74 + 2*x^72 + 3*x^70 + 2*x^68 + 3*x^64 + 4*x^62 + 3*x^60 + 3*x^58 + 4*x^56 + 3*x^54 + 3*x^52 + 4*x^50 + 2*x^48 + 2*x^46 + 3*x^40 + 2*x^38 + 3*x^32 + x^30 + 2*x^24 + 3*x^22 + x^20 + 2*x^16 + 2*x^14 + 4*x^12 + 2*x^8 + x^6 + 2*x^4 + 3*x^2 + 2) dy) + dV(0), V(((2*x^112 + 4*x^108 + x^106 + 3*x^104 + 4*x^100 + 2*x^98 + 4*x^96 + 2*x^92 + x^90 + 3*x^88 + x^86 + 3*x^84 + x^82 + 3*x^80 + 2*x^78 + 3*x^76 + x^74 + 4*x^70 + 3*x^68 + x^66 + 2*x^64 + x^62 + 3*x^60 + 2*x^58 + 4*x^52 + x^50 + 2*x^48 + 4*x^46 + x^44 + x^42 + 4*x^40 + 2*x^38 + 4*x^36 + 3*x^32 + 3*x^28 + 4*x^26 + 3*x^24 + 3*x^20 + 2*x^18 + 3*x^16 + 4*x^14 + 3*x^8 + 3*x^6 + 4*x^2 + 3)/x^6)*y) )
( [(4*x^18 + x^10 + 4*x^8 + 2*x^6 + x^4 + 3*x^2)*y] d[x] + [x^23 + 4*x^19 + 4*x^15 + 4*x^11 + 2*x^9 + 4*x^7 + x^5 + 2*x^3 + 2*x] d[y] + V(((3*x^164 + 4*x^160 + x^156 + x^154 + 3*x^152 + x^150 + 4*x^148 + x^146 + 2*x^144 + 3*x^140 + 2*x^138 + x^134 + 2*x^132 + 2*x^130 + 2*x^128 + 2*x^126 + 4*x^124 + 4*x^122 + 2*x^120 + 3*x^118 + 4*x^116 + 4*x^114 + 2*x^110 + x^108 + 4*x^106 + 2*x^100 + 2*x^98 + 2*x^96 + x^94 + 3*x^92 + 2*x^90 + 4*x^88 + x^86 + 4*x^84 + 2*x^82 + 4*x^80 + 2*x^78 + 3*x^72 + x^70 + x^68 + x^64 + x^60 + x^58 + 2*x^56 + 2*x^54 + 3*x^52 + 3*x^50 + x^48 + 3*x^46 + 3*x^44 + x^40 + 4*x^36 + 3*x^34 + 3*x^32 + 3*x^30 + x^28 + 4*x^26 + 2*x^24 + 3*x^22 + 2*x^20 + x^18 + 4*x^16 + 2*x^12 + 2*x^10 + x^6 + 2*x^4 + x^2)*y) dx + (2*x^169 + 4*x^165 + 3*x^161 + 2*x^159 + 3*x^157 + 2*x^155 + 4*x^153 + 3*x^151 + 3*x^149 + 2*x^147 + x^145 + 3*x^143 + x^141 + 3*x^139 + x^137 + 4*x^135 + 4*x^129 + 3*x^121 + 2*x^119 + 3*x^117 + 2*x^115 + x^113 + 2*x^111 + 2*x^109 + 3*x^107 + x^105 + 3*x^103 + 2*x^101 + x^99 + x^97 + x^95 + 3*x^93 + x^87 + 2*x^85 + x^83 + 2*x^81 + 2*x^79 + 2*x^77 + 3*x^75 + 4*x^73 + 2*x^69 + 2*x^67 + 3*x^65 + 2*x^63 + 2*x^61 + 3*x^59 + 2*x^57 + 4*x^55 + x^53 + 2*x^51 + 4*x^49 + 3*x^47 + x^45 + x^43 + 4*x^41 + x^39 + 3*x^37 + 4*x^33 + 3*x^31 + 4*x^29 + 3*x^27 + 3*x^25 + x^19 + 2*x^17 + 3*x^13 + 2*x^11 + 4*x^9 + 3*x^7 + 4*x^3 + 4*x) dy) + dV(0), [2/x*y] + V(((x^146 + 2*x^142 + 3*x^140 + 4*x^138 + 2*x^134 + x^132 + 2*x^130 + 2*x^126 + 3*x^124 + x^122 + x^120 + 3*x^118 + 3*x^116 + x^114 + 2*x^112 + x^110 + 3*x^108 + x^106 + 3*x^102 + x^100 + 2*x^96 + 3*x^94 + 4*x^92 + 2*x^90 + 2*x^88 + 2*x^84 + 2*x^82 + x^80 + x^78 + 2*x^76 + 4*x^72 + x^70 + 4*x^68 + 2*x^66 + x^64 + 3*x^62 + 2*x^60 + 2*x^58 + 2*x^56 + 4*x^52 + x^50 + 2*x^48 + 2*x^46 + x^42 + 2*x^38 + 3*x^36 + 3*x^34 + 2*x^32 + 4*x^30 + 3*x^28 + x^26 + x^24 + 3*x^18 + 4*x^14 + x^12 + 4*x^10 + 2*x^8 + 3*x^6 + 4*x^4 + 3*x^2 + 1)/x^5)*y) )
( [(3*x^17 + 4*x^13 + 3*x^7 + x^5 + 2*x^3 + 2*x)*y] d[x] + [2*x^22 + 4*x^18 + 4*x^14 + 4*x^10 + 3*x^8 + 4*x^6 + 4*x^4 + 3] d[y] + V(((x^159 + 2*x^155 + 2*x^151 + 4*x^149 + x^147 + 2*x^145 + 3*x^143 + x^141 + 3*x^139 + 4*x^137 + 2*x^135 + 2*x^133 + x^131 + x^129 + 4*x^127 + x^125 + 3*x^123 + 2*x^121 + 3*x^119 + 3*x^115 + 2*x^111 + 3*x^107 + 4*x^103 + 2*x^101 + 2*x^99 + 3*x^97 + 4*x^95 + 3*x^93 + 4*x^91 + x^89 + 4*x^87 + 4*x^85 + x^83 + 2*x^77 + 2*x^69 + 3*x^67 + 3*x^63 + 4*x^61 + 4*x^59 + x^55 + 3*x^53 + x^51 + 4*x^47 + 3*x^45 + 4*x^43 + 3*x^41 + 2*x^39 + x^37 + 2*x^33 + 2*x^31 + x^29 + 4*x^27 + x^25 + 2*x^23 + x^19 + 4*x^17 + x^15 + x^13 + 4*x^11 + 4*x^7 + x^5 + 3*x^3 + 2*x)*y) dx + (4*x^164 + 4*x^160 + 2*x^154 + x^152 + 3*x^148 + x^146 + 4*x^144 + 3*x^142 + 2*x^140 + x^138 + 3*x^136 + 3*x^134 + 3*x^132 + 4*x^130 + 4*x^128 + 4*x^126 + 4*x^124 + x^122 + 2*x^118 + 3*x^116 + x^112 + 3*x^110 + x^108 + 3*x^106 + 4*x^104 + 2*x^102 + 2*x^98 + 4*x^96 + x^94 + 2*x^92 + 3*x^88 + x^86 + 2*x^84 + 4*x^82 + 4*x^78 + 4*x^72 + 4*x^70 + 2*x^68 + 3*x^66 + 3*x^64 + 4*x^62 + 2*x^60 + 3*x^56 + x^48 + 4*x^46 + 3*x^44 + x^40 + x^38 + x^32 + 4*x^30 + 2*x^28 + 2*x^26 + 2*x^24 + x^22 + 2*x^20 + 4*x^16 + 4*x^14 + x^12 + 3*x^10 + 3*x^8 + 2*x^6 + 4*x^2 + 3) dy) + dV(0), [2/x^2*y] + V(((2*x^142 + 4*x^138 + x^136 + 3*x^134 + 4*x^130 + 2*x^128 + 4*x^126 + x^120 + 4*x^118 + x^112 + 4*x^110 + 4*x^106 + x^104 + x^102 + 3*x^100 + x^98 + 4*x^96 + x^94 + 2*x^92 + x^90 + 2*x^88 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + 2*x^76 + 4*x^74 + x^72 + 3*x^70 + 3*x^68 + x^66 + 2*x^64 + 2*x^62 + 4*x^60 + 3*x^58 + 3*x^56 + 4*x^54 + 4*x^52 + 3*x^50 + 3*x^48 + 3*x^46 + 2*x^44 + 4*x^42 + x^40 + 3*x^38 + x^36 + 3*x^34 + 3*x^32 + 4*x^28 + 3*x^26 + 3*x^24 + 3*x^22 + x^18 + 3*x^16 + 4*x^14 + 4*x^6 + 3*x^4 + 4)/x^6)*y) )
( [(2*x^16 + 3*x^12 + 4*x^8 + 2*x^6 + x^4 + 3*x^2)*y] d[x] + [3*x^21 + 4*x^17 + 4*x^13 + 3*x^9 + 4*x^7 + x^5 + 2*x^3 + 2*x] d[y] + V(((4*x^154 + 4*x^150 + 4*x^144 + x^142 + 4*x^140 + 2*x^138 + 4*x^136 + 4*x^134 + 2*x^132 + 4*x^130 + x^128 + 2*x^126 + 3*x^124 + 2*x^122 + 3*x^120 + 3*x^116 + 4*x^114 + 3*x^112 + x^106 + 3*x^104 + 3*x^102 + 2*x^98 + 3*x^96 + 4*x^94 + x^92 + 4*x^88 + 4*x^84 + x^80 + x^78 + 4*x^74 + 3*x^72 + 2*x^70 + 2*x^68 + 3*x^66 + x^64 + 4*x^62 + 3*x^60 + 4*x^56 + 3*x^54 + 3*x^50 + 4*x^48 + 3*x^46 + 4*x^42 + 2*x^38 + 4*x^36 + 3*x^34 + 4*x^32 + 2*x^28 + 3*x^26 + 2*x^20 + 2*x^16 + 3*x^14 + 3*x^10 + 2*x^8 + 2*x^6 + 4*x^4)*y) dx + (x^159 + 4*x^151 + 4*x^147 + 3*x^145 + 4*x^143 + 3*x^141 + 2*x^139 + x^137 + 3*x^135 + 2*x^133 + 4*x^131 + 3*x^129 + 4*x^127 + 4*x^125 + 2*x^123 + x^121 + 4*x^119 + 3*x^117 + x^113 + 3*x^111 + 4*x^109 + 3*x^103 + 3*x^99 + 3*x^97 + 4*x^95 + 3*x^91 + 2*x^89 + 4*x^87 + 2*x^83 + 3*x^81 + 4*x^79 + 4*x^77 + 4*x^73 + 2*x^71 + 3*x^69 + 2*x^65 + 2*x^63 + x^61 + x^59 + 2*x^55 + 2*x^53 + x^51 + 3*x^49 + 2*x^45 + 2*x^43 + x^41 + 4*x^39 + 4*x^37 + 3*x^35 + 3*x^33 + x^31 + x^29 + x^27 + 2*x^25 + 2*x^21 + 2*x^19 + 4*x^17 + 2*x^15 + 3*x^9 + x^7 + 2*x^5 + x^3) dy) + dV(0), [2/x^3*y] + V(((3*x^138 + x^134 + 4*x^132 + 2*x^130 + x^126 + 3*x^124 + x^122 + 3*x^118 + 4*x^116 + 2*x^114 + 4*x^112 + 2*x^110 + 4*x^108 + 2*x^106 + 3*x^104 + 2*x^102 + 4*x^100 + x^98 + x^96 + 4*x^94 + 2*x^92 + 2*x^90 + 2*x^88 + 4*x^86 + x^82 + 2*x^80 + 2*x^78 + 3*x^76 + 3*x^70 + 4*x^66 + x^64 + 4*x^62 + x^58 + 4*x^56 + 4*x^54 + x^52 + 2*x^50 + 3*x^48 + 2*x^46 + x^44 + x^42 + 4*x^40 + x^38 + x^34 + 4*x^32 + 3*x^30 + 3*x^26 + 2*x^22 + 3*x^20 + 3*x^18 + x^16 + x^14 + 4*x^12 + 2*x^10 + 2*x^8 + 4*x^6 + 3*x^4 + 2*x^2 + 4)/x^7)*y) )
( [(x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x)*y] d[x] + [4*x^20 + 4*x^16 + 4*x^12 + 4*x^8 + 4*x^4 + 1] d[y] + V(((2*x^149 + x^139 + 2*x^135 + x^131 + 2*x^127 + 4*x^125 + x^123 + x^121 + 3*x^119 + x^117 + 2*x^111 + 2*x^109 + 4*x^107 + 4*x^105 + 3*x^103 + 2*x^101 + 3*x^99 + 4*x^97 + 2*x^95 + 3*x^93 + 2*x^89 + 3*x^83 + x^81 + x^79 + 2*x^77 + 3*x^73 + 3*x^71 + 2*x^69 + x^67 + 2*x^63 + 3*x^61 + 4*x^59 + 2*x^57 + 3*x^55 + 4*x^53 + 4*x^51 + x^47 + 2*x^45 + 2*x^43 + 3*x^37 + x^35 + 4*x^33 + 2*x^31 + 2*x^29 + 3*x^27 + x^25 + 4*x^23 + 2*x^21 + 4*x^19 + 2*x^17 + 3*x^15 + 3*x^13 + 3*x^11 + x^9 + 2*x^3 + 3*x)*y) dx + (3*x^154 + 2*x^150 + x^144 + x^140 + 3*x^136 + x^134 + x^132 + 4*x^130 + 3*x^128 + 2*x^126 + x^122 + 4*x^120 + 3*x^118 + 3*x^114 + x^112 + 3*x^110 + 4*x^108 + 4*x^106 + 4*x^102 + 3*x^96 + 3*x^94 + x^90 + 3*x^86 + 2*x^84 + 3*x^82 + x^80 + x^78 + 3*x^76 + 4*x^74 + 3*x^66 + x^64 + 3*x^62 + 4*x^60 + 2*x^58 + 2*x^54 + x^52 + 4*x^50 + x^48 + 2*x^46 + 4*x^44 + 3*x^42 + 3*x^40 + 2*x^38 + 3*x^36 + x^32 + 3*x^24 + 4*x^22 + 2*x^18 + x^16 + 4*x^14 + x^12 + x^10 + 4*x^8 + 4*x^4 + x^2 + 2) dy) + dV(0), [2/x^4*y] + V(((4*x^132 + 3*x^128 + 2*x^126 + x^124 + 3*x^120 + 4*x^118 + 3*x^116 + x^112 + 2*x^110 + 3*x^106 + 4*x^104 + 2*x^102 + x^98 + 2*x^94 + x^92 + 4*x^90 + 2*x^88 + 3*x^84 + 2*x^82 + 2*x^80 + 3*x^78 + 3*x^76 + 2*x^74 + 2*x^72 + x^70 + 2*x^68 + 4*x^66 + 4*x^62 + 4*x^60 + x^58 + x^56 + 3*x^54 + 2*x^52 + 3*x^48 + 3*x^44 + 3*x^42 + 4*x^40 + x^38 + 2*x^36 + 2*x^34 + 3*x^32 + 3*x^30 + 2*x^28 + 3*x^26 + 3*x^22 + 4*x^20 + 3*x^18 + x^16 + 3*x^14 + 2*x^12 + 3*x^10 + 3*x^8 + 4*x^6 + x^4 + 2)/x^6)*y) )
( [(x^10 + 2*x^6 + 2*x^2)*y] d[x] + [4*x^15 + 4*x^11 + x^5 + 2*x^3 + 3*x] d[y] + V(((2*x^124 + x^114 + x^112 + 2*x^110 + x^108 + 3*x^104 + x^102 + 3*x^100 + 4*x^96 + x^94 + x^92 + 4*x^90 + 4*x^86 + 3*x^82 + 3*x^80 + 4*x^78 + 3*x^74 + 2*x^72 + 3*x^70 + 4*x^68 + 2*x^66 + 2*x^64 + 4*x^60 + 3*x^58 + x^54 + 4*x^52 + 2*x^48 + 4*x^42 + x^40 + 3*x^36 + 3*x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 2*x^20 + 4*x^18 + 3*x^16 + 3*x^14 + 2*x^12 + 4*x^10 + 3*x^8 + 3*x^6 + 2*x^2)*y) dx + (3*x^129 + 2*x^125 + x^119 + 4*x^117 + x^115 + 4*x^111 + 4*x^109 + 2*x^107 + 3*x^105 + 2*x^101 + x^99 + 2*x^97 + 2*x^95 + 4*x^91 + x^87 + x^85 + 4*x^83 + x^81 + x^79 + 4*x^77 + 3*x^75 + 3*x^73 + 4*x^71 + 2*x^67 + 4*x^65 + x^63 + 2*x^61 + 3*x^59 + 4*x^57 + x^55 + 3*x^53 + 4*x^49 + x^45 + x^39 + 4*x^37 + 2*x^35 + 3*x^33 + x^31 + 2*x^29 + x^25 + 3*x^23 + 4*x^21 + x^19 + x^15 + 2*x^13 + x^11 + 4*x^9 + 3*x^7 + 2*x^3 + 3*x) dy) + dV(0), [2/x^5*y] + V(((4*x^106 + 3*x^102 + 2*x^100 + x^98 + 3*x^94 + 4*x^92 + 3*x^90 + x^86 + 2*x^84 + 3*x^80 + 4*x^78 + 2*x^76 + x^72 + 2*x^68 + 2*x^66 + 4*x^64 + 4*x^62 + 3*x^60 + 2*x^58 + 3*x^56 + 4*x^54 + x^52 + 3*x^50 + x^48 + 3*x^46 + x^44 + 2*x^42 + 4*x^40 + 4*x^38 + 3*x^36 + x^34 + x^32 + 3*x^30 + x^24 + 3*x^22 + 2*x^20 + 2*x^18 + x^16 + x^12 + 3*x^8 + x^6 + 4)/x^5)*y) )
( [(4*x^13 + x^5)*y] d[x] + [x^18 + 4*x^14 + 4*x^10 + 4*x^8 + x^6 + 4*x^4] d[y] + V(((3*x^139 + 4*x^135 + x^131 + x^129 + 3*x^127 + x^125 + 2*x^123 + 4*x^121 + 2*x^119 + 2*x^117 + x^115 + x^113 + x^109 + 2*x^107 + 3*x^103 + 2*x^101 + x^97 + x^95 + x^93 + 3*x^91 + x^89 + 4*x^87 + 4*x^85 + 3*x^83 + x^81 + 4*x^77 + x^75 + 4*x^73 + x^71 + 4*x^69 + x^65 + 4*x^61 + x^59 + 3*x^57 + x^55 + 4*x^49 + 2*x^47 + x^45 + 2*x^43 + 4*x^41 + 2*x^39 + 3*x^35 + 3*x^33 + 2*x^29 + 2*x^27 + x^25 + 4*x^23 + x^21 + 2*x^17 + 2*x^15 + 4*x^13 + x^11 + 2*x^7 + x^5 + 4*x^3 + 2*x)*y) dx + (2*x^144 + 4*x^140 + 3*x^136 + 2*x^134 + 3*x^132 + 2*x^130 + x^128 + x^124 + 3*x^122 + 3*x^120 + 4*x^118 + 2*x^116 + x^112 + 2*x^110 + 3*x^108 + 4*x^106 + 3*x^104 + 4*x^102 + 4*x^100 + x^98 + x^94 + 2*x^92 + 4*x^90 + 3*x^86 + 3*x^84 + x^82 + 3*x^80 + 2*x^78 + 2*x^74 + x^70 + 3*x^68 + x^66 + x^64 + 3*x^60 + 2*x^58 + 3*x^56 + x^54 + 3*x^52 + 4*x^50 + 3*x^46 + 4*x^44 + 2*x^42 + 4*x^40 + 2*x^38 + 2*x^36 + 3*x^34 + 2*x^32 + x^30 + 3*x^24 + x^22 + 3*x^20 + 4*x^18 + 2*x^16 + 2*x^12 + 2*x^10 + 3*x^6 + x^4 + 3*x^2 + 3) dy) + dV(0), [2/x^6*y] + V(((x^120 + 2*x^116 + 3*x^114 + 4*x^112 + 2*x^108 + x^106 + 2*x^104 + 2*x^100 + 3*x^98 + x^96 + x^94 + 3*x^92 + 3*x^90 + x^88 + 2*x^86 + x^84 + 3*x^82 + x^80 + 3*x^76 + x^74 + x^70 + 3*x^68 + 2*x^66 + 4*x^64 + 3*x^62 + 2*x^60 + 4*x^52 + x^50 + x^48 + 2*x^46 + 2*x^44 + x^40 + 3*x^38 + 4*x^34 + 2*x^32 + 3*x^30 + x^28 + 2*x^26 + x^24 + 2*x^22 + 4*x^20 + 3*x^16 + x^14 + 4*x^12 + 2*x^10 + 3*x^8 + 3*x^6 + 2*x^4 + 2)/x^4)*y) )
( [(3*x^12 + 4*x^8 + 3*x^4)*y] d[x] + [2*x^17 + 4*x^13 + x^9 + 3*x^7 + 3*x^5 + 2*x^3] d[y] + V(((x^134 + 2*x^130 + 2*x^126 + 4*x^124 + 3*x^122 + 2*x^120 + 4*x^118 + x^116 + 4*x^114 + 3*x^110 + x^108 + 2*x^104 + x^102 + x^100 + 3*x^98 + 3*x^96 + 2*x^94 + 4*x^92 + 3*x^90 + 4*x^88 + 4*x^86 + x^84 + 2*x^82 + 2*x^80 + 3*x^76 + 3*x^74 + 2*x^72 + 2*x^70 + 4*x^68 + 3*x^64 + 2*x^62 + 3*x^58 + 3*x^54 + 4*x^52 + 3*x^50 + 2*x^48 + 4*x^42 + 3*x^40 + 2*x^38 + 3*x^36 + 2*x^34 + 2*x^30 + 3*x^28 + 2*x^26 + x^24 + 2*x^22 + 3*x^18 + 4*x^16 + 4*x^14 + 2*x^12 + 3*x^10 + x^8 + x^2)*y) dx + (4*x^139 + 4*x^135 + 2*x^129 + 4*x^127 + 4*x^123 + x^121 + 4*x^119 + 4*x^117 + 2*x^115 + x^113 + x^107 + x^103 + 2*x^101 + x^99 + 4*x^97 + 3*x^93 + 3*x^91 + 3*x^89 + 2*x^85 + 4*x^83 + x^81 + x^75 + 2*x^73 + 3*x^69 + 3*x^67 + 2*x^65 + 3*x^63 + 4*x^61 + 2*x^59 + 2*x^57 + 2*x^55 + x^53 + 4*x^49 + 2*x^47 + 2*x^45 + 3*x^39 + 2*x^37 + x^35 + 3*x^33 + 4*x^31 + 4*x^27 + x^25 + x^23 + 3*x^21 + 2*x^19 + x^17 + 4*x^15 + 3*x^13 + 2*x^9 + 3*x^7 + 4*x^5 + x^3 + 4*x) dy) + dV(0), [2/x^7*y] + V(((2*x^118 + 4*x^114 + x^112 + 3*x^110 + 4*x^106 + 2*x^104 + 4*x^102 + x^96 + 4*x^94 + x^88 + 4*x^86 + 4*x^82 + x^80 + 3*x^78 + 3*x^76 + 4*x^70 + 2*x^62 + 4*x^60 + 4*x^58 + 2*x^56 + 4*x^54 + 3*x^52 + 4*x^50 + x^46 + 4*x^42 + 4*x^38 + 4*x^36 + x^34 + 2*x^30 + 4*x^28 + 4*x^26 + 4*x^22 + 4*x^20 + 2*x^18 + 4*x^12 + 2*x^10 + 4*x^8 + 2*x^4 + 3*x^2 + 2)/x^7)*y) )
[6nsage: C.de_rham_basis()
[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, (1/(x*y)) dx)]
[6nsage: C1.de_rham_basis()
[((1/y) dx, 0, (1/y) dx),
((x/y) dx, 0, (x/y) dx),
((x^2/y) dx, 0, (x^2/y) dx),
((x^3/y) dx, 0, (x^3/y) dx),
((x^4/y) dx, 0, (x^4/y) dx),
((x^5/y) dx, 0, (x^5/y) dx),
((x^6/y) dx, 0, (x^6/y) dx),
(((-2*x^13 - 2*x^9 - 2*x^3 - x)/y) dx, 2/x*y, ((-1)/(x*y)) dx),
(((x^12 - x^8 - x^4 + x^2 + 1)/y) dx, 2/x^2*y, (2/(x^2*y)) dx),
(((-x^11 - 2*x^3 - x)/y) dx, 2/x^3*y, (2/(x*y)) dx),
(((2*x^10 + x^6 + 2*x^2 + 2)/y) dx, 2/x^4*y, ((-2)/(x^4*y)) dx),
(((2*x^5 + x)/y) dx, 2/x^5*y, ((-2*x^2 + 1)/(x^5*y)) dx),
(((-2*x^8 - 2*x^4)/y) dx, 2/x^6*y, ((2*x^4 + x^2 - 1)/(x^6*y)) dx),
(((x^7 - x^3)/y) dx, 2/x^7*y, ((x^6 - x^4 - x^2 + 2)/(x^7*y)) dx)]
[6nsage: quit()
[23;0t
~/Research/2021 De Rham/DeRhamComputation/sage$ cd ..
~/Research/2021 De Rham/DeRhamComputation$ git add -u
~/Research/2021 De Rham/DeRhamComputation$ git commit -m "naprawione regular form; superelliptyczne maja C.x_series itd"
[master 64fe2ee] naprawione regular form; superelliptyczne maja C.x_series itd
10 files changed, 20233 insertions(+), 46862 deletions(-)
~/Research/2021 De Rham/DeRhamComputation$ git push
Username for 'https://git.wmi.amu.edu.pl': 3Cardano
Password for 'https://3Cardano@git.wmi.amu.edu.pl':
remote: Unauthorized
fatal: Authentication failed for 'https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git/'
~/Research/2021 De Rham/DeRhamComputation$ git push
Username for 'https://git.wmi.amu.edu.pl': jgarnek
Password for 'https://jgarnek@git.wmi.amu.edu.pl':
Enumerating objects: 30, done.
Counting objects: 100% (30/30), done.
Delta compression using up to 4 threads
Compressing objects: 100% (16/16), done.
Writing objects: 100% (16/16), 71.97 KiB | 402.00 KiB/s, done.
Total 16 (delta 13), reused 0 (delta 0)
remote: . Processing 1 references
remote: Processed 1 references in total
To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git
eda1cca..64fe2ee master -> master
~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.8, Release Date: 2023-02-11 │
│ Create a "Sage Worksheet" file for the notebook interface. │
│ Enhanced for CoCalc. │
│ Using Python 3.11.1. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
[22;0t[6nsage[6n[6nsage: load('init.sage')
Computing 0. basis element
Computing 1. basis element
( [3*x*y] d[x] + [3*x^2 + 2] d[y] + V(((3*x^19 + 2*x^17 + x^15 + x^13 + 3*x^9 + 4*x^7 + x^5 + x^3 + x)*y) dx + (3*x^20 + 4*x^18 + 4*x^16 + 4*x^12 + 3*x^10 + x^8 + 2*x^6 + 4) dy) + dV(0), V((4*x^14 + x^12 + 3*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 4)*y) )
( [3*x^2*y] d[x] + [3*x^3 + 2*x] d[y] + V(((3*x^24 + 4*x^22 + x^20 + 3*x^18 + 3*x^16 + 3*x^10 + 2*x^8 + 3*x^4 + 3*x^2)*y) dx + (3*x^25 + x^23 + 2*x^21 + 2*x^19 + 2*x^15 + 3*x^11 + 4*x^9 + 3*x^7 + 3*x^5 + 2*x) dy) + dV(0), [2/x*y] + V(((4*x^20 + x^18 + 3*x^16 + 3*x^14 + x^12 + x^10 + 3*x^8 + 4*x^6 + 4*x^4 + 3*x^2 + 4)/x)*y) )
[6nsasage: B1[0]
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In [2], line 1
----> 1 B1[Integer(0)]
 
