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1, 6], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], 154 x 154 dense matrix over Finite Field of size 7]
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [51], 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>:4, 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>:14, in <module>

File <string>:24, in group_action_matrices_holo(AS)

File <string>:12, in group_action_matrices(space, list_of_group_elements)

TypeError: unsupported operand type(s) for +=: 'sage.matrix.matrix_modn_dense_float.Matrix_modn_dense_float' and 'list'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(),[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: matrix(GF(3), 3, 3)

[?7h[?12l[?25h[?2004l[?7h[0 0 0]
[0 0 0]
[0 0 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.fct_field[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l}[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmatrix(GF(3), 3, 3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAmatrix(GF(3), 3, 3)[?7h[?12l[?25h[?25l[?7l matrix(GF(3), 3, 3)[?7h[?12l[?25h[?25l[?7l=matrix(GF(3), 3, 3)[?7h[?12l[?25h[?25l[?7l matrix(GF(3), 3, 3)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A = matrix(GF(3), 3, 3)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = matrix(GF(3), 3, 3)[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: A[1, 2]

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[1, 2][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: A[1, 2] = 3

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[1, 2] = 3[?7h[?12l[?25h[?25l[?7lsage: A

[?7h[?12l[?25h[?2004l[?7h[0 0 0]
[0 0 0]
[0 0 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[1, 2] = 3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: A[1, 2] = 2

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[1, 2] = 2[?7h[?12l[?25h[?25l[?7lsage: A

[?7h[?12l[?25h[?2004l[?7h[0 0 0]
[0 0 2]
[0 0 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[1, 2] = 2[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A[:, 2] = vector([1, 1, 1])

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[:, 2] = vector([1, 1, 1])[?7h[?12l[?25h[?25l[?7lsage: A

[?7h[?12l[?25h[?2004l[?7h[0 0 1]
[0 0 1]
[0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1;3S[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7lini.sage')[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l(it.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
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>:7, 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>:2, in <module>

File <string>:73, in as_form()

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

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 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>:7, 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>:2, in <module>

File <string>:73, in as_form()

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

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 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>:7, 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>:2, in <module>

File <string>:73, in as_form()

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

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

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            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>:4, 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>:14, in <module>

File <string>:21, in group_action_matrices_holo(AS)

File <string>:10, in group_action_matrices(space, list_of_group_elements)

File <string>:77, in coordinates(self, basis)

AttributeError: 'as_form' object has no attribute 'holomorphic_differentials_basis'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lini.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ltess.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [7], 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>:4, 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>:14, in <module>

File <string>:21, in group_action_matrices_holo(AS)

File <string>:11, in group_action_matrices(space, list_of_group_elements)

TypeError: list indices must be integers or slices, not tuple
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lini.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ltess.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Input In [9], 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>:4, 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>:14, in <module>

File <string>:21, in group_action_matrices_holo(AS)

File <string>:11, in group_action_matrices(space, list_of_group_elements)

IndexError: list index out of range
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lini.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ltess.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004lWARNING: your terminal doesn't support cursor position requests (CPR).

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lini.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ltess.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

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KeyboardInterrupt

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

[?7h[?12l[?25h[?2004l^C^C
KeyboardInterrupt

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lini.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ltess.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