NameError: name 'B1' is not defined
[6nsage: B[0]
([(1/(x^3 + x))*y] d[x] + V(((-x^2 + 2)/(x^4*y + 2*x^2*y + y)) dx) + dV([((4*x^18 + 4*x^16 + 4*x^14 + x^8 + x^6 + x^4)/(x^4 + 2*x^2 + 1))*y]), V((4*x^14 + x^12 + 3*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 4)*y), [(1/(x^3 + x))*y] d[x] + V(((-x^2 + 2)/(x^4*y + 2*x^2*y + y)) dx) + dV([((4*x^2 + 1)/(x^4 + 2*x^2 + 1))*y]))
[6nsage: B[0].omega0.regular_form()
[3*x*y] d[x] + [3*x^2 + 2] d[y] + V(((3*x^19 + 2*x^17 + x^15 + x^13 + 3*x^9 + 4*x^7 + x^5 + x^3 + x)*y) dx + (3*x^20 + 4*x^18 + 4*x^16 + 4*x^12 + 3*x^10 + x^8 + 2*x^6 + 4) dy) + dV(0)
[6nsagsage: B[0].omega0.r()
(1/y) dx
[6nsage: B[0].omega0.r().regular_form()
(3*x*y) dx + (3*x^2 + 2) dy
[6nsage: sage: f1 = f(x = x^5 - x)
[6nsage: C1 = superelliptic(f1, m, prec = 500)
[6nsage: C1.de_rham_basis()
[((1/y) dx, 0, (1/y) dx),
((x/y) dx, 0, (x/y) dx),
((x^2/y) dx, 0, (x^2/y) dx),
((x^3/y) dx, 0, (x^3/y) dx),
((x^4/y) dx, 0, (x^4/y) dx),
((x^5/y) dx, 0, (x^5/y) dx),
((x^6/y) dx, 0, (x^6/y) dx),
(((-2*x^13 - 2*x^9 - 2*x^3 - x)/y) dx, 2/x*y, ((-1)/(x*y)) dx),
(((x^12 - x^8 - x^4 + x^2 + 1)/y) dx, 2/x^2*y, (2/(x^2*y)) dx),
(((-x^11 - 2*x^3 - x)/y) dx, 2/x^3*y, (2/(x*y)) dx),
(((2*x^10 + x^6 + 2*x^2 + 2)/y) dx, 2/x^4*y, ((-2)/(x^4*y)) dx),
(((2*x^5 + x)/y) dx, 2/x^5*y, ((-2*x^2 + 1)/(x^5*y)) dx),
(((-2*x^8 - 2*x^4)/y) dx, 2/x^6*y, ((2*x^4 + x^2 - 1)/(x^6*y)) dx),
(((x^7 - x^3)/y) dx, 2/x^7*y, ((x^6 - x^4 - x^2 + 2)/(x^7*y)) dx)]
[6nsage:sage: (x^5 - x)^4
x^20 + x^16 + x^12 + x^8 + x^4
[6nsage: p
5
[6nsage: C1
Superelliptic curve with the equation y^2 = x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x over Finite Field of size 5
[6nsage: C
Superelliptic curve with the equation y^2 = x^3 + x over Finite Field of size 5
[6nsage: C.de_rham_basis()[4]
---------------------------------------------------------------------------
IndexError Traceback (most recent call last)
Cell In [14], line 1
----> 1 C.de_rham_basis()[Integer(4)]
 
IndexError: list index out of range
[6nsage: C.de_rham_basis()[0]
((1/y) dx, 0, (1/y) dx)
[6nsage: C1.de_rham_basis()[4]
((x^4/y) dx, 0, (x^4/y) dx)
[6nsage: C1.de_rham_basis()[4].omega0.regular_form()
((3*x^9 + 2*x^5)*y) dx + (2*x^14 + x^10 + 2*x^6 + 3*x^4) dy
sage: adic_expansion_polynomial(3*x^9 + 2*x^5, x^5 - x)
3*x^4*t
sage: adic_expansion_polynomial(2*x^14 + x^10 + 2*x^6 + 3*x^4, x^5 - x)
2*x^4*t^2 + 3*x^4
sage: adic_expansion_polynomial(x^119 + 4*x^115 + 4*x^111 + x^107 + 3*x^105 + 3*x^103 + x^101 + 3*x^99 + x^97 + 4*x^95 + 3*x^933+ 3*x^89 + 2*x^87 + 4*x^85 + 2*x^8
....: + 4*x^81 + x^79 + 4*x^69 + x^65 + 4*x^63 + 4*x^59 + 3*x^57 + 3*x^55 + x^53 + x^51 + 4*x^47 + 3*x^45 + 4*x^43 + 2*x^41 + 2*x^39 + 3*x^37 + 4*x^35 + 3*x^33 +
....: 2*x^31 + 3*x^29 + 4*x^25 + x^23 + 3*x^21 + 4*x^19 + 2*x^17 + x^15 + x^13 + 2*x^9 + x^7 + 2*x^5 + 4*x, x^5 - x)
(x^4 + 2)*t^23 + 2*x*t^22 + 3*t^21 + (3*x^3 + 4*x)*t^20 + (2*x^4 + x^2 + 3)*t^19 + (2*x^3 + x)*t^18 + (3*x^4 + 4*x^2)*t^17 + (4*x^3 + x)*t^16 + (4*x^4 + 4*x^2 + 1)*t^15 + (4*x^3 + 4*x)*t^14 + (4*x^4 + 3*x^2 + 4)*t^13 + (3*x^3 + 4*x)*t^12 + (3*x^4 + 1)*t^11 + 3*x*t^10 + (2*x^4 + 4*x^2 + 2)*t^9 + (x^3 + 4*x)*t^8 + (4*x^4 + x^2 + 2)*t^7 + (3*x^3 + x)*t^6 + (4*x^4 + x^2)*t^5 + 4*x^3*t^4 + (x^4 + 4*x^2)*t^3 + t
sage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller(
....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +
....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.7^55 + C1.x^53 + C1.x^51 + 4*C1.x^4
....: + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +
....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y).teichmuller() *C1.x.teichmuller().diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114
....: + 3*C1.x^112 + 2*C1.x^110 + 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 1*C1.x^88 + 2*C1.x^84 + C1.x^82 + C
....: .x^80 + 4*C1.x^78 + 4*C1.x^76 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 43C1.x^54 + 4*C1.x^52 + 3*C1.x^50 +
....: *C1.x^48 + 3*C1.x^46 + 4*C1.x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*
....: 1.x^6 + 4*C1.x^4 + 4*C1.x^2 + C1.one).teichmuller()*C1.y.diffn()).verschiebung()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Cell In [21], line 1
----> 1 om = ((Integer(3)*C1.x**Integer(9) + Integer(2)*C1.x**Integer(5))*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (Integer(2)*C1.x**Integer(14) + C1.x**Integer(10) + Integer(2)*C1.x**Integer(6) + Integer(3)*C1.x**Integer(4)).teichmuller() * C1.y.teichmuller().diffn() + (((C1.x**Integer(119) + Integer(4)*C1.x**Integer(115) + Integer(4)*C1.x**Integer(111) + C1.x**Integer(107) + Integer(3)*C1.x**Integer(105) + Integer(3)*C1.x**Integer(103) + C1.x**Integer(101) + Integer(3)*C1.x**Integer(99) + C1.x**Integer(97) + Integer(4)*C1.x**Integer(95) + Integer(3)*C1.x**Integer(93) + Integer(3)*C1.x**Integer(89) + Integer(2)*C1.x**Integer(87) + Integer(4)*C1.x**Integer(85) + Integer(2)*C1.x**Integer(83) + Integer(4)*C1.x**Integer(81) + C1.x**Integer(79) + Integer(4)*C1.x**Integer(69) + C1.x**Integer(65) + Integer(4)*C1.x**Integer(63) + Integer(4)*C1.x**Integer(59) + Integer(3)*C1.x**Integer(57) + Integer(3)*C1.x**Integer(55) + C1.x**Integer(53) + C1.x**Integer(51) + Integer(4)*C1.x**Integer(47) + Integer(3)*C1.x**Integer(45) + Integer(4)*C1.x**Integer(43) + Integer(2)*C1.x**Integer(41) + Integer(2)*C1.x**Integer(39) + Integer(3)*C1.x**Integer(37) + Integer(4)*C1.x**Integer(35) + Integer(3)*C1.x**Integer(33) + Integer(2)*C1.x**Integer(31) + Integer(3)*C1.x**Integer(29) + Integer(4)*C1.x**Integer(25) + C1.x**Integer(23) + Integer(3)*C1.x**Integer(21) + Integer(4)*C1.x**Integer(19) + Integer(2)*C1.x**Integer(17) + C1.x**Integer(15) + C1.x**Integer(13) + Integer(2)*C1.x**Integer(9) + C1.x**Integer(7) + Integer(2)*C1.x**Integer(5) + Integer(4)*C1.x)*C1.y).teichmuller() *C1.x.teichmuller().diffn() + (Integer(4)*C1.x**Integer(124) + Integer(2)*C1.x**Integer(120) + C1.x**Integer(114) + Integer(3)*C1.x**Integer(112) + Integer(2)*C1.x**Integer(110) + Integer(3)*C1.x**Integer(108) + C1.x**Integer(106) + Integer(2)*C1.x**Integer(100) + C1.x**Integer(98) + Integer(3)*C1.x**Integer(96) + C1.x**Integer(94) + Integer(3)*C1.x**Integer(92) + Integer(4)*C1.x**Integer(90) + Integer(3)*C1.x**Integer(88) + Integer(2)*C1.x**Integer(84) + C1.x**Integer(82) + C1.x**Integer(80) + Integer(4)*C1.x**Integer(78) + Integer(4)*C1.x**Integer(76) + C1.x**Integer(74) + Integer(4)*C1.x**Integer(72) + Integer(3)*C1.x**Integer(70) + C1.x**Integer(66) + Integer(3)*C1.x**Integer(64) + Integer(2)*C1.x**Integer(62) + C1.x**Integer(58) + C1.x**Integer(56) + Integer(4)*C1.x**Integer(54) + Integer(4)*C1.x**Integer(52) + Integer(3)*C1.x**Integer(50) + Integer(3)*C1.x**Integer(48) + Integer(3)*C1.x**Integer(46) + Integer(4)*C1.x**Integer(40) + Integer(2)*C1.x**Integer(34) + Integer(3)*C1.x**Integer(32) + Integer(3)*C1.x**Integer(28) + Integer(4)*C1.x**Integer(26) + Integer(4)*C1.x**Integer(24) + Integer(4)*C1.x**Integer(22) + Integer(4)*C1.x**Integer(20) + Integer(2)*C1.x**Integer(14) + Integer(4)*C1.x**Integer(10) + Integer(3)*C1.x**Integer(8) + Integer(2)*C1.x**Integer(6) + Integer(4)*C1.x**Integer(4) + Integer(4)*C1.x**Integer(2) + C1.one).teichmuller()*C1.y.diffn()).verschiebung()
 