[?7h[?12l[?25h[?2004l0 0 [1, 0] (1) * dx
0 1 [1, 0] (z1) * dx
0 2 [1, 0] (z1^2) * dx
0 3 [1, 0] (z1^3) * dx
0 4 [1, 0] ((-3*x^2*z0^5*z1 - 2*x^2*z0^5 + 2*x^3*z0^3*z1 + 2*x^3*z0^3 + 3*x^4*z0*z1 + 3*x^2*y*z0^2*z1 - 3*x^4*z0 + 2*x^3*y*z1 + y*z1^4 + 3*x^3*y)/y) * dx
0 5 [1, 0] ((x^2*z0^5*z1 - x^2*z0^5 - 3*x^3*z0^3*z1 - x*z0*z1^5 + x^3*z0^3 - x^4*z0*z1 - x^2*y*z0^2*z1 + y*z1^5 + 2*x^4*z0 - 3*x^3*y*z1 - 2*x^3*y)/y) * dx
0 6 [1, 0] ((-3*z0^3*z1^6 - 3*x^2*z0^5*z1 + 2*x*z0*z1^6 - 3*x^2*z0^5 + 2*x^3*z0^3*z1 + y*z1^6 + 3*x^3*z0^3 + 3*x^4*z0*z1 + 3*x^2*y*z0^2*z1 - x^4*z0 + 2*x^3*y*z1 + x^3*y)/y) * dx
0 7 [1, 0] (z0) * dx
0 8 [1, 0] (z0*z1) * dx
0 9 [1, 0] (z0*z1^2) * dx
0 10 [1, 0] ((-x^2*z1^3 + y*z0*z1^3)/y) * dx
0 11 [1, 0] ((3*x^2*z0^6*z1 + 2*x^2*z0^6 - 3*x^3*z0^4*z1 - 3*x^3*z0^4 - 2*x^4*z0^2*z1 + x^2*y*z0^3*z1 + 2*x^4*z0^2 - x^5*z1 + 2*x^3*y*z0*z1 - x^2*z1^4 + y*z0*z1^4 + 3*x^5 + 3*x^3*y*z0 - x^2*z1^3)/y) * dx
0 12 [1, 0] ((-x^2*z0^6*z1 + x^2*z0^6 + x^3*z0^4*z1 + 3*x*z0^2*z1^5 + 2*x^3*z0^4 + 3*x^4*z0^2*z1 + 2*x^2*y*z0^3*z1 + 3*x^2*z1^5 + y*z0*z1^5 + x^4*z0^2 - 2*x^5*z1 - 3*x^3*y*z0*z1 - 2*x^5 - 2*x^3*y*z0 + x^2*z1^3)/y) * dx
0 13 [1, 0] ((z0^4*z1^6 + 3*x^2*z0^6*z1 + x*z0^2*z1^6 + 3*x^2*z0^6 - 3*x^3*z0^4*z1 - 3*x^2*z1^6 + y*z0*z1^6 - x^3*z0^4 - 2*x^4*z0^2*z1 + x^2*y*z0^3*z1 + 3*x^4*z0^2 - x^5*z1 + 2*x^3*y*z0*z1 + x^5 + x^3*y*z0 + x^2*z1^3)/y) * dx
0 14 [1, 0] (z0^2) * dx
0 15 [1, 0] (z0^2*z1) * dx
0 16 [1, 0] ((-x^2*z0*z1^2 + y*z0^2*z1^2)/y) * dx
0 17 [1, 0] ((3*x*z0^3*z1^3 + 3*x^2*z0*z1^3 + y*z0^2*z1^3)/y) * dx
0 18 [1, 0] ((-3*x^3*z0^5*z1 - 3*x*y*z0^6*z1 + 3*x^3*z0^5 - 3*x^4*z0^3*z1 - 3*x^2*y*z0^4*z1 + 3*x*z0^3*z1^4 + 2*x^4*z0^3 - x^2*y*z0^4 - 3*x^5*z0*z1 - 3*x^3*y*z0^2*z1 - 3*x*z0^3*z1^3 + 3*x^2*z0*z1^4 + y*z0^2*z1^4 + x^5*z0 - 2*x^3*y*z0^2 - 3*x^4*y*z1 + 3*x^2*z0*z1^3 - 3*x^4*y + x^2*z0*z1^2)/y) * dx
0 19 [1, 0] ((-2*x^3*z0^5*z1 - 2*x*y*z0^6*z1 + 2*x*z0^3*z1^5 - 3*x^3*z0^5 - 2*x^4*z0^3*z1 - 2*x^2*y*z0^4*z1 - x^2*z0*z1^5 + y*z0^2*z1^5 - 2*x^4*z0^3 + x^2*y*z0^4 - 2*x^5*z0*z1 - 2*x^3*y*z0^2*z1 + x*z0^3*z1^3 - 2*x*y*z1^5 - x^5*z0 + 2*x^3*y*z0^2 - 2*x^4*y*z1 - x^2*z0*z1^3 + 3*x^4*y - 2*x^2*z0*z1^2)/y) * dx
0 20 [1, 0] ((-z0^5*z1^6 + 3*x*z0^3*z1^6 - x^3*z0^5*z1 - x*y*z0^6*z1 + x^2*z0*z1^6 + y*z0^2*z1^6 - 2*x^3*z0^5 - x^4*z0^3*z1 - x^2*y*z0^4*z1 + 3*x*y*z1^6 + x^4*z0^3 + 3*x^2*y*z0^4 - x^5*z0*z1 - x^3*y*z0^2*z1 + x*z0^3*z1^3 - 3*x^5*z0 - x^3*y*z0^2 - x^4*y*z1 - x^2*z0*z1^3 + 2*x^4*y + 3*x^2*z0*z1^2)/y) * dx
0 21 [1, 0] (z0^3) * dx
0 22 [1, 0] ((y*z0^3*z1 - x^3*z1)/y) * dx
0 23 [1, 0] ((2*x^2*z0^2*z1^2 + y*z0^3*z1^2 - 3*x^3*z1^2)/y) * dx
0 24 [1, 0] ((-3*x*z0^4*z1^3 + x^2*z0^2*z1^3 + y*z0^3*z1^3 + x^3*z1^3)/y) * dx
0 25 [1, 0] ((-2*x*z0^4*z1^4 + 2*x^2*z0^2*z1^4 + y*z0^3*z1^4 - 2*x^3*z1^4 + x*y*z0*z1^4)/y) * dx
0 26 [1, 0] ((-2*x*z0^4*z1^5 + x^3*z0^6 + 3*x*z0^4*z1^4 + 2*x^2*z0^2*z1^5 + y*z0^3*z1^5 + x^4*z0^4 + x^2*y*z0^5 - 3*x*z0^4*z1^3 + 3*x^2*z0^2*z1^4 - 2*x^3*z1^5 + x*y*z0*z1^5 + x^5*z0^2 + x^3*y*z0^3 - x^2*z0^2*z1^3 - 2*x^3*z1^4 + 3*x*y*z0*z1^4 + x^6 + x^4*y*z0 + 3*x^2*z0^2*z1^2 - 3*x^3*z1^3 - 3*x^3*z1^2 + 2*x^3*z1)/y) * dx
0 27 [1, 0] ((3*z0^6*z1^6 - 3*x*z0^4*z1^6 - 2*x^2*z0^2*z1^6 + y*z0^3*z1^6 + 2*x^3*z0^6 - 2*x*z0^4*z1^4 - x^3*z1^6 + 2*x*y*z0*z1^6 + 2*x^4*z0^4 + 2*x^2*y*z0^5 - 2*x*z0^4*z1^3 - 2*x^2*z0^2*z1^4 + 2*x^5*z0^2 + 2*x^3*y*z0^3 - 3*x^2*z0^2*z1^3 - x^3*z1^4 - 2*x*y*z0*z1^4 + 2*x^6 + 2*x^4*y*z0 - 3*x^2*z0^2*z1^2 - 2*x^3*z1^3 + 3*x^3*z1^2 + 3*x^3*z1)/y) * dx
0 28 [1, 0] ((y*z0^4 - x^3*z0)/y) * dx
0 29 [1, 0] ((2*x^2*z0^3*z1 + y*z0^4*z1 - 3*x^3*z0*z1)/y) * dx
0 30 [1, 0] ((-2*x^2*z0^3*z1^2 + y*z0^4*z1^2 + 2*x^3*z0*z1^2 - x^2*y*z1^2)/y) * dx
0 31 [1, 0] ((-x*z0^5*z1^3 - x^2*z0^3*z1^3 + y*z0^4*z1^3 - 3*x^3*z0*z1^3 - 3*x^2*y*z1^3)/y) * dx
0 32 [1, 0] ((-3*x*z0^5*z1^4 - 2*x^2*z0^3*z1^4 + y*z0^4*z1^4 - x^3*z0*z1^4 + 2*x*y*z0^2*z1^4 + 3*x^2*y*z1^4)/y) * dx
0 33 [1, 0] ((-x^2*z0^4 + y*z0^5 + 3*x^3*z0^2 - 3*x^4)/y) * dx
0 34 [1, 0] ((-x^2*z0^4*z1 + y*z0^5*z1 + x^2*z0^4 + 3*x^3*z0^2*z1 - 2*x^3*z0^2 - 3*x^4*z1 + x^4)/y) * dx
0 35 [1, 0] ((x^2*z0^4*z1^2 + y*z0^5*z1^2 - 2*x^3*z0^2*z1^2 - 3*x^2*z0^4 - 2*x^4*z1^2 + 2*x^2*y*z0*z1^2 - x^3*z0^2 - 3*x^4)/y) * dx
0 36 [1, 0] ((-2*x*z0^6*z1^3 - 3*x^2*z0^4*z1^3 + y*z0^5*z1^3 + 3*x^3*z0^2*z1^3 + 2*x^4*z1^3 - x^2*y*z0*z1^3 + x^2*z0^4 - 2*x^3*z0^2 + x^4)/y) * dx