File <string>:81, in __add__(self, other)
 
AttributeError: 'NoneType' object has no attribute 'h1'
sage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller(
....: .diffn()
 
[6nsage:
sage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller(
....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +
....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.7^55 + C1.x^53 + C1.x^51 + 4*C1.x^4
....: + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +
....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 +
....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x782 + C1.x^80 + 4*C1.x^78 + 4*C1.x^
....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1..^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1
....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2
....: + C1.one)*C1.y.diffn()).verschiebung()
sage: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^743+ C1.x^72 + 3*C1.x^70 + C1.x^68 +
....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34
....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*Co.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1.
....: ne)/C1.x^2)*C1.y).verschiebung()
[6nsage: xi = superelliptic_drw_cech(xi, f); xi = xi.reduce(); print(xi.regular_form())
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In [25], line 1
----> 1 xi = superelliptic_drw_cech(xi, f); xi = xi.reduce(); print(xi.regular_form())
 
NameError: name 'xi' is not defined
[6nsage: xi = superelliptic_drw_cech(om, f); xi = xi.reduce(); print(xi.regular_form())
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Cell In [26], line 1
----> 1 xi = superelliptic_drw_cech(om, f); xi = xi.reduce(); print(xi.regular_form())
 
File <string>:6, in __init__(self, omega0, f)
 
File /ext/sage/9.8/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
493 """
--> 494 return self.getattr_from_category(name)
495
496 cdef getattr_from_category(self, name):
 
File /ext/sage/9.8/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
505 else:
506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
508
509 def __dir__(self):
 
File /ext/sage/9.8/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
359 dummy_error_message.cls = type(self)
360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
362 attribute = <object>attr
363 # Check for a descriptor (__get__ in Python)
 
AttributeError: 'sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint' object has no attribute 'diffn'
[6nsage: sage: xi = superelliptic_drw_cech(om, ff); xi = xi.reduce(); print(xi.regular_form())
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Cell In [27], line 1
----> 1 xi = superelliptic_drw_cech(om, ff); xi = xi.reduce(); print(xi.regular_form())
 
File <string>:92, in regular_drw_cech(cocycle)
 
File <string>:84, in regular_drw_form(omega)
 
File <string>:9, in decomposition_g0_pth_power(fct)
 
AttributeError: 'NoneType' object has no attribute 'int'
[6nsage: xi
([(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((x^38 + 2*x^34 + 3*x^32 + x^30 + 4*x^28 + 4*x^26 + 4*x^24 + 3*x^20 + x^18 + 2*x^16 + 4*x^12 + 2*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 2)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y]), V(1/x^2*y), [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^32 + 3*x^30 + x^28 + 2*x^24 + 3*x^20 + 4*x^18 + 2*x^16 + 4*x^14 + 4*x^12 + 2*x^10 + 2*x^6 + 1)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y]))
[6nsasage: xi.r()
((x^4/y) dx, 0, (x^4/y) dx)
[6nsage: xi.regular_form()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Cell In [30], line 1
----> 1 xi.regular_form()
 
File <string>:92, in regular_drw_cech(cocycle)
 
File <string>:84, in regular_drw_form(omega)
 
File <string>:9, in decomposition_g0_pth_power(fct)
 
AttributeError: 'NoneType' object has no attribute 'int'
sage: def decomposition_g0_pth_power(fct):
....: print(fct)
....: C = fct.curve
....: Fxy, Rxy, xy, y = C.fct_field
....: if fct.function in Rxy:
....: return (fct, 0*C.x)
....: '''Decompose fct as g0 + A^p, if possible. Output: (g0, A).'''
....: omega = fct.diffn().regular_form()
....: print(omega)
....: g0 = omega.int()
....: A = (fct - g0).pth_root()
....: return (g0, A)
....:
sage: xi.regular_form()
((3*x^98 + x^94 + 4*x^92 + 2*x^90 + x^86 + 3*x^84 + x^82 + 3*x^78 + 4*x^76 + 2*x^74 + 4*x^72 + 2*x^70 + 4*x^68 + 2*x^66 + 3*x^64 + 2*x^62 + 4*x^60 + x^56 + 2*x^54 + 4*x^52 + 3*x^50 + 4*x^48 + 2*x^46 + 3*x^44 + x^38 + 4*x^36 + 3*x^34 + x^32 + 4*x^30 + 4*x^28 + x^26 + 3*x^24 + x^22 + 2*x^18 + 2*x^14 + x^12 + 2*x^10 + 2*x^6 + 3*x^4 + 2*x^2 + 2)/x^2)*y
None
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Cell In [32], line 1
----> 1 xi.regular_form()
 
File <string>:92, in regular_drw_cech(cocycle)
 
File <string>:84, in regular_drw_form(omega)
 
Cell In [31], line 10, in decomposition_g0_pth_power(fct)
8 omega = fct.diffn().regular_form()
9 print(omega)
---> 10 g0 = omega.int()
11 A = (fct - g0).pth_root()
12 return (g0, A)
 
AttributeError: 'NoneType' object has no attribute 'int'
[6nsage: load('init.sage')
Computing 0. basis element
^C---------------------------------------------------------------------------
KeyError Traceback (most recent call last)
File /ext/sage/9.8/src/sage/structure/category_object.pyx:839, in sage.structure.category_object.CategoryObject.getattr_from_category()
838 try:
--> 839 return self.__cached_methods[name]
840 except KeyError:
 
KeyError: '_mpoly_base_ring'
 
During handling of the above exception, another exception occurred:
 
AttributeError Traceback (most recent call last)
File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_ring.py:1117, in PolynomialRing_general._mpoly_base_ring(self, variables)
1116 try:
-> 1117 return self.base_ring()._mpoly_base_ring(variables[:variables.index(var)])
1118 except AttributeError:
 
File /ext/sage/9.8/src/sage/structure/category_object.pyx:833, in sage.structure.category_object.CategoryObject.__getattr__()
832 """
--> 833 return self.getattr_from_category(name)
834
 
File /ext/sage/9.8/src/sage/structure/category_object.pyx:848, in sage.structure.category_object.CategoryObject.getattr_from_category()
847
--> 848 attr = getattr_from_other_class(self, cls, name)
849 self.__cached_methods[name] = attr
 
File /ext/sage/9.8/src/sage/cpython/getattr.pyx:356, in sage.cpython.getattr.getattr_from_other_class()
355 dummy_error_message.name = name
--> 356 raise AttributeError(dummy_error_message)
357 cdef PyObject* attr = instance_getattr(cls, name)
 
AttributeError: 'FpT_with_category' object has no attribute '_mpoly_base_ring'
 
During handling of the above exception, another exception occurred:
 
KeyboardInterrupt Traceback (most recent call last)
Cell In [33], line 1
----> 1 load('init.sage')
 
File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:32
 
File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
173
174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
176 return
177
 
File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
270 add_attached_file(fpath)
271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
273 elif ext == '.spyx' or ext == '.pyx':
274 if attach:
 
File <string>:11
 
File <string>:44, in crystalline_cohomology_basis(self, prec, info)
 
File <string>:24, in de_rham_witt_lift(cech_class, prec)
 
File <string>:6, in de_rham_witt_lift_form0(omega)
 
File <string>:73, in diffn(self, dy_w)
 
File <string>:177, in dy_w(C)
 
File /ext/sage/9.8/src/sage/rings/rational.pyx:2406, in sage.rings.rational.Rational.__mul__()
2404 return x
2405
-> 2406 return coercion_model.bin_op(left, right, operator.mul)
2407
2408 cpdef _mul_(self, right):
 
File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:48, in __rmul__(self, other)
 
File /ext/sage/9.8/src/sage/structure/element.pyx:1527, in sage.structure.element.Element.__mul__()
1525 if not err:
1526 return (<Element>right)._mul_long(value)
-> 1527 return coercion_model.bin_op(left, right, mul)
1528 except TypeError:
1529 return NotImplemented
 
File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:43, in __rmul__(self, other)
 
File /ext/sage/9.8/src/sage/structure/element.pyx:1527, in sage.structure.element.Element.__mul__()
1525 if not err:
1526 return (<Element>right)._mul_long(value)
-> 1527 return coercion_model.bin_op(left, right, mul)
1528 except TypeError:
1529 return NotImplemented
 
File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:43, in __rmul__(self, other)
 
File <string>:31, in __add__(self, other)
 
File <string>:82, in __pow__(self, exp)
 
File <string>:14, in __init__(self, C, g)
 