0 37 [1, 0] ((x*z0^6*z1^4 + x^2*z0^4*z1^4 + y*z0^5*z1^4 + x^3*z0^2*z1^4 + x*y*z0^3*z1^4 + x^4*z1^4 + x^2*y*z0*z1^4 - x^2*z0^4 + 2*x^3*z0^2 - x^4)/y) * dx
0 38 [1, 0] ((3*x^2*z0^5 + y*z0^6 - x^3*z0^3 + 3*x^4*z0 + x^3*y)/y) * dx
0 39 [1, 0] ((-3*x^2*z0^5*z1 + y*z0^6*z1 + 3*x^3*z0^3*z1 + 2*x^4*z0*z1 - x^2*y*z0^2*z1 - 2*x^3*y*z1)/y) * dx
0 40 [1, 0] ((-3*x^2*z0^5*z1^2 + y*z0^6*z1^2 - 2*x^2*z0^5*z1 + 3*x^3*z0^3*z1^2 + 3*x^2*z0^5 - x^3*z0^3*z1 + 2*x^4*z0*z1^2 - x^2*y*z0^2*z1^2 - 3*x^3*z0^3 + 2*x^4*z0*z1 + 2*x^2*y*z0^2*z1 - 2*x^3*y*z1^2 + x^4*z0 - x^3*y*z1 - x^3*y)/y) * dx
0 41 [1, 0] ((x^2*z0^5*z1^3 + y*z0^6*z1^3 + x^3*z0^3*z1^3 + x*y*z0^4*z1^3 + 3*x^2*z0^5*z1 + x^4*z0*z1^3 + x^2*y*z0^2*z1^3 + x^2*z0^5 - 2*x^3*z0^3*z1 + x^3*y*z1^3 - x^3*z0^3 - 3*x^4*z0*z1 - 3*x^2*y*z0^2*z1 - 2*x^4*z0 - 2*x^3*y*z1 + 2*x^3*y)/y) * dx
0 42 [1, 0] (1/y) * dx
0 43 [1, 0] (z1/y) * dx
0 44 [1, 0] (z1^2/y) * dx
0 45 [1, 0] (z1^3/y) * dx
0 46 [1, 0] (z1^4/y) * dx
0 47 [1, 0] (z1^5/y) * dx
0 48 [1, 0] (z1^6/y) * dx
0 49 [1, 0] (z0/y) * dx
0 50 [1, 0] (z0*z1/y) * dx
0 51 [1, 0] (z0*z1^2/y) * dx
0 52 [1, 0] (z0*z1^3/y) * dx
0 53 [1, 0] (z0*z1^4/y) * dx
0 54 [1, 0] (z0*z1^5/y) * dx
0 55 [1, 0] (z0*z1^6/y) * dx
0 56 [1, 0] (z0^2/y) * dx
0 57 [1, 0] (z0^2*z1/y) * dx
0 58 [1, 0] (z0^2*z1^2/y) * dx
0 59 [1, 0] (z0^2*z1^3/y) * dx
0 60 [1, 0] (z0^2*z1^4/y) * dx
0 61 [1, 0] ((z0^2*z1^5 - x^2*z0^4 + 2*x^3*z0^2 - x^4)/y) * dx
0 62 [1, 0] ((z0^2*z1^6 - x*z1^6 - x^2*z0^4 + 2*x^3*z0^2 - x^4)/y) * dx
0 63 [1, 0] (z0^3/y) * dx
0 64 [1, 0] (z0^3*z1/y) * dx
0 65 [1, 0] (z0^3*z1^2/y) * dx
0 66 [1, 0] (z0^3*z1^3/y) * dx
0 67 [1, 0] ((-3*x^2*z0^5*z1 - 2*x^2*z0^5 + 2*x^3*z0^3*z1 + z0^3*z1^4 + 2*x^3*z0^3 + 3*x^4*z0*z1 + 3*x^2*y*z0^2*z1 - 3*x^4*z0 + 2*x^3*y*z1 + 3*x^3*y)/y) * dx
0 68 [1, 0] ((-2*x^2*z0^5*z1 + z0^3*z1^5 + 2*x^2*z0^5 - x^3*z0^3*z1 - x*z0*z1^5 - 2*x^3*z0^3 + 2*x^4*z0*z1 + 2*x^2*y*z0^2*z1 + 3*x^4*z0 - x^3*y*z1 - 3*x^3*y)/y) * dx
0 69 [1, 0] (z0^4/y) * dx
0 70 [1, 0] (z0^4*z1/y) * dx
0 71 [1, 0] (z0^4*z1^2/y) * dx
0 72 [1, 0] ((z0^4*z1^3 - x^2*z1^3)/y) * dx
0 73 [1, 0] ((-2*x^2*z0^6*z1 + x^2*z0^6 + 2*x^3*z0^4*z1 + z0^4*z1^4 + 2*x^3*z0^4 - x^4*z0^2*z1 - 3*x^2*y*z0^3*z1 + x^4*z0^2 + 3*x^5*z1 + x^3*y*z0*z1 - x^2*z1^4 - 2*x^5 - 2*x^3*y*z0 + 3*x^2*z1^3)/y) * dx
0 74 [1, 0] ((x^2*z0^6*z1 + z0^4*z1^5 - x^2*z0^6 - x^3*z0^4*z1 - 2*x*z0^2*z1^5 - 2*x^3*z0^4 - 3*x^4*z0^2*z1 - 2*x^2*y*z0^3*z1 + x^2*z1^5 - x^4*z0^2 + 2*x^5*z1 + 3*x^3*y*z0*z1 + 2*x^5 + 2*x^3*y*z0 - x^2*z1^3)/y) * dx
0 75 [1, 0] (z0^5/y) * dx
0 76 [1, 0] (z0^5*z1/y) * dx
0 77 [1, 0] ((z0^5*z1^2 - x^2*z0*z1^2)/y) * dx
0 78 [1, 0] ((z0^5*z1^3 - 2*x*z0^3*z1^3 + x^2*z0*z1^3)/y) * dx
0 79 [1, 0] ((3*x^3*z0^5*z1 + 3*x*y*z0^6*z1 + z0^5*z1^4 - 3*x^3*z0^5 + 3*x^4*z0^3*z1 + 3*x^2*y*z0^4*z1 - 2*x*z0^3*z1^4 - 2*x^4*z0^3 + x^2*y*z0^4 + 3*x^5*z0*z1 + 3*x^3*y*z0^2*z1 + 3*x*z0^3*z1^3 + x^2*z0*z1^4 - x^5*z0 + 2*x^3*y*z0^2 + 3*x^4*y*z1 - 3*x^2*z0*z1^3 + 3*x^4*y - x^2*z0*z1^2)/y) * dx
0 80 [1, 0] ((z0^5*z1^5 - 2*x^3*z0^5*z1 - 2*x*y*z0^6*z1 - x*z0^3*z1^5 - 3*x^3*z0^5 - 2*x^4*z0^3*z1 - 2*x^2*y*z0^4*z1 - 2*x^2*z0*z1^5 - 2*x^4*z0^3 + x^2*y*z0^4 - 2*x^5*z0*z1 - 2*x^3*y*z0^2*z1 + x*z0^3*z1^3 + 2*x*y*z1^5 - x^5*z0 + 2*x^3*y*z0^2 - 2*x^4*y*z1 - x^2*z0*z1^3 + 3*x^4*y - 2*x^2*z0*z1^2)/y) * dx
0 81 [1, 0] (z0^6/y) * dx
0 82 [1, 0] ((z0^6*z1 - x^3*z1)/y) * dx
0 83 [1, 0] ((z0^6*z1^2 - 3*x^2*z0^2*z1^2 + 2*x^3*z1^2)/y) * dx
0 84 [1, 0] ((z0^6*z1^3 - 3*x*z0^4*z1^3 + 3*x^2*z0^2*z1^3 - x^3*z1^3)/y) * dx
0 85 [1, 0] ((z0^6*z1^4 + 2*x*z0^4*z1^4 + x^2*z0^2*z1^4 - 2*x^3*z1^4 - 2*x*y*z0*z1^4)/y) * dx
0 86 [1, 0] ((z0^6*z1^5 + 2*x*z0^4*z1^5 + 2*x^3*z0^6 - x*z0^4*z1^4 + x^2*z0^2*z1^5 + 2*x^4*z0^4 + 2*x^2*y*z0^5 + x*z0^4*z1^3 - x^2*z0^2*z1^4 - 2*x^3*z1^5 - 2*x*y*z0*z1^5 + 2*x^5*z0^2 + 2*x^3*y*z0^3 - 2*x^2*z0^2*z1^3 + 3*x^3*z1^4 - x*y*z0*z1^4 + 2*x^6 + 2*x^4*y*z0 - x^2*z0^2*z1^2 + x^3*z1^3 + x^3*z1^2 - 3*x^3*z1)/y) * dx
0 87 [1, 0] (x) * dx
0 88 [1, 0] (x*z1) * dx
0 89 [1, 0] ((-x^2*z0*z1^2 + x*y*z1^2)/y) * dx
0 90 [1, 0] ((-3*x*z0^3*z1^3 + 2*x^2*z0*z1^3 + x*y*z1^3)/y) * dx
0 91 [1, 0] ((2*x^3*z0^5*z1 + 2*x*y*z0^6*z1 - 2*x^3*z0^5 + 2*x^4*z0^3*z1 + 2*x^2*y*z0^4*z1 - 3*x*z0^3*z1^4 + x^4*z0^3 + 3*x^2*y*z0^4 + 2*x^5*z0*z1 + 2*x^3*y*z0^2*z1 + 2*x*z0^3*z1^3 + 2*x^2*z0*z1^4 - 3*x^5*z0 - x^3*y*z0^2 + 2*x^4*y*z1 - 2*x^2*z0*z1^3 + x*y*z1^4 + 2*x^4*y - 3*x^2*z0*z1^2)/y) * dx
0 92 [1, 0] (x*z0) * dx
0 93 [1, 0] ((-x^3*z1 + x*y*z0*z1)/y) * dx
0 94 [1, 0] ((3*x^2*z0^2*z1^2 + 3*x^3*z1^2 + x*y*z0*z1^2)/y) * dx
0 95 [1, 0] ((x*z0^4*z1^3 + x^2*z0^2*z1^3 - 3*x^3*z1^3 + x*y*z0*z1^3)/y) * dx
0 96 [1, 0] ((-x^3*z0 + x*y*z0^2)/y) * dx
0 97 [1, 0] ((3*x^2*z0^3*z1 + 3*x^3*z0*z1 + x*y*z0^2*z1)/y) * dx
0 98 [1, 0] ((2*x^2*z0^3*z1^2 - x^3*z0*z1^2 + x*y*z0^2*z1^2 - 2*x^2*y*z1^2)/y) * dx
0 99 [1, 0] ((-x*z0^5*z1^3 + 3*x^2*z0^3*z1^3 + x^3*z0*z1^3 + x*y*z0^2*z1^3 + 3*x^2*y*z1^3)/y) * dx
0 100 [1, 0] ((-3*x^2*z0^4 + x^3*z0^2 + x*y*z0^3 + x^4)/y) * dx
0 101 [1, 0] ((-3*x^2*z0^4*z1 - 3*x^2*z0^4 + x^3*z0^2*z1 + x*y*z0^3*z1 - x^3*z0^2 + x^4*z1 - 3*x^4)/y) * dx
0 102 [1, 0] ((-2*x^2*z0^4*z1^2 + 2*x^3*z0^2*z1^2 + x*y*z0^3*z1^2 + x^2*z0^4 - 2*x^4*z1^2 + x^2*y*z0*z1^2 - 2*x^3*z0^2 + x^4)/y) * dx
0 103 [1, 0] ((3*x*z0^6*z1^3 - 3*x^2*z0^4*z1^3 - 2*x^3*z0^2*z1^3 + x*y*z0^3*z1^3 - x^4*z1^3 + 2*x^2*y*z0*z1^3 - x^2*z0^4 + 2*x^3*z0^2 - x^4)/y) * dx
0 104 [1, 0] ((-x^2*z0^5 - x^3*z0^3 + x*y*z0^4 - 3*x^4*z0 - 3*x^3*y)/y) * dx
0 105 [1, 0] ((-3*x^2*z0^5*z1 - 2*x^3*z0^3*z1 + x*y*z0^4*z1 - x^4*z0*z1 + 2*x^2*y*z0^2*z1 + 3*x^3*y*z1)/y) * dx
0 106 [1, 0] ((-3*x^2*z0^5*z1^2 + 2*x^2*z0^5*z1 - 2*x^3*z0^3*z1^2 + x*y*z0^4*z1^2 - 3*x^2*z0^5 + x^3*z0^3*z1 - x^4*z0*z1^2 + 2*x^2*y*z0^2*z1^2 + 3*x^3*z0^3 - 2*x^4*z0*z1 - 2*x^2*y*z0^2*z1 + 3*x^3*y*z1^2 - x^4*z0 + x^3*y*z1 + x^3*y)/y) * dx
0 107 [1, 0] ((-2*x^2*z0^6 - 3*x^3*z0^4 + x*y*z0^5 + 3*x^4*z0^2 + 2*x^5 - x^3*y*z0)/y) * dx
0 108 [1, 0] ((x^2*z0^6*z1 + x^3*z0^4*z1 + x*y*z0^5*z1 + x^4*z0^2*z1 + x^2*y*z0^3*z1 + x^5*z1 + x^3*y*z0*z1)/y) * dx
0 109 [1, 0] ((x^2*z0^6*z1^2 - 3*x^2*z0^6*z1 + x^3*z0^4*z1^2 + x*y*z0^5*z1^2 + x^2*z0^6 + 3*x^3*z0^4*z1 + x^4*z0^2*z1^2 + x^2*y*z0^3*z1^2 + 2*x^3*z0^4 + 2*x^4*z0^2*z1 - x^2*y*z0^3*z1 + x^5*z1^2 + x^3*y*z0*z1^2 + x^4*z0^2 + x^5*z1 - 2*x^3*y*z0*z1 - 2*x^5 - 2*x^3*y*z0 + 2*x^2*z1^3)/y) * dx
0 110 [1, 0] ((x^3*z0^5 + x*y*z0^6 + x^4*z0^3 + x^2*y*z0^4 + x^5*z0 + x^3*y*z0^2 + x^4*y)/y) * dx
0 111 [1, 0] (x/y) * dx
0 112 [1, 0] (x*z1/y) * dx
0 113 [1, 0] (x*z1^2/y) * dx
0 114 [1, 0] (x*z1^3/y) * dx
0 115 [1, 0] (x*z1^4/y) * dx
0 116 [1, 0] ((-x^2*z0^4 + x*z1^5 + 2*x^3*z0^2 - x^4)/y) * dx
0 117 [1, 0] (x*z0/y) * dx
0 118 [1, 0] (x*z0*z1/y) * dx
0 119 [1, 0] (x*z0*z1^2/y) * dx
0 120 [1, 0] (x*z0*z1^3/y) * dx
0 121 [1, 0] ((-3*x^2*z0^5*z1 - 2*x^2*z0^5 + 2*x^3*z0^3*z1 + 2*x^3*z0^3 + 3*x^4*z0*z1 + 3*x^2*y*z0^2*z1 + x*z0*z1^4 - 3*x^4*z0 + 2*x^3*y*z1 + 3*x^3*y)/y) * dx
0 122 [1, 0] (x*z0^2/y) * dx
0 123 [1, 0] (x*z0^2*z1/y) * dx
0 124 [1, 0] (x*z0^2*z1^2/y) * dx
0 125 [1, 0] ((x*z0^2*z1^3 - x^2*z1^3)/y) * dx
0 126 [1, 0] ((-x^2*z0^6*z1 - 3*x^2*z0^6 + x^3*z0^4*z1 + x^3*z0^4 + 3*x^4*z0^2*z1 + 2*x^2*y*z0^3*z1 + x*z0^2*z1^4 - 3*x^4*z0^2 - 2*x^5*z1 - 3*x^3*y*z0*z1 - x^2*z1^4 - x^5 - x^3*y*z0 - 2*x^2*z1^3)/y) * dx
0 127 [1, 0] (x*z0^3/y) * dx
0 128 [1, 0] (x*z0^3*z1/y) * dx
0 129 [1, 0] ((x*z0^3*z1^2 - x^2*z0*z1^2)/y) * dx
0 130 [1, 0] (x*z0^4/y) * dx
0 131 [1, 0] ((x*z0^4*z1 - x^3*z1)/y) * dx
0 132 [1, 0] ((x*z0^4*z1^2 - 2*x^2*z0^2*z1^2 + x^3*z1^2)/y) * dx
0 133 [1, 0] ((x*z0^5 - x^3*z0)/y) * dx
0 134 [1, 0] ((x*z0^5*z1 - 2*x^2*z0^3*z1 + x^3*z0*z1)/y) * dx
0 135 [1, 0] ((x*z0^5*z1^2 - x^2*z0^3*z1^2 - 2*x^3*z0*z1^2 + 2*x^2*y*z1^2)/y) * dx
0 136 [1, 0] ((x*z0^6 - 3*x^2*z0^4 + 3*x^3*z0^2 - x^4)/y) * dx
0 137 [1, 0] ((x*z0^6*z1 - 3*x^2*z0^4*z1 - x^2*z0^4 + 3*x^3*z0^2*z1 + 2*x^3*z0^2 - x^4*z1 - x^4)/y) * dx
0 138 [1, 0] ((x*z0^6*z1^2 + 2*x^2*z0^4*z1^2 + x^3*z0^2*z1^2 + 2*x^2*z0^4 - 2*x^4*z1^2 - 2*x^2*y*z0*z1^2 + 3*x^3*z0^2 + 2*x^4)/y) * dx
0 139 [1, 0] ((-x^3*z0 + x^2*y)/y) * dx
0 140 [1, 0] ((-3*x^2*z0^3*z1 + 2*x^3*z0*z1 + x^2*y*z1)/y) * dx
0 141 [1, 0] ((x^2*z0^4 + x^3*z0^2 - 3*x^4 + x^2*y*z0)/y) * dx
0 142 [1, 0] ((x^2*z0^4*z1 + 3*x^2*z0^4 + x^3*z0^2*z1 + x^3*z0^2 - 3*x^4*z1 + x^2*y*z0*z1 + 3*x^4)/y) * dx
0 143 [1, 0] ((-x^2*z0^5 + 3*x^3*z0^3 + x^4*z0 + x^2*y*z0^2 + 3*x^3*y)/y) * dx
0 144 [1, 0] ((3*x^2*z0^6 - 3*x^3*z0^4 - 2*x^4*z0^2 + x^2*y*z0^3 - x^5 + 2*x^3*y*z0)/y) * dx
0 145 [1, 0] (x^2/y) * dx
0 146 [1, 0] (x^2*z1/y) * dx
0 147 [1, 0] (x^2*z1^2/y) * dx
0 148 [1, 0] (x^2*z0/y) * dx
0 149 [1, 0] (x^2*z0*z1/y) * dx
0 150 [1, 0] (x^2*z0^2/y) * dx
0 151 [1, 0] ((x^2*z0^2*z1 - x^3*z1)/y) * dx
0 152 [1, 0] ((x^2*z0^3 - x^3*z0)/y) * dx
0 153 [1, 0] (x^3/y) * dx
1 0 [0, 1] (1) * dx
1 1 [0, 1] (z1) * dx
1 2 [0, 1] (z1^2) * dx
1 3 [0, 1] (z1^3) * dx