File <string>:263, in reduction(C, g)
 
File /ext/sage/9.8/src/sage/structure/parent.pyx:896, in sage.structure.parent.Parent.__call__()
894 if mor is not None:
895 if no_extra_args:
--> 896 return mor._call_(x)
897 else:
898 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.8/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.8/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:920, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
918
919 elif isinstance(element, polynomial_element.Polynomial):
--> 920 if base_ring.has_coerce_map_from(element.parent()._mpoly_base_ring(self.variable_names())):
921 return self(element._mpoly_dict_recursive(self.variable_names(), base_ring))
922
 
File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_ring.py:1119, in PolynomialRing_general._mpoly_base_ring(self, variables)
1117 return self.base_ring()._mpoly_base_ring(variables[:variables.index(var)])
1118 except AttributeError:
-> 1119 return self.base_ring()
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
sage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller(
....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +
....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.7^55 + C1.x^53 + C1.x^51 + 4*C1.x^4
....: + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +
....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 +
....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x782 + C1.x^80 + 4*C1.x^78 + 4*C1.x^
....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1..^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1
....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2
....: + C1.one)*C1.y.diffn()).verschiebung()
....:
....: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^743+ C1.x^72 + 3*C1.x^70 + C1.x^68 +
....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34
....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*Co.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1.
....: ne)/C1.x^2)*C1.y).verschiebung()
....:
....: xi = superelliptic_drw_cech(om, ff); xi = xi.reduce(); print(xi.regular_form())
 
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
File <string>:59, in __mul__(self, other)
 
File <string>:261, in reduction(C, g)
 
File /ext/sage/9.8/src/sage/structure/element.pyx:1515, in sage.structure.element.Element.__mul__()
1514 if BOTH_ARE_ELEMENT(cl):
-> 1515 return coercion_model.bin_op(left, right, mul)
1516
 
File /ext/sage/9.8/src/sage/structure/coerce.pyx:1200, in sage.structure.coerce.CoercionModel.bin_op()
1199 try:
-> 1200 xy = self.canonical_coercion(x, y)
1201 except TypeError:
 
File /ext/sage/9.8/src/sage/structure/coerce.pyx:1311, in sage.structure.coerce.CoercionModel.canonical_coercion()
1310 if x_map is not None:
-> 1311 x_elt = (<Map>x_map)._call_(x)
1312 else:
 
File /ext/sage/9.8/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
286 cdef Map m
--> 287 cdef Element e = method(C)
288 if e is None:
 
File /ext/sage/9.8/src/sage/rings/polynomial/multi_polynomial.pyx:198, in sage.rings.polynomial.multi_polynomial.MPolynomial._polynomial_()
197 if var in self._parent.variable_names():
--> 198 return R(self.polynomial(self._parent(var)))
199 return R([self])
 
File /ext/sage/9.8/src/sage/rings/polynomial/multi_polynomial.pyx:410, in sage.rings.polynomial.multi_polynomial.MPolynomial.polynomial()
409 # Make polynomial ring over all variables except var.
--> 410 S = R.base_ring()[tuple(Z)]
411 ring = S[var]
 
File /ext/sage/9.8/src/sage/structure/parent.pyx:1274, in sage.structure.parent.Parent.__getitem__()
1273 return self.list()[n]
-> 1274 return meth(n)
1275
 
File /ext/sage/9.8/src/sage/categories/rings.py:1220, in Rings.ParentMethods.__getitem__(self, arg)
1219 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-> 1220 return PolynomialRing(self, elts)
 
File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_ring_constructor.py:678, in PolynomialRing(base_ring, *args, **kwds)
676 raise TypeError("you must specify the names of the variables")
--> 678 names = normalize_names(n, names)
680 # At this point, we have only handled the "names" keyword if it was
681 # needed. Since we know the variable names, it would logically be
682 # an error to specify an additional "names" keyword. However,
(...)
685 # and we allow this for historical reasons. However, the names
686 # must be consistent!
 
File /ext/sage/9.8/src/sage/structure/category_object.pyx:900, in sage.structure.category_object.normalize_names()
899
--> 900 cpdef normalize_names(Py_ssize_t ngens, names):
901 r"""
 
File /ext/sage/9.8/src/sage/structure/category_object.pyx:993, in sage.structure.category_object.normalize_names()
992 # Convert names to strings and strip whitespace
--> 993 names = [str(x).strip() for x in names]
994 else:
 
File /ext/sage/9.8/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
193 return super().__repr__()
--> 194 result = reprfunc()
195 if isinstance(result, str):
 
File /ext/sage/9.8/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2464, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular._repr_()
2463 cdef ring *_ring = self._parent_ring
-> 2464 s = singular_polynomial_str(self._poly, _ring)
2465 return s
 
File /ext/sage/9.8/src/sage/libs/singular/polynomial.pyx:440, in sage.libs.singular.polynomial.singular_polynomial_str()
439 s = bytes_to_str(p_String(p, r, r))
--> 440 s = plusminus_pattern.sub("\\1 \\2 ", s)
441 s = parenthvar_pattern.sub("\\1", s)
 
File /ext/sage/9.8/local/var/lib/sage/venv-python3.11.1/lib/python3.11/re/__init__.py:315, in _subx(pattern, template)
313 return _parser.expand_template(template, match)
--> 315 def _subx(pattern, template):
316 # internal: Pattern.sub/subn implementation helper
317 template = _compile_repl(template, pattern)
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
 
During handling of the above exception, another exception occurred:
 
AttributeError Traceback (most recent call last)
Cell In [34], line 1
----> 1 om = ((Integer(3)*C1.x**Integer(9) + Integer(2)*C1.x**Integer(5))*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (Integer(2)*C1.x**Integer(14) + C1.x**Integer(10) + Integer(2)*C1.x**Integer(6) + Integer(3)*C1.x**Integer(4)).teichmuller() * C1.y.teichmuller().diffn() + (((C1.x**Integer(119) + Integer(4)*C1.x**Integer(115) + Integer(4)*C1.x**Integer(111) + C1.x**Integer(107) + Integer(3)*C1.x**Integer(105) + Integer(3)*C1.x**Integer(103) + C1.x**Integer(101) + Integer(3)*C1.x**Integer(99) + C1.x**Integer(97) + Integer(4)*C1.x**Integer(95) + Integer(3)*C1.x**Integer(93) + Integer(3)*C1.x**Integer(89) + Integer(2)*C1.x**Integer(87) + Integer(4)*C1.x**Integer(85) + Integer(2)*C1.x**Integer(83) + Integer(4)*C1.x**Integer(81) + C1.x**Integer(79) + Integer(4)*C1.x**Integer(69) + C1.x**Integer(65) + Integer(4)*C1.x**Integer(63) + Integer(4)*C1.x**Integer(59) + Integer(3)*C1.x**Integer(57) + Integer(3)*C1.x**Integer(55) + C1.x**Integer(53) + C1.x**Integer(51) + Integer(4)*C1.x**Integer(47) + Integer(3)*C1.x**Integer(45) + Integer(4)*C1.x**Integer(43) + Integer(2)*C1.x**Integer(41) + Integer(2)*C1.x**Integer(39) + Integer(3)*C1.x**Integer(37) + Integer(4)*C1.x**Integer(35) + Integer(3)*C1.x**Integer(33) + Integer(2)*C1.x**Integer(31) + Integer(3)*C1.x**Integer(29) + Integer(4)*C1.x**Integer(25) + C1.x**Integer(23) + Integer(3)*C1.x**Integer(21) + Integer(4)*C1.x**Integer(19) + Integer(2)*C1.x**Integer(17) + C1.x**Integer(15) + C1.x**Integer(13) + Integer(2)*C1.x**Integer(9) + C1.x**Integer(7) + Integer(2)*C1.x**Integer(5) + Integer(4)*C1.x)*C1.y) *C1.x.diffn() + (Integer(4)*C1.x**Integer(124) + Integer(2)*C1.x**Integer(120) + C1.x**Integer(114) + Integer(3)*C1.x**Integer(112) + Integer(2)*C1.x**Integer(110) + Integer(3)*C1.x**Integer(108) + C1.x**Integer(106) + Integer(2)*C1.x**Integer(100) + C1.x**Integer(98) + Integer(3)*C1.x**Integer(96) + C1.x**Integer(94) + Integer(3)*C1.x**Integer(92) + Integer(4)*C1.x**Integer(90) + Integer(3)*C1.x**Integer(88) + Integer(2)*C1.x**Integer(84) + C1.x**Integer(82) + C1.x**Integer(80) + Integer(4)*C1.x**Integer(78) + Integer(4)*C1.x**Integer(76) + C1.x**Integer(74) + Integer(4)*C1.x**Integer(72) + Integer(3)*C1.x**Integer(70) + C1.x**Integer(66) + Integer(3)*C1.x**Integer(64) + Integer(2)*C1.x**Integer(62) + C1.x**Integer(58) + C1.x**Integer(56) + Integer(4)*C1.x**Integer(54) + Integer(4)*C1.x**Integer(52) + Integer(3)*C1.x**Integer(50) + Integer(3)*C1.x**Integer(48) + Integer(3)*C1.x**Integer(46) + Integer(4)*C1.x**Integer(40) + Integer(2)*C1.x**Integer(34) + Integer(3)*C1.x**Integer(32) + Integer(3)*C1.x**Integer(28) + Integer(4)*C1.x**Integer(26) + Integer(4)*C1.x**Integer(24) + Integer(4)*C1.x**Integer(22) + Integer(4)*C1.x**Integer(20) + Integer(2)*C1.x**Integer(14) + Integer(4)*C1.x**Integer(10) + Integer(3)*C1.x**Integer(8) + Integer(2)*C1.x**Integer(6) + Integer(4)*C1.x**Integer(4) + Integer(4)*C1.x**Integer(2) + C1.one)*C1.y.diffn()).verschiebung()
3 ff = (((Integer(2)*C1.x**Integer(98) + Integer(4)*C1.x**Integer(94) + C1.x**Integer(92) + Integer(3)*C1.x**Integer(90) + Integer(4)*C1.x**Integer(86) + Integer(2)*C1.x**Integer(84) + Integer(4)*C1.x**Integer(82) + Integer(2)*C1.x**Integer(78) + C1.x**Integer(76) + Integer(3)*C1.x**Integer(74) + C1.x**Integer(72) + Integer(3)*C1.x**Integer(70) + C1.x**Integer(68) + Integer(3)*C1.x**Integer(66) + Integer(2)*C1.x**Integer(64) + Integer(3)*C1.x**Integer(62) + C1.x**Integer(60) + Integer(4)*C1.x**Integer(56) + Integer(3)*C1.x**Integer(54) + C1.x**Integer(52) + Integer(2)*C1.x**Integer(50) + C1.x**Integer(48) + Integer(3)*C1.x**Integer(46) + Integer(2)*C1.x**Integer(44) + Integer(4)*C1.x**Integer(38) + C1.x**Integer(36) + Integer(2)*C1.x**Integer(34) + Integer(4)*C1.x**Integer(32) + C1.x**Integer(30) + C1.x**Integer(28) + Integer(4)*C1.x**Integer(26) + Integer(2)*C1.x**Integer(24) + Integer(4)*C1.x**Integer(22) + Integer(3)*C1.x**Integer(18) + Integer(3)*C1.x**Integer(14) + Integer(4)*C1.x**Integer(12) + Integer(3)*C1.x**Integer(10) + Integer(3)*C1.x**Integer(6) + Integer(2)*C1.x**Integer(4) + Integer(3)*C1.x**Integer(2) + Integer(4)*C1.one)/C1.x**Integer(2))*C1.y).verschiebung()
5 xi = superelliptic_drw_cech(om, ff); xi = xi.reduce(); print(xi.regular_form())
 
File <string>:73, in diffn(self, dy_w)
 
File <string>:177, in dy_w(C)
 
File <string>:149, in auxilliary_derivative(P)
 
File <string>:55, in __rmul__(self, other)
 