1 4 [0, 1] ((-3*x^2*z0^5*z1 - 2*x^2*z0^5 + 2*x^3*z0^3*z1 + 2*x^3*z0^3 + 3*x^4*z0*z1 + 3*x^2*y*z0^2*z1 - 3*x^4*z0 + 2*x^3*y*z1 + y*z1^4 + 3*x^3*y)/y) * dx
1 5 [0, 1] ((x^2*z0^5*z1 - x^2*z0^5 - 3*x^3*z0^3*z1 - x*z0*z1^5 + x^3*z0^3 - x^4*z0*z1 - x^2*y*z0^2*z1 + y*z1^5 + 2*x^4*z0 - 3*x^3*y*z1 - 2*x^3*y)/y) * dx
1 6 [0, 1] ((-3*z0^3*z1^6 - 3*x^2*z0^5*z1 + 2*x*z0*z1^6 - 3*x^2*z0^5 + 2*x^3*z0^3*z1 + y*z1^6 + 3*x^3*z0^3 + 3*x^4*z0*z1 + 3*x^2*y*z0^2*z1 - x^4*z0 + 2*x^3*y*z1 + x^3*y)/y) * dx
1 7 [0, 1] (z0) * dx
1 8 [0, 1] (z0*z1) * dx
1 9 [0, 1] (z0*z1^2) * dx
1 10 [0, 1] ((-x^2*z1^3 + y*z0*z1^3)/y) * dx
1 11 [0, 1] ((3*x^2*z0^6*z1 + 2*x^2*z0^6 - 3*x^3*z0^4*z1 - 3*x^3*z0^4 - 2*x^4*z0^2*z1 + x^2*y*z0^3*z1 + 2*x^4*z0^2 - x^5*z1 + 2*x^3*y*z0*z1 - x^2*z1^4 + y*z0*z1^4 + 3*x^5 + 3*x^3*y*z0 - x^2*z1^3)/y) * dx
1 12 [0, 1] ((-x^2*z0^6*z1 + x^2*z0^6 + x^3*z0^4*z1 + 3*x*z0^2*z1^5 + 2*x^3*z0^4 + 3*x^4*z0^2*z1 + 2*x^2*y*z0^3*z1 + 3*x^2*z1^5 + y*z0*z1^5 + x^4*z0^2 - 2*x^5*z1 - 3*x^3*y*z0*z1 - 2*x^5 - 2*x^3*y*z0 + x^2*z1^3)/y) * dx
1 13 [0, 1] ((z0^4*z1^6 + 3*x^2*z0^6*z1 + x*z0^2*z1^6 + 3*x^2*z0^6 - 3*x^3*z0^4*z1 - 3*x^2*z1^6 + y*z0*z1^6 - x^3*z0^4 - 2*x^4*z0^2*z1 + x^2*y*z0^3*z1 + 3*x^4*z0^2 - x^5*z1 + 2*x^3*y*z0*z1 + x^5 + x^3*y*z0 + x^2*z1^3)/y) * dx
1 14 [0, 1] (z0^2) * dx
1 15 [0, 1] (z0^2*z1) * dx
1 16 [0, 1] ((-x^2*z0*z1^2 + y*z0^2*z1^2)/y) * dx
1 17 [0, 1] ((3*x*z0^3*z1^3 + 3*x^2*z0*z1^3 + y*z0^2*z1^3)/y) * dx
1 18 [0, 1] ((-3*x^3*z0^5*z1 - 3*x*y*z0^6*z1 + 3*x^3*z0^5 - 3*x^4*z0^3*z1 - 3*x^2*y*z0^4*z1 + 3*x*z0^3*z1^4 + 2*x^4*z0^3 - x^2*y*z0^4 - 3*x^5*z0*z1 - 3*x^3*y*z0^2*z1 - 3*x*z0^3*z1^3 + 3*x^2*z0*z1^4 + y*z0^2*z1^4 + x^5*z0 - 2*x^3*y*z0^2 - 3*x^4*y*z1 + 3*x^2*z0*z1^3 - 3*x^4*y + x^2*z0*z1^2)/y) * dx
1 19 [0, 1] ((-2*x^3*z0^5*z1 - 2*x*y*z0^6*z1 + 2*x*z0^3*z1^5 - 3*x^3*z0^5 - 2*x^4*z0^3*z1 - 2*x^2*y*z0^4*z1 - x^2*z0*z1^5 + y*z0^2*z1^5 - 2*x^4*z0^3 + x^2*y*z0^4 - 2*x^5*z0*z1 - 2*x^3*y*z0^2*z1 + x*z0^3*z1^3 - 2*x*y*z1^5 - x^5*z0 + 2*x^3*y*z0^2 - 2*x^4*y*z1 - x^2*z0*z1^3 + 3*x^4*y - 2*x^2*z0*z1^2)/y) * dx
1 20 [0, 1] ((-z0^5*z1^6 + 3*x*z0^3*z1^6 - x^3*z0^5*z1 - x*y*z0^6*z1 + x^2*z0*z1^6 + y*z0^2*z1^6 - 2*x^3*z0^5 - x^4*z0^3*z1 - x^2*y*z0^4*z1 + 3*x*y*z1^6 + x^4*z0^3 + 3*x^2*y*z0^4 - x^5*z0*z1 - x^3*y*z0^2*z1 + x*z0^3*z1^3 - 3*x^5*z0 - x^3*y*z0^2 - x^4*y*z1 - x^2*z0*z1^3 + 2*x^4*y + 3*x^2*z0*z1^2)/y) * dx
1 21 [0, 1] (z0^3) * dx
1 22 [0, 1] ((y*z0^3*z1 - x^3*z1)/y) * dx
1 23 [0, 1] ((2*x^2*z0^2*z1^2 + y*z0^3*z1^2 - 3*x^3*z1^2)/y) * dx
1 24 [0, 1] ((-3*x*z0^4*z1^3 + x^2*z0^2*z1^3 + y*z0^3*z1^3 + x^3*z1^3)/y) * dx
1 25 [0, 1] ((-2*x*z0^4*z1^4 + 2*x^2*z0^2*z1^4 + y*z0^3*z1^4 - 2*x^3*z1^4 + x*y*z0*z1^4)/y) * dx
1 26 [0, 1] ((-2*x*z0^4*z1^5 + x^3*z0^6 + 3*x*z0^4*z1^4 + 2*x^2*z0^2*z1^5 + y*z0^3*z1^5 + x^4*z0^4 + x^2*y*z0^5 - 3*x*z0^4*z1^3 + 3*x^2*z0^2*z1^4 - 2*x^3*z1^5 + x*y*z0*z1^5 + x^5*z0^2 + x^3*y*z0^3 - x^2*z0^2*z1^3 - 2*x^3*z1^4 + 3*x*y*z0*z1^4 + x^6 + x^4*y*z0 + 3*x^2*z0^2*z1^2 - 3*x^3*z1^3 - 3*x^3*z1^2 + 2*x^3*z1)/y) * dx
1 27 [0, 1] ((3*z0^6*z1^6 - 3*x*z0^4*z1^6 - 2*x^2*z0^2*z1^6 + y*z0^3*z1^6 + 2*x^3*z0^6 - 2*x*z0^4*z1^4 - x^3*z1^6 + 2*x*y*z0*z1^6 + 2*x^4*z0^4 + 2*x^2*y*z0^5 - 2*x*z0^4*z1^3 - 2*x^2*z0^2*z1^4 + 2*x^5*z0^2 + 2*x^3*y*z0^3 - 3*x^2*z0^2*z1^3 - x^3*z1^4 - 2*x*y*z0*z1^4 + 2*x^6 + 2*x^4*y*z0 - 3*x^2*z0^2*z1^2 - 2*x^3*z1^3 + 3*x^3*z1^2 + 3*x^3*z1)/y) * dx
1 28 [0, 1] ((y*z0^4 - x^3*z0)/y) * dx
1 29 [0, 1] ((2*x^2*z0^3*z1 + y*z0^4*z1 - 3*x^3*z0*z1)/y) * dx
1 30 [0, 1] ((-2*x^2*z0^3*z1^2 + y*z0^4*z1^2 + 2*x^3*z0*z1^2 - x^2*y*z1^2)/y) * dx
1 31 [0, 1] ((-x*z0^5*z1^3 - x^2*z0^3*z1^3 + y*z0^4*z1^3 - 3*x^3*z0*z1^3 - 3*x^2*y*z1^3)/y) * dx
1 32 [0, 1] ((-3*x*z0^5*z1^4 - 2*x^2*z0^3*z1^4 + y*z0^4*z1^4 - x^3*z0*z1^4 + 2*x*y*z0^2*z1^4 + 3*x^2*y*z1^4)/y) * dx
1 33 [0, 1] ((-x^2*z0^4 + y*z0^5 + 3*x^3*z0^2 - 3*x^4)/y) * dx
1 34 [0, 1] ((-x^2*z0^4*z1 + y*z0^5*z1 + x^2*z0^4 + 3*x^3*z0^2*z1 - 2*x^3*z0^2 - 3*x^4*z1 + x^4)/y) * dx
1 35 [0, 1] ((x^2*z0^4*z1^2 + y*z0^5*z1^2 - 2*x^3*z0^2*z1^2 - 3*x^2*z0^4 - 2*x^4*z1^2 + 2*x^2*y*z0*z1^2 - x^3*z0^2 - 3*x^4)/y) * dx
1 36 [0, 1] ((-2*x*z0^6*z1^3 - 3*x^2*z0^4*z1^3 + y*z0^5*z1^3 + 3*x^3*z0^2*z1^3 + 2*x^4*z1^3 - x^2*y*z0*z1^3 + x^2*z0^4 - 2*x^3*z0^2 + x^4)/y) * dx
1 37 [0, 1] ((x*z0^6*z1^4 + x^2*z0^4*z1^4 + y*z0^5*z1^4 + x^3*z0^2*z1^4 + x*y*z0^3*z1^4 + x^4*z1^4 + x^2*y*z0*z1^4 - x^2*z0^4 + 2*x^3*z0^2 - x^4)/y) * dx