File /ext/sage/9.8/src/sage/rings/integer.pyx:1961, in sage.rings.integer.Integer.__mul__()
1959 return y
1960
-> 1961 return coercion_model.bin_op(left, right, operator.mul)
1962
1963 cpdef _mul_(self, right):
 
File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:55, in __rmul__(self, other)
 
File /ext/sage/9.8/src/sage/rings/integer.pyx:1961, in sage.rings.integer.Integer.__mul__()
1959 return y
1960
-> 1961 return coercion_model.bin_op(left, right, operator.mul)
1962
1963 cpdef _mul_(self, right):
 
File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
[... skipping similar frames: __rmul__ at line 55 (9 times), sage.rings.integer.Integer.__mul__ at line 1961 (8 times), sage.structure.coerce.CoercionModel.bin_op at line 1242 (8 times)]
 
File /ext/sage/9.8/src/sage/rings/integer.pyx:1961, in sage.rings.integer.Integer.__mul__()
1959 return y
1960
-> 1961 return coercion_model.bin_op(left, right, operator.mul)
1962
1963 cpdef _mul_(self, right):
 
File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:55, in __rmul__(self, other)
 
File <string>:84, in __add__(self, other)
 
File <string>:31, in __add__(self, other)
 
File <string>:63, in __mul__(self, other)
 
AttributeError: 'superelliptic_function' object has no attribute 'form'
sage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller(
....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +
....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.7^55 + C1.x^53 + C1.x^51 + 4*C1.x^4
....: + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +
....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 +
....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x782 + C1.x^80 + 4*C1.x^78 + 4*C1.x^
....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1..^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1
....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2
....: + C1.one)*C1.y.diffn()).verschiebung()
....:
....: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^743+ C1.x^72 + 3*C1.x^70 + C1.x^68 +
....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34
....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*Co.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1.
....: ne)/C1.x^2)*C1.y).verschiebung()
....:
....: xi = superelliptic_drw_cech(om, ff)
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Cell In [35], line 1
----> 1 om = ((Integer(3)*C1.x**Integer(9) + Integer(2)*C1.x**Integer(5))*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (Integer(2)*C1.x**Integer(14) + C1.x**Integer(10) + Integer(2)*C1.x**Integer(6) + Integer(3)*C1.x**Integer(4)).teichmuller() * C1.y.teichmuller().diffn() + (((C1.x**Integer(119) + Integer(4)*C1.x**Integer(115) + Integer(4)*C1.x**Integer(111) + C1.x**Integer(107) + Integer(3)*C1.x**Integer(105) + Integer(3)*C1.x**Integer(103) + C1.x**Integer(101) + Integer(3)*C1.x**Integer(99) + C1.x**Integer(97) + Integer(4)*C1.x**Integer(95) + Integer(3)*C1.x**Integer(93) + Integer(3)*C1.x**Integer(89) + Integer(2)*C1.x**Integer(87) + Integer(4)*C1.x**Integer(85) + Integer(2)*C1.x**Integer(83) + Integer(4)*C1.x**Integer(81) + C1.x**Integer(79) + Integer(4)*C1.x**Integer(69) + C1.x**Integer(65) + Integer(4)*C1.x**Integer(63) + Integer(4)*C1.x**Integer(59) + Integer(3)*C1.x**Integer(57) + Integer(3)*C1.x**Integer(55) + C1.x**Integer(53) + C1.x**Integer(51) + Integer(4)*C1.x**Integer(47) + Integer(3)*C1.x**Integer(45) + Integer(4)*C1.x**Integer(43) + Integer(2)*C1.x**Integer(41) + Integer(2)*C1.x**Integer(39) + Integer(3)*C1.x**Integer(37) + Integer(4)*C1.x**Integer(35) + Integer(3)*C1.x**Integer(33) + Integer(2)*C1.x**Integer(31) + Integer(3)*C1.x**Integer(29) + Integer(4)*C1.x**Integer(25) + C1.x**Integer(23) + Integer(3)*C1.x**Integer(21) + Integer(4)*C1.x**Integer(19) + Integer(2)*C1.x**Integer(17) + C1.x**Integer(15) + C1.x**Integer(13) + Integer(2)*C1.x**Integer(9) + C1.x**Integer(7) + Integer(2)*C1.x**Integer(5) + Integer(4)*C1.x)*C1.y) *C1.x.diffn() + (Integer(4)*C1.x**Integer(124) + Integer(2)*C1.x**Integer(120) + C1.x**Integer(114) + Integer(3)*C1.x**Integer(112) + Integer(2)*C1.x**Integer(110) + Integer(3)*C1.x**Integer(108) + C1.x**Integer(106) + Integer(2)*C1.x**Integer(100) + C1.x**Integer(98) + Integer(3)*C1.x**Integer(96) + C1.x**Integer(94) + Integer(3)*C1.x**Integer(92) + Integer(4)*C1.x**Integer(90) + Integer(3)*C1.x**Integer(88) + Integer(2)*C1.x**Integer(84) + C1.x**Integer(82) + C1.x**Integer(80) + Integer(4)*C1.x**Integer(78) + Integer(4)*C1.x**Integer(76) + C1.x**Integer(74) + Integer(4)*C1.x**Integer(72) + Integer(3)*C1.x**Integer(70) + C1.x**Integer(66) + Integer(3)*C1.x**Integer(64) + Integer(2)*C1.x**Integer(62) + C1.x**Integer(58) + C1.x**Integer(56) + Integer(4)*C1.x**Integer(54) + Integer(4)*C1.x**Integer(52) + Integer(3)*C1.x**Integer(50) + Integer(3)*C1.x**Integer(48) + Integer(3)*C1.x**Integer(46) + Integer(4)*C1.x**Integer(40) + Integer(2)*C1.x**Integer(34) + Integer(3)*C1.x**Integer(32) + Integer(3)*C1.x**Integer(28) + Integer(4)*C1.x**Integer(26) + Integer(4)*C1.x**Integer(24) + Integer(4)*C1.x**Integer(22) + Integer(4)*C1.x**Integer(20) + Integer(2)*C1.x**Integer(14) + Integer(4)*C1.x**Integer(10) + Integer(3)*C1.x**Integer(8) + Integer(2)*C1.x**Integer(6) + Integer(4)*C1.x**Integer(4) + Integer(4)*C1.x**Integer(2) + C1.one)*C1.y.diffn()).verschiebung()
3 ff = (((Integer(2)*C1.x**Integer(98) + Integer(4)*C1.x**Integer(94) + C1.x**Integer(92) + Integer(3)*C1.x**Integer(90) + Integer(4)*C1.x**Integer(86) + Integer(2)*C1.x**Integer(84) + Integer(4)*C1.x**Integer(82) + Integer(2)*C1.x**Integer(78) + C1.x**Integer(76) + Integer(3)*C1.x**Integer(74) + C1.x**Integer(72) + Integer(3)*C1.x**Integer(70) + C1.x**Integer(68) + Integer(3)*C1.x**Integer(66) + Integer(2)*C1.x**Integer(64) + Integer(3)*C1.x**Integer(62) + C1.x**Integer(60) + Integer(4)*C1.x**Integer(56) + Integer(3)*C1.x**Integer(54) + C1.x**Integer(52) + Integer(2)*C1.x**Integer(50) + C1.x**Integer(48) + Integer(3)*C1.x**Integer(46) + Integer(2)*C1.x**Integer(44) + Integer(4)*C1.x**Integer(38) + C1.x**Integer(36) + Integer(2)*C1.x**Integer(34) + Integer(4)*C1.x**Integer(32) + C1.x**Integer(30) + C1.x**Integer(28) + Integer(4)*C1.x**Integer(26) + Integer(2)*C1.x**Integer(24) + Integer(4)*C1.x**Integer(22) + Integer(3)*C1.x**Integer(18) + Integer(3)*C1.x**Integer(14) + Integer(4)*C1.x**Integer(12) + Integer(3)*C1.x**Integer(10) + Integer(3)*C1.x**Integer(6) + Integer(2)*C1.x**Integer(4) + Integer(3)*C1.x**Integer(2) + Integer(4)*C1.one)/C1.x**Integer(2))*C1.y).verschiebung()
5 xi = superelliptic_drw_cech(om, ff)
 
File <string>:73, in diffn(self, dy_w)
 
File <string>:177, in dy_w(C)
 
File /ext/sage/9.8/src/sage/rings/rational.pyx:2406, in sage.rings.rational.Rational.__mul__()
2404 return x
2405
-> 2406 return coercion_model.bin_op(left, right, operator.mul)
2407
2408 cpdef _mul_(self, right):
 
File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:48, in __rmul__(self, other)
 
File /ext/sage/9.8/src/sage/structure/element.pyx:1527, in sage.structure.element.Element.__mul__()
1525 if not err:
1526 return (<Element>right)._mul_long(value)
-> 1527 return coercion_model.bin_op(left, right, mul)
1528 except TypeError:
1529 return NotImplemented
 
File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:43, in __rmul__(self, other)
 
File /ext/sage/9.8/src/sage/structure/element.pyx:1527, in sage.structure.element.Element.__mul__()
1525 if not err:
1526 return (<Element>right)._mul_long(value)
-> 1527 return coercion_model.bin_op(left, right, mul)
1528 except TypeError:
1529 return NotImplemented
 
File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:43, in __rmul__(self, other)
 
[... skipping similar frames: __rmul__ at line 43 (10 times), sage.structure.coerce.CoercionModel.bin_op at line 1242 (10 times), sage.structure.element.Element.__mul__ at line 1527 (10 times)]
 
File /ext/sage/9.8/src/sage/structure/element.pyx:1527, in sage.structure.element.Element.__mul__()
1525 if not err:
1526 return (<Element>right)._mul_long(value)
-> 1527 return coercion_model.bin_op(left, right, mul)
1528 except TypeError:
1529 return NotImplemented
 
File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:43, in __rmul__(self, other)
 
File <string>:31, in __add__(self, other)
 
File <string>:82, in __pow__(self, exp)
 
File <string>:14, in __init__(self, C, g)
 
File <string>:253, in reduction(C, g)
 
File /ext/sage/9.8/src/sage/structure/parent.pyx:896, in sage.structure.parent.Parent.__call__()
894 if mor is not None:
895 if no_extra_args:
--> 896 return mor._call_(x)
897 else:
898 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.8/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.8/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce)
704 x0, y0 = x, y
705 try:
--> 706 x, y = resolve_fractions(x0, y0)
707 except (AttributeError, TypeError):
708 raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
709 x0, y0, self))
 
File /ext/sage/9.8/src/sage/rings/fraction_field.py:683, in FractionField_generic._element_constructor_.<locals>.resolve_fractions(x, y)
682 def resolve_fractions(x, y):
--> 683 xn = x.numerator()
684 xd = x.denominator()
685 yn = y.numerator()
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
sage: f1 = f(x = x^5 - x)
sage: C1 = superelliptic(f1, m, prec = 500)
sage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller(
....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +
....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.7^55 + C1.x^53 + C1.x^51 + 4*C1.x^4
....: + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +
....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 +
....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x782 + C1.x^80 + 4*C1.x^78 + 4*C1.x^
....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1..^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1
....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2
....: + C1.one)*C1.y.diffn()).verschiebung()
....:
....: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^743+ C1.x^72 + 3*C1.x^70 + C1.x^68 +
....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34
....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*Co.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1.
....: ne)/C1.x^2)*C1.y).verschiebung()
....:
....: xi = superelliptic_drw_cech(om, ff)
[6nsage: xi.reduce()
^C---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
File <string>:58, in __mul__(self, other)
 
AttributeError: 'superelliptic_form' object has no attribute 'function'
 
During handling of the above exception, another exception occurred:
 
KeyboardInterrupt Traceback (most recent call last)
Cell In [39], line 1
----> 1 xi.reduce()
 
File <string>:18, in reduce(self)
 
File <string>:73, in diffn(self, dy_w)
 
File <string>:177, in dy_w(C)
 
File <string>:149, in auxilliary_derivative(P)
 
File <string>:55, in __rmul__(self, other)
 