1 38 [0, 1] ((3*x^2*z0^5 + y*z0^6 - x^3*z0^3 + 3*x^4*z0 + x^3*y)/y) * dx
1 39 [0, 1] ((-3*x^2*z0^5*z1 + y*z0^6*z1 + 3*x^3*z0^3*z1 + 2*x^4*z0*z1 - x^2*y*z0^2*z1 - 2*x^3*y*z1)/y) * dx
1 40 [0, 1] ((-3*x^2*z0^5*z1^2 + y*z0^6*z1^2 - 2*x^2*z0^5*z1 + 3*x^3*z0^3*z1^2 + 3*x^2*z0^5 - x^3*z0^3*z1 + 2*x^4*z0*z1^2 - x^2*y*z0^2*z1^2 - 3*x^3*z0^3 + 2*x^4*z0*z1 + 2*x^2*y*z0^2*z1 - 2*x^3*y*z1^2 + x^4*z0 - x^3*y*z1 - x^3*y)/y) * dx
1 41 [0, 1] ((x^2*z0^5*z1^3 + y*z0^6*z1^3 + x^3*z0^3*z1^3 + x*y*z0^4*z1^3 + 3*x^2*z0^5*z1 + x^4*z0*z1^3 + x^2*y*z0^2*z1^3 + x^2*z0^5 - 2*x^3*z0^3*z1 + x^3*y*z1^3 - x^3*z0^3 - 3*x^4*z0*z1 - 3*x^2*y*z0^2*z1 - 2*x^4*z0 - 2*x^3*y*z1 + 2*x^3*y)/y) * dx
1 42 [0, 1] (1/y) * dx
1 43 [0, 1] (z1/y) * dx
1 44 [0, 1] (z1^2/y) * dx
1 45 [0, 1] (z1^3/y) * dx
1 46 [0, 1] (z1^4/y) * dx
1 47 [0, 1] (z1^5/y) * dx
1 48 [0, 1] (z1^6/y) * dx
1 49 [0, 1] (z0/y) * dx
1 50 [0, 1] (z0*z1/y) * dx
1 51 [0, 1] (z0*z1^2/y) * dx
1 52 [0, 1] (z0*z1^3/y) * dx
1 53 [0, 1] (z0*z1^4/y) * dx
1 54 [0, 1] (z0*z1^5/y) * dx
1 55 [0, 1] (z0*z1^6/y) * dx
1 56 [0, 1] (z0^2/y) * dx
1 57 [0, 1] (z0^2*z1/y) * dx
1 58 [0, 1] (z0^2*z1^2/y) * dx
1 59 [0, 1] (z0^2*z1^3/y) * dx
1 60 [0, 1] (z0^2*z1^4/y) * dx
1 61 [0, 1] ((z0^2*z1^5 - x^2*z0^4 + 2*x^3*z0^2 - x^4)/y) * dx
1 62 [0, 1] ((z0^2*z1^6 - x*z1^6 - x^2*z0^4 + 2*x^3*z0^2 - x^4)/y) * dx
1 63 [0, 1] (z0^3/y) * dx
1 64 [0, 1] (z0^3*z1/y) * dx
1 65 [0, 1] (z0^3*z1^2/y) * dx
1 66 [0, 1] (z0^3*z1^3/y) * dx
1 67 [0, 1] ((-3*x^2*z0^5*z1 - 2*x^2*z0^5 + 2*x^3*z0^3*z1 + z0^3*z1^4 + 2*x^3*z0^3 + 3*x^4*z0*z1 + 3*x^2*y*z0^2*z1 - 3*x^4*z0 + 2*x^3*y*z1 + 3*x^3*y)/y) * dx
1 68 [0, 1] ((-2*x^2*z0^5*z1 + z0^3*z1^5 + 2*x^2*z0^5 - x^3*z0^3*z1 - x*z0*z1^5 - 2*x^3*z0^3 + 2*x^4*z0*z1 + 2*x^2*y*z0^2*z1 + 3*x^4*z0 - x^3*y*z1 - 3*x^3*y)/y) * dx
1 69 [0, 1] (z0^4/y) * dx
1 70 [0, 1] (z0^4*z1/y) * dx
1 71 [0, 1] (z0^4*z1^2/y) * dx
1 72 [0, 1] ((z0^4*z1^3 - x^2*z1^3)/y) * dx
1 73 [0, 1] ((-2*x^2*z0^6*z1 + x^2*z0^6 + 2*x^3*z0^4*z1 + z0^4*z1^4 + 2*x^3*z0^4 - x^4*z0^2*z1 - 3*x^2*y*z0^3*z1 + x^4*z0^2 + 3*x^5*z1 + x^3*y*z0*z1 - x^2*z1^4 - 2*x^5 - 2*x^3*y*z0 + 3*x^2*z1^3)/y) * dx
1 74 [0, 1] ((x^2*z0^6*z1 + z0^4*z1^5 - x^2*z0^6 - x^3*z0^4*z1 - 2*x*z0^2*z1^5 - 2*x^3*z0^4 - 3*x^4*z0^2*z1 - 2*x^2*y*z0^3*z1 + x^2*z1^5 - x^4*z0^2 + 2*x^5*z1 + 3*x^3*y*z0*z1 + 2*x^5 + 2*x^3*y*z0 - x^2*z1^3)/y) * dx
1 75 [0, 1] (z0^5/y) * dx
1 76 [0, 1] (z0^5*z1/y) * dx
1 77 [0, 1] ((z0^5*z1^2 - x^2*z0*z1^2)/y) * dx
1 78 [0, 1] ((z0^5*z1^3 - 2*x*z0^3*z1^3 + x^2*z0*z1^3)/y) * dx
1 79 [0, 1] ((3*x^3*z0^5*z1 + 3*x*y*z0^6*z1 + z0^5*z1^4 - 3*x^3*z0^5 + 3*x^4*z0^3*z1 + 3*x^2*y*z0^4*z1 - 2*x*z0^3*z1^4 - 2*x^4*z0^3 + x^2*y*z0^4 + 3*x^5*z0*z1 + 3*x^3*y*z0^2*z1 + 3*x*z0^3*z1^3 + x^2*z0*z1^4 - x^5*z0 + 2*x^3*y*z0^2 + 3*x^4*y*z1 - 3*x^2*z0*z1^3 + 3*x^4*y - x^2*z0*z1^2)/y) * dx
1 80 [0, 1] ((z0^5*z1^5 - 2*x^3*z0^5*z1 - 2*x*y*z0^6*z1 - x*z0^3*z1^5 - 3*x^3*z0^5 - 2*x^4*z0^3*z1 - 2*x^2*y*z0^4*z1 - 2*x^2*z0*z1^5 - 2*x^4*z0^3 + x^2*y*z0^4 - 2*x^5*z0*z1 - 2*x^3*y*z0^2*z1 + x*z0^3*z1^3 + 2*x*y*z1^5 - x^5*z0 + 2*x^3*y*z0^2 - 2*x^4*y*z1 - x^2*z0*z1^3 + 3*x^4*y - 2*x^2*z0*z1^2)/y) * dx
1 81 [0, 1] (z0^6/y) * dx
1 82 [0, 1] ((z0^6*z1 - x^3*z1)/y) * dx
1 83 [0, 1] ((z0^6*z1^2 - 3*x^2*z0^2*z1^2 + 2*x^3*z1^2)/y) * dx
1 84 [0, 1] ((z0^6*z1^3 - 3*x*z0^4*z1^3 + 3*x^2*z0^2*z1^3 - x^3*z1^3)/y) * dx
1 85 [0, 1] ((z0^6*z1^4 + 2*x*z0^4*z1^4 + x^2*z0^2*z1^4 - 2*x^3*z1^4 - 2*x*y*z0*z1^4)/y) * dx
1 86 [0, 1] ((z0^6*z1^5 + 2*x*z0^4*z1^5 + 2*x^3*z0^6 - x*z0^4*z1^4 + x^2*z0^2*z1^5 + 2*x^4*z0^4 + 2*x^2*y*z0^5 + x*z0^4*z1^3 - x^2*z0^2*z1^4 - 2*x^3*z1^5 - 2*x*y*z0*z1^5 + 2*x^5*z0^2 + 2*x^3*y*z0^3 - 2*x^2*z0^2*z1^3 + 3*x^3*z1^4 - x*y*z0*z1^4 + 2*x^6 + 2*x^4*y*z0 - x^2*z0^2*z1^2 + x^3*z1^3 + x^3*z1^2 - 3*x^3*z1)/y) * dx
1 87 [0, 1] (x) * dx
1 88 [0, 1] (x*z1) * dx
1 89 [0, 1] ((-x^2*z0*z1^2 + x*y*z1^2)/y) * dx
1 90 [0, 1] ((-3*x*z0^3*z1^3 + 2*x^2*z0*z1^3 + x*y*z1^3)/y) * dx
1 91 [0, 1] ((2*x^3*z0^5*z1 + 2*x*y*z0^6*z1 - 2*x^3*z0^5 + 2*x^4*z0^3*z1 + 2*x^2*y*z0^4*z1 - 3*x*z0^3*z1^4 + x^4*z0^3 + 3*x^2*y*z0^4 + 2*x^5*z0*z1 + 2*x^3*y*z0^2*z1 + 2*x*z0^3*z1^3 + 2*x^2*z0*z1^4 - 3*x^5*z0 - x^3*y*z0^2 + 2*x^4*y*z1 - 2*x^2*z0*z1^3 + x*y*z1^4 + 2*x^4*y - 3*x^2*z0*z1^2)/y) * dx
1 92 [0, 1] (x*z0) * dx
1 93 [0, 1] ((-x^3*z1 + x*y*z0*z1)/y) * dx
1 94 [0, 1] ((3*x^2*z0^2*z1^2 + 3*x^3*z1^2 + x*y*z0*z1^2)/y) * dx
1 95 [0, 1] ((x*z0^4*z1^3 + x^2*z0^2*z1^3 - 3*x^3*z1^3 + x*y*z0*z1^3)/y) * dx
1 96 [0, 1] ((-x^3*z0 + x*y*z0^2)/y) * dx
1 97 [0, 1] ((3*x^2*z0^3*z1 + 3*x^3*z0*z1 + x*y*z0^2*z1)/y) * dx
1 98 [0, 1] ((2*x^2*z0^3*z1^2 - x^3*z0*z1^2 + x*y*z0^2*z1^2 - 2*x^2*y*z1^2)/y) * dx
1 99 [0, 1] ((-x*z0^5*z1^3 + 3*x^2*z0^3*z1^3 + x^3*z0*z1^3 + x*y*z0^2*z1^3 + 3*x^2*y*z1^3)/y) * dx
1 100 [0, 1] ((-3*x^2*z0^4 + x^3*z0^2 + x*y*z0^3 + x^4)/y) * dx
1 101 [0, 1] ((-3*x^2*z0^4*z1 - 3*x^2*z0^4 + x^3*z0^2*z1 + x*y*z0^3*z1 - x^3*z0^2 + x^4*z1 - 3*x^4)/y) * dx
1 102 [0, 1] ((-2*x^2*z0^4*z1^2 + 2*x^3*z0^2*z1^2 + x*y*z0^3*z1^2 + x^2*z0^4 - 2*x^4*z1^2 + x^2*y*z0*z1^2 - 2*x^3*z0^2 + x^4)/y) * dx
1 103 [0, 1] ((3*x*z0^6*z1^3 - 3*x^2*z0^4*z1^3 - 2*x^3*z0^2*z1^3 + x*y*z0^3*z1^3 - x^4*z1^3 + 2*x^2*y*z0*z1^3 - x^2*z0^4 + 2*x^3*z0^2 - x^4)/y) * dx
1 104 [0, 1] ((-x^2*z0^5 - x^3*z0^3 + x*y*z0^4 - 3*x^4*z0 - 3*x^3*y)/y) * dx
1 105 [0, 1] ((-3*x^2*z0^5*z1 - 2*x^3*z0^3*z1 + x*y*z0^4*z1 - x^4*z0*z1 + 2*x^2*y*z0^2*z1 + 3*x^3*y*z1)/y) * dx
1 106 [0, 1] ((-3*x^2*z0^5*z1^2 + 2*x^2*z0^5*z1 - 2*x^3*z0^3*z1^2 + x*y*z0^4*z1^2 - 3*x^2*z0^5 + x^3*z0^3*z1 - x^4*z0*z1^2 + 2*x^2*y*z0^2*z1^2 + 3*x^3*z0^3 - 2*x^4*z0*z1 - 2*x^2*y*z0^2*z1 + 3*x^3*y*z1^2 - x^4*z0 + x^3*y*z1 + x^3*y)/y) * dx
1 107 [0, 1] ((-2*x^2*z0^6 - 3*x^3*z0^4 + x*y*z0^5 + 3*x^4*z0^2 + 2*x^5 - x^3*y*z0)/y) * dx
1 108 [0, 1] ((x^2*z0^6*z1 + x^3*z0^4*z1 + x*y*z0^5*z1 + x^4*z0^2*z1 + x^2*y*z0^3*z1 + x^5*z1 + x^3*y*z0*z1)/y) * dx
1 109 [0, 1] ((x^2*z0^6*z1^2 - 3*x^2*z0^6*z1 + x^3*z0^4*z1^2 + x*y*z0^5*z1^2 + x^2*z0^6 + 3*x^3*z0^4*z1 + x^4*z0^2*z1^2 + x^2*y*z0^3*z1^2 + 2*x^3*z0^4 + 2*x^4*z0^2*z1 - x^2*y*z0^3*z1 + x^5*z1^2 + x^3*y*z0*z1^2 + x^4*z0^2 + x^5*z1 - 2*x^3*y*z0*z1 - 2*x^5 - 2*x^3*y*z0 + 2*x^2*z1^3)/y) * dx
1 110 [0, 1] ((x^3*z0^5 + x*y*z0^6 + x^4*z0^3 + x^2*y*z0^4 + x^5*z0 + x^3*y*z0^2 + x^4*y)/y) * dx
1 111 [0, 1] (x/y) * dx
1 112 [0, 1] (x*z1/y) * dx
1 113 [0, 1] (x*z1^2/y) * dx
1 114 [0, 1] (x*z1^3/y) * dx
1 115 [0, 1] (x*z1^4/y) * dx
1 116 [0, 1] ((-x^2*z0^4 + x*z1^5 + 2*x^3*z0^2 - x^4)/y) * dx
1 117 [0, 1] (x*z0/y) * dx
1 118 [0, 1] (x*z0*z1/y) * dx
1 119 [0, 1] (x*z0*z1^2/y) * dx
1 120 [0, 1] (x*z0*z1^3/y) * dx
1 121 [0, 1] ((-3*x^2*z0^5*z1 - 2*x^2*z0^5 + 2*x^3*z0^3*z1 + 2*x^3*z0^3 + 3*x^4*z0*z1 + 3*x^2*y*z0^2*z1 + x*z0*z1^4 - 3*x^4*z0 + 2*x^3*y*z1 + 3*x^3*y)/y) * dx
1 122 [0, 1] (x*z0^2/y) * dx
1 123 [0, 1] (x*z0^2*z1/y) * dx
1 124 [0, 1] (x*z0^2*z1^2/y) * dx
1 125 [0, 1] ((x*z0^2*z1^3 - x^2*z1^3)/y) * dx
1 126 [0, 1] ((-x^2*z0^6*z1 - 3*x^2*z0^6 + x^3*z0^4*z1 + x^3*z0^4 + 3*x^4*z0^2*z1 + 2*x^2*y*z0^3*z1 + x*z0^2*z1^4 - 3*x^4*z0^2 - 2*x^5*z1 - 3*x^3*y*z0*z1 - x^2*z1^4 - x^5 - x^3*y*z0 - 2*x^2*z1^3)/y) * dx
1 127 [0, 1] (x*z0^3/y) * dx
1 128 [0, 1] (x*z0^3*z1/y) * dx
1 129 [0, 1] ((x*z0^3*z1^2 - x^2*z0*z1^2)/y) * dx
1 130 [0, 1] (x*z0^4/y) * dx
1 131 [0, 1] ((x*z0^4*z1 - x^3*z1)/y) * dx
1 132 [0, 1] ((x*z0^4*z1^2 - 2*x^2*z0^2*z1^2 + x^3*z1^2)/y) * dx
1 133 [0, 1] ((x*z0^5 - x^3*z0)/y) * dx
1 134 [0, 1] ((x*z0^5*z1 - 2*x^2*z0^3*z1 + x^3*z0*z1)/y) * dx
1 135 [0, 1] ((x*z0^5*z1^2 - x^2*z0^3*z1^2 - 2*x^3*z0*z1^2 + 2*x^2*y*z1^2)/y) * dx
1 136 [0, 1] ((x*z0^6 - 3*x^2*z0^4 + 3*x^3*z0^2 - x^4)/y) * dx
1 137 [0, 1] ((x*z0^6*z1 - 3*x^2*z0^4*z1 - x^2*z0^4 + 3*x^3*z0^2*z1 + 2*x^3*z0^2 - x^4*z1 - x^4)/y) * dx
1 138 [0, 1] ((x*z0^6*z1^2 + 2*x^2*z0^4*z1^2 + x^3*z0^2*z1^2 + 2*x^2*z0^4 - 2*x^4*z1^2 - 2*x^2*y*z0*z1^2 + 3*x^3*z0^2 + 2*x^4)/y) * dx
1 139 [0, 1] ((-x^3*z0 + x^2*y)/y) * dx
1 140 [0, 1] ((-3*x^2*z0^3*z1 + 2*x^3*z0*z1 + x^2*y*z1)/y) * dx
1 141 [0, 1] ((x^2*z0^4 + x^3*z0^2 - 3*x^4 + x^2*y*z0)/y) * dx
1 142 [0, 1] ((x^2*z0^4*z1 + 3*x^2*z0^4 + x^3*z0^2*z1 + x^3*z0^2 - 3*x^4*z1 + x^2*y*z0*z1 + 3*x^4)/y) * dx
1 143 [0, 1] ((-x^2*z0^5 + 3*x^3*z0^3 + x^4*z0 + x^2*y*z0^2 + 3*x^3*y)/y) * dx
1 144 [0, 1] ((3*x^2*z0^6 - 3*x^3*z0^4 - 2*x^4*z0^2 + x^2*y*z0^3 - x^5 + 2*x^3*y*z0)/y) * dx
1 145 [0, 1] (x^2/y) * dx
1 146 [0, 1] (x^2*z1/y) * dx
1 147 [0, 1] (x^2*z1^2/y) * dx
1 148 [0, 1] (x^2*z0/y) * dx
1 149 [0, 1] (x^2*z0*z1/y) * dx
1 150 [0, 1] (x^2*z0^2/y) * dx
1 151 [0, 1] ((x^2*z0^2*z1 - x^3*z1)/y) * dx
1 152 [0, 1] ((x^2*z0^3 - x^3*z0)/y) * dx
1 153 [0, 1] (x^3/y) * dx
True
True
True
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lini.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ltess.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