File /ext/sage/9.8/src/sage/rings/integer.pyx:1961, in sage.rings.integer.Integer.__mul__()
1959 return y
1960
-> 1961 return coercion_model.bin_op(left, right, operator.mul)
1962
1963 cpdef _mul_(self, right):
 
File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:55, in __rmul__(self, other)
 
File /ext/sage/9.8/src/sage/rings/integer.pyx:1961, in sage.rings.integer.Integer.__mul__()
1959 return y
1960
-> 1961 return coercion_model.bin_op(left, right, operator.mul)
1962
1963 cpdef _mul_(self, right):
 
File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
[... skipping similar frames: __rmul__ at line 55 (4 times), sage.rings.integer.Integer.__mul__ at line 1961 (3 times), sage.structure.coerce.CoercionModel.bin_op at line 1242 (3 times)]
 
File /ext/sage/9.8/src/sage/rings/integer.pyx:1961, in sage.rings.integer.Integer.__mul__()
1959 return y
1960
-> 1961 return coercion_model.bin_op(left, right, operator.mul)
1962
1963 cpdef _mul_(self, right):
 
File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:55, in __rmul__(self, other)
 
File <string>:84, in __add__(self, other)
 
File <string>:65, in __mul__(self, other)
 
File <string>:65, in __mul__(self, other)
 
File <string>:7, in __init__(self, C, g)
 
File <string>:282, in reduction_form(C, g)
 
File <string>:260, in reduction(C, g)
 
File /ext/sage/9.8/src/sage/arith/misc.py:2021, in xgcd(a, b)
1933 r"""
1934 Return a triple ``(g,s,t)`` such that `g = s\cdot a+t\cdot b = \gcd(a,b)`.
1935
(...)
2018 (1, 7*a^2/b^2, (((-h)*a)/b^2)*y + 1/b)
2019 """
2020 try:
-> 2021 return a.xgcd(b)
2022 except AttributeError:
2023 a = py_scalar_to_element(a)
 
File /ext/sage/9.8/src/sage/structure/element.pyx:4497, in sage.structure.element.coerce_binop.new_method()
4495 def new_method(self, other, *args, **kwargs):
4496 if have_same_parent(self, other):
-> 4497 return method(self, other, *args, **kwargs)
4498 else:
4499 a, b = coercion_model.canonical_coercion(self, other)
 
File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_element.pyx:8931, in sage.rings.polynomial.polynomial_element.Polynomial.xgcd()
8929 """
8930 if hasattr(self.base_ring(), '_xgcd_univariate_polynomial'):
-> 8931 return self.base_ring()._xgcd_univariate_polynomial(self, other)
8932 else:
8933 raise NotImplementedError("%s does not provide an xgcd implementation for univariate polynomials"%self.base_ring())
 
File /ext/sage/9.8/src/sage/categories/fields.py:285, in Fields.ParentMethods._xgcd_univariate_polynomial(self, a, b)
282 a = a.monic()
283 return a
--> 285 def _xgcd_univariate_polynomial(self, a, b):
286 r"""
287 Return an extended gcd of ``a`` and ``b``.
288
(...)
359 (0, 0, 0)
360 """
361 R = a.parent()
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
sage: def reducee(self):
....: ^IC = self.curve
....: ^Ifct = self.f
....: ^If_first_comp = fct.t
....: ^If_second_comp = fct.f
....: ^Idecomp_first_comp = decomposition_g0_g8(f_first_comp)
....: ^Idecomp_second_comp = decomposition_g0_g8(f_second_comp)
....: ^Inew = self
....: ^Iprint(decomp_first_comp, decomp_second_comp)
....: ^Inew.omega0 -= decomposition_g0_g8(f_first_comp)[0].teichmuller().diffn()
....: ^Inew.omega0 -= decomposition_g0_g8(f_second_comp)[0].verschiebung().diffn()
....: ^Iprint(new.omega0)
....: ^Inew.f = decomposition_g0_g8(f_first_comp)[2].teichmuller() + decomposition_g0_g8(f_second_comp)[2].verschiebung()
....: ^Inew.omega8 = new.omega0 - new.f.diffn()
....: ^Ireturn new
....:
[6nsage: reducee(xi)
(0, 0, 0) (((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/x^2)*y, 0, 1/x^2*y)
[(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((x^38 + 2*x^34 + 3*x^32 + x^30 + 4*x^28 + 4*x^26 + 4*x^24 + 3*x^20 + x^18 + 2*x^16 + 4*x^12 + 2*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 2)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y])
([(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((x^38 + 2*x^34 + 3*x^32 + x^30 + 4*x^28 + 4*x^26 + 4*x^24 + 3*x^20 + x^18 + 2*x^16 + 4*x^12 + 2*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 2)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y]), V(1/x^2*y), [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^32 + 3*x^30 + x^28 + 2*x^24 + 3*x^20 + 4*x^18 + 2*x^16 + 4*x^14 + 4*x^12 + 2*x^10 + 2*x^6 + 1)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y]))
sage: def reducee(self):
....: ^IC = self.curve
....: ^Ifct = self.f
....: ^If_first_comp = fct.t
....: ^If_second_comp = fct.f
....: ^Idecomp_first_comp = decomposition_g0_g8(f_first_comp)
....: ^Idecomp_second_comp = decomposition_g0_g8(f_second_comp)
....: ^Inew = self
....: ^Iprint('decomp_first_comp[0], decomp_second_comp[0]', decomp_first_comp[0], decomp_second_comp[0])
....: ^Inew.omega0 -= decomposition_g0_g8(f_first_comp)[0].teichmuller().diffn()
....: ^Inew.omega0 -= decomposition_g0_g8(f_second_comp)[0].verschiebung().diffn()
....: ^Iprint('new.omega0', new.omega0)
....: ^Inew.f = decomposition_g0_g8(f_first_comp)[2].teichmuller() + decomposition_g0_g8(f_second_comp)[2].verschiebung()
....: ^Inew.omega8 = new.omega0 - new.f.diffn()
....: ^Ireturn new
....:
[6nsage: reducee(xi)
decomp_first_comp[0], decomp_second_comp[0] 0 2/x^2*y
new.omega0 [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^36 + 3*x^32 + 3*x^30 + 3*x^26 + x^24 + 3*x^18 + 2*x^16 + 2*x^14 + 3*x^12 + 4*x^10 + 2*x^8 + 2*x^6 + 3*x^4 + 4*x^2 + 2)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y])
([(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^36 + 3*x^32 + 3*x^30 + 3*x^26 + x^24 + 3*x^18 + 2*x^16 + 2*x^14 + 3*x^12 + 4*x^10 + 2*x^8 + 2*x^6 + 3*x^4 + 4*x^2 + 2)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(4/x^2*y), [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^32 + 3*x^30 + x^28 + 2*x^24 + 3*x^20 + 4*x^18 + 2*x^16 + 4*x^14 + 4*x^12 + 2*x^10 + 2*x^6 + 1)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y]))
sage: xi.f.t
0
sage: decomposition_g0_g8(xi.f.t)
(0, 0, 0)
[6nsage: decomposition_g0_g8(xi.f.t)
(0, 0, 0)
sage: xi.f
V(4/x^2*y)
sage: def aa(self):
....: new = self
....: ^Inew += 1
....: ^Ireturn new
Cell In [48], line 3
new += Integer(1)
^
TabError: inconsistent use of tabs and spaces in indentation
 
sage: def aa(self):
....: ^Inew = self
....: ^Inew += 1
....: ^Ireturn new
....:
[6nsage: d = 1
sage: aa(d)
2
[6nsage: d
1
sage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller(
....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +
....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.7^55 + C1.x^53 + C1.x^51 + 4*C1.x^4
....: + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +
....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 +
....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x782 + C1.x^80 + 4*C1.x^78 + 4*C1.x^
....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1..^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1
....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2
....: + C1.one)*C1.y.diffn()).verschiebung()
....:
....: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^743+ C1.x^72 + 3*C1.x^70 + C1.x^68 +
....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34
....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*Co.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1.
....: ne)/C1.x^2)*C1.y).verschiebung()
....:
....: xi = superelliptic_drw_cech(om, ff)
 
[6nsage:
[6nsage: reducee(xi)
decomp_first_comp[0], decomp_second_comp[0] 0 ((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/x^2)*y
new.omega0 [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((x^38 + 2*x^34 + 3*x^32 + x^30 + 4*x^28 + 4*x^26 + 4*x^24 + 3*x^20 + x^18 + 2*x^16 + 4*x^12 + 2*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 2)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y])
([(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((x^38 + 2*x^34 + 3*x^32 + x^30 + 4*x^28 + 4*x^26 + 4*x^24 + 3*x^20 + x^18 + 2*x^16 + 4*x^12 + 2*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 2)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y]), V(1/x^2*y), [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^32 + 3*x^30 + x^28 + 2*x^24 + 3*x^20 + 4*x^18 + 2*x^16 + 4*x^14 + 4*x^12 + 2*x^10 + 2*x^6 + 1)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y]))
[6nsage: reducee(xi)
decomp_first_comp[0], decomp_second_comp[0] 0 2/x^2*y
new.omega0 [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^36 + 3*x^32 + 3*x^30 + 3*x^26 + x^24 + 3*x^18 + 2*x^16 + 2*x^14 + 3*x^12 + 4*x^10 + 2*x^8 + 2*x^6 + 3*x^4 + 4*x^2 + 2)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y])
([(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^36 + 3*x^32 + 3*x^30 + 3*x^26 + x^24 + 3*x^18 + 2*x^16 + 2*x^14 + 3*x^12 + 4*x^10 + 2*x^8 + 2*x^6 + 3*x^4 + 4*x^2 + 2)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(4/x^2*y), [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^32 + 3*x^30 + x^28 + 2*x^24 + 3*x^20 + 4*x^18 + 2*x^16 + 4*x^14 + 4*x^12 + 2*x^10 + 2*x^6 + 1)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y]))
[6nsage: sage: decomposition_g0_g8(ff)
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Cell In [56], line 1
----> 1 decomposition_g0_g8(ff)
 
File <string>:7, in decomposition_g0_g8(fct, prec)
 
AttributeError: 'superelliptic_witt' object has no attribute 'coordinates'
[6nsage: decomposition_g0_g8(ff.f)
(((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/x^2)*y,
0,
1/x^2*y)
[6nsage: decomposition_g0_g8(ff.f)[0]
((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/x^2)*y
[6nsage: sage: Fxy, Rxy, x, y=C1.fct_field
[6nsage: decomposition_g0_g8(ff.f)[0] in Rxy
False
[6nsage: (C1.y/C1.x^2).expansion_at_infty()
t^-11 + 3*t^29 + 4*t^89 + t^109 + 2*t^129 + 2*t^149 + 4*t^169 + t^229 + 2*t^269 + t^289 + 2*t^309 + 3*t^329 + t^369 + 2*t^389 + 3*t^449 + t^469 + O(t^489)
sage: ff.f.coordinates()
[0, 3, 0, 0, 0, 0, 0]
sage: ff - 3*C1.cohomology_of_structure_sheaf_basis()[1]
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Cell In [63], line 1
----> 1 ff - Integer(3)*C1.cohomology_of_structure_sheaf_basis()[Integer(1)]
 
File <string>:35, in __sub__(self, other)
 
File <string>:29, in __add__(self, other)
 
AttributeError: 'superelliptic_function' object has no attribute 't'
[6nsage: aa = ff.f - 3*C1.cohomology_of_structure_sheaf_basis()[1]
[6nsasage: decomposition_g0_g8(aa)
(((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 1)/x^2)*y,
0,
2/x^2*y)
[6nsage: decomposition_g0_g8(ff.f)
(((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/x^2)*y,
0,
1/x^2*y)
[6nsage: ff.f.coordinates()
[0, 3, 0, 0, 0, 0, 0]
[6nsage: 3*C1.cohomology_of_structure_sheaf_basis()[1]
1/x^2*y
[6nsage: ff.f.coordinates()
[0, 3, 0, 0, 0, 0, 0]
[6nsage: aa.coordinates()
[0, 1, 0, 0, 0, 0, 0]
[6nsage: aa = ff.f + 3*C1.cohomology_of_structure_sheaf_basis()[1]
[6nsage: aa.coordinates()
[0, 0, 0, 0, 0, 0, 0]
sage: for b in C1.cohomology_of_structure_sheaf_basis():
....: print(b.coordinates())
....:
[4, 0, 0, 0, 0, 0, 0]
[0, 4, 0, 0, 0, 0, 0]
[0, 0, 4, 0, 0, 0, 0]
[0, 0, 0, 4, 0, 0, 0]
[0, 0, 0, 0, 4, 0, 0]
[0, 0, 0, 0, 0, 4, 0]
[0, 0, 0, 0, 0, 0, 4]
[6nsage: load('init.sage')
Computing 0. basis element
Computing 1. basis element
( [3*x*y] d[x] + [3*x^2 + 2] d[y] + V(((3*x^19 + 2*x^17 + x^15 + x^13 + 3*x^9 + 4*x^7 + x^5 + x^3 + x)*y) dx + (3*x^20 + 4*x^18 + 4*x^16 + 4*x^12 + 3*x^10 + x^8 + 2*x^6 + 4) dy) + dV(0), V((4*x^14 + x^12 + 3*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 4)*y) )
( [3*x^2*y] d[x] + [3*x^3 + 2*x] d[y] + V(((3*x^24 + 4*x^22 + x^20 + 3*x^18 + 3*x^16 + 3*x^10 + 2*x^8 + 3*x^4 + 3*x^2)*y) dx + (3*x^25 + x^23 + 2*x^21 + 2*x^19 + 2*x^15 + 3*x^11 + 4*x^9 + 3*x^7 + 3*x^5 + 2*x) dy) + dV(0), [2/x*y] + V(((4*x^20 + x^18 + 3*x^16 + 3*x^14 + x^12 + x^10 + 3*x^8 + 4*x^6 + 4*x^4 + 3*x^2 + 4)/x)*y) )
[6nsage: f1 = f(x = x^5 - x)
[6nsage: C1 = superelliptic(f1, m, prec = 500)
sage: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^743+ C1.x^72 + 3*C1.x^70 + C1.x^68 +
....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34
....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*Co.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1.
....: ne)/C1.x^2)*C1.y).verschiebung()
[6nsage: decomposition_g0_g8(ff.f)
((2*x^96 + 4*x^92 + x^90 + 3*x^88 + 4*x^84 + 2*x^82 + 4*x^80 + 2*x^76 + x^74 + 3*x^72 + x^70 + 3*x^68 + x^66 + 3*x^64 + 2*x^62 + 3*x^60 + x^58 + 4*x^54 + 3*x^52 + x^50 + 2*x^48 + x^46 + 3*x^44 + 2*x^42 + 4*x^36 + x^34 + 2*x^32 + 4*x^30 + x^28 + x^26 + 4*x^24 + 2*x^22 + 4*x^20 + 3*x^16 + 3*x^12 + 4*x^10 + 3*x^8 + 3*x^4 + 2*x^2 + 3)*y,
0,
4/x^2*y)
sage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller(
....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +
....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.7^55 + C1.x^53 + C1.x^51 + 4*C1.x^4
....: + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +
....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 +
....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x782 + C1.x^80 + 4*C1.x^78 + 4*C1.x^
....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1..^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1
....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2
....: + C1.one)*C1.y.diffn()).verschiebung()
[6nsage: xi = superelliptic_drw_cech(om, ff)
[6nsage: sage: xi.reduce()
(0, 0, 0) ((2*x^96 + 4*x^92 + x^90 + 3*x^88 + 4*x^84 + 2*x^82 + 4*x^80 + 2*x^76 + x^74 + 3*x^72 + x^70 + 3*x^68 + x^66 + 3*x^64 + 2*x^62 + 3*x^60 + x^58 + 4*x^54 + 3*x^52 + x^50 + 2*x^48 + x^46 + 3*x^44 + 2*x^42 + 4*x^36 + x^34 + 2*x^32 + 4*x^30 + x^28 + x^26 + 4*x^24 + 2*x^22 + 4*x^20 + 3*x^16 + 3*x^12 + 4*x^10 + 3*x^8 + 3*x^4 + 2*x^2 + 3)*y, 0, 4/x^2*y)
[(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^36 + 3*x^32 + 3*x^30 + 3*x^26 + x^24 + 3*x^18 + 2*x^16 + 2*x^14 + 3*x^12 + 4*x^10 + 2*x^8 + 2*x^6 + 3*x^4 + 4*x^2 + 2)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y])
([(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^36 + 3*x^32 + 3*x^30 + 3*x^26 + x^24 + 3*x^18 + 2*x^16 + 2*x^14 + 3*x^12 + 4*x^10 + 2*x^8 + 2*x^6 + 3*x^4 + 4*x^2 + 2)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(4/x^2*y), [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^32 + 3*x^30 + x^28 + 2*x^24 + 3*x^20 + 4*x^18 + 2*x^16 + 4*x^14 + 4*x^12 + 2*x^10 + 2*x^6 + 1)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y]))
[6nsage: xi.reduce()
(0, 0, 0) (0, 0, 4/x^2*y)
[(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^36 + 3*x^32 + 3*x^30 + 3*x^26 + x^24 + 3*x^18 + 2*x^16 + 2*x^14 + 3*x^12 + 4*x^10 + 2*x^8 + 2*x^6 + 3*x^4 + 4*x^2 + 2)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y])
([(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^36 + 3*x^32 + 3*x^30 + 3*x^26 + x^24 + 3*x^18 + 2*x^16 + 2*x^14 + 3*x^12 + 4*x^10 + 2*x^8 + 2*x^6 + 3*x^4 + 4*x^2 + 2)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(4/x^2*y), [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^32 + 3*x^30 + x^28 + 2*x^24 + 3*x^20 + 4*x^18 + 2*x^16 + 4*x^14 + 4*x^12 + 2*x^10 + 2*x^6 + 1)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y]))
[6nsage: xi.reduce()
(0, 0, 0) (0, 0, 4/x^2*y)
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Cell In [83], line 1
----> 1 xi.reduce()
 
File <string>:20, in reduce(self)
 
File <string>:73, in diffn(self, dy_w)
 
File <string>:177, in dy_w(C)
 
File /ext/sage/9.8/src/sage/rings/rational.pyx:2406, in sage.rings.rational.Rational.__mul__()
2404 return x
2405
-> 2406 return coercion_model.bin_op(left, right, operator.mul)
2407
2408 cpdef _mul_(self, right):
 
File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:48, in __rmul__(self, other)
 
File /ext/sage/9.8/src/sage/structure/element.pyx:1527, in sage.structure.element.Element.__mul__()
1525 if not err:
1526 return (<Element>right)._mul_long(value)
-> 1527 return coercion_model.bin_op(left, right, mul)
1528 except TypeError:
1529 return NotImplemented
 
File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:43, in __rmul__(self, other)
 
File /ext/sage/9.8/src/sage/structure/element.pyx:1527, in sage.structure.element.Element.__mul__()
1525 if not err:
1526 return (<Element>right)._mul_long(value)
-> 1527 return coercion_model.bin_op(left, right, mul)
1528 except TypeError:
1529 return NotImplemented
 
File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:43, in __rmul__(self, other)
 
[... skipping similar frames: __rmul__ at line 43 (6 times), sage.structure.coerce.CoercionModel.bin_op at line 1242 (6 times), sage.structure.element.Element.__mul__ at line 1527 (6 times)]
 
File /ext/sage/9.8/src/sage/structure/element.pyx:1527, in sage.structure.element.Element.__mul__()
1525 if not err:
1526 return (<Element>right)._mul_long(value)
-> 1527 return coercion_model.bin_op(left, right, mul)
1528 except TypeError:
1529 return NotImplemented
 
File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
1240 mul_method = getattr(y, '__r%s__'%op_name, None)
1241 if mul_method is not None:
-> 1242 res = mul_method(x)
1243 if res is not None and res is not NotImplemented:
1244 return res
 
File <string>:43, in __rmul__(self, other)
 
File <string>:31, in __add__(self, other)
 
File <string>:82, in __pow__(self, exp)
 
File <string>:14, in __init__(self, C, g)
 
File <string>:253, in reduction(C, g)
 
File /ext/sage/9.8/src/sage/structure/parent.pyx:896, in sage.structure.parent.Parent.__call__()
894 if mor is not None:
895 if no_extra_args:
--> 896 return mor._call_(x)
897 else:
898 return mor._call_with_args(x, args, kwds)
 
File /ext/sage/9.8/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
154 cdef Parent C = self._codomain
155 try:
--> 156 return C._element_constructor(x)
157 except Exception:
158 if print_warnings:
 
File /ext/sage/9.8/src/sage/rings/fraction_field.py:711, in FractionField_generic._element_constructor_(self, x, y, coerce)
708 raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
709 x0, y0, self))
710 try:
--> 711 return self._element_class(self, x, y, coerce=coerce)
712 except TypeError:
713 if parent(x) is parent(x0):
 
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
 
KeyboardInterrupt:
sage: class test:
....: ^Idef __init__(self, gg):
....: ^I^Iself.gg = gg
....: ^I
....: ^Idef aa(self):
....: ^I^Inew = self.gg
....: ^I^Inew += 1
....: ^I^Ireturn new
....:
[6nsage: D = test(1)
[6nsage: D.aa()
2
[6nsage: D
<__main__.test object at 0x7f22ef213390>
[6nsage: D.gg
1
[6nsage: load('init.sage')
Computing 0. basis element
Computing 1. basis element
( [3*x*y] d[x] + [3*x^2 + 2] d[y] + V(((3*x^19 + 2*x^17 + x^15 + x^13 + 3*x^9 + 4*x^7 + x^5 + x^3 + x)*y) dx + (3*x^20 + 4*x^18 + 4*x^16 + 4*x^12 + 3*x^10 + x^8 + 2*x^6 + 4) dy) + dV(0), V((4*x^14 + x^12 + 3*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 4)*y) )
( [3*x^2*y] d[x] + [3*x^3 + 2*x] d[y] + V(((3*x^24 + 4*x^22 + x^20 + 3*x^18 + 3*x^16 + 3*x^10 + 2*x^8 + 3*x^4 + 3*x^2)*y) dx + (3*x^25 + x^23 + 2*x^21 + 2*x^19 + 2*x^15 + 3*x^11 + 4*x^9 + 3*x^7 + 3*x^5 + 2*x) dy) + dV(0), [2/x*y] + V(((4*x^20 + x^18 + 3*x^16 + 3*x^14 + x^12 + x^10 + 3*x^8 + 4*x^6 + 4*x^4 + 3*x^2 + 4)/x)*y) )
sage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller(
....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +
....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.7^55 + C1.x^53 + C1.x^51 + 4*C1.x^4
....: + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +
....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 +
....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x782 + C1.x^80 + 4*C1.x^78 + 4*C1.x^
....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1..^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1
....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2
....: + C1.one)*C1.y.diffn()).verschiebung()
[6nsage: C2 = superelliptic(x^7 + x + 1, 2)
sage: for b in C2.cohomology_of_structure_sheaf_basis():
....: print(b.coordinates())
....:
[1, 0, 0]
[0, 1, 0]
[0, 0, 1]
sage: for b in C2.de_rham_basis():
....: print(b.coordinates())
....:
(1, 0, 0, 0, 0, 0)
(0, 1, 0, 0, 0, 0)
(0, 0, 1, 0, 0, 0)
(0, 0, 0, 1, 0, 0)
(0, 0, 0, 0, 1, 0)
(0, 0, 0, 0, 0, 1)
sage: for b in C2.holomorphic_differentials_basis():
....: print(b.coordinates())
....:
[1, 0, 0]
[0, 1, 0]
[0, 0, 1]
[6nsage: quit()
[23;0t
~/Research/2021 De Rham/DeRhamComputation/sage$ cd ..
~/Research/2021 De Rham/DeRhamComputation$ git add -u