[?7h[?12l[?25h[?2004lTrue
True
True
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS.fct_field[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis(threshold = 20)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lini.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS.fct_field[?7h[?12l[?25h[?25l[?7lsage: AS

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 2^2 with the equations:
z0^2 - z0 = x^3
z1^2 - z1 = a*x^3

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgroup_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lsage: group_action_matrices_dR(AS)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [10], in <cell line: 1>()
----> 1 group_action_matrices_dR(AS)

File <string>:29, in group_action_matrices_dR(AS)

NameError: name 'threshold' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgroup_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lgroup_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lsage: group_action_matrices_dR(AS)

[?7h[?12l[?25h[?2004lz1/x
/ext/sage/9.7/src/sage/rings/polynomial/polynomial_singular_interface.py:372:
********************************************************************************
Denominators of fraction field elements are sometimes dropped without warning.
This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696.
********************************************************************************
z0*z1/x
z0*z1/x^2
[?7h[
[    1 a + 1     0     0     0     a]  [1 1 0 0 0 1]
[    0     1     0     0     0     0]  [0 1 0 0 0 0]
[    0     0     1     0     a     0]  [0 0 1 0 1 0]
[    0     0     0     1     1     0]  [0 0 0 1 a 0]
[    0     0     0     0     1     0]  [0 0 0 0 1 0]
[    0     0     0     0     0     1], [0 0 0 0 0 1]
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgroup_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAgroup_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l,group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lBgroup_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l=group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_dR(AS)

[?7h[?12l[?25h[?2004lz1/x
z0*z1/x
z0*z1/x^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(f)[?7h[?12l[?25h[?25l[?7lsage: p

[?7h[?12l[?25h[?2004l[?7h2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lind[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgroup_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l = x + y^2[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g = AS.genus()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = AS.genus()[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lg = AS.genus()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l = matrix(GF(3), 3, 3)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lind[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lid[?7h[?12l[?25h[?25l[?7lide[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A^2 == identity_matrix(F, 6)

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA^2 == identity_matrix(F, 6)[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l&[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lsage: A*B == B*A

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA*B == B*A[?7h[?12l[?25h[?25l[?7l^2identity_matrix(F, 6)[?7h[?12l[?25h[?25l[?7lg =AS.genus()[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lgroup_actionmarices_dR(AS)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lgroup_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lA, B = groupacion_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lg = AS.genus()[?7h[?12l[?25h[?25l[?7lA^2== identity_matrix(F, 6)[?7h[?12l[?25h[?25l[?7l*BB*A[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA*B == B*A[?7h[?12l[?25h[?25l[?7l^2identity_matrix(F, 6)[?7h[?12l[?25h[?25l[?7lg =AS.genus()[?7h[?12l[?25h[?25l[?7lA^2== identity_matrix(F, 6)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^2 = identity_matrix(F, 6)[?7h[?12l[?25h[?25l[?7lB^2 = identity_matrix(F, 6)[?7h[?12l[?25h[?25l[?7lsage: B^2 == identity_matrix(F, 6)

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmatrix(GF(3), 3, 3)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lgmathisA, B)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lathis(A, B)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B)

[?7h[?12l[?25h[?2004l>> A := MatrixAlgebra<GF(4),6|[1, a + 1, 0, 0, 0, a, 0, 1, 0, 0, 0, 0, 0, 0, 1
                                  ^
User error: Identifier 'a' has not been declared or assigned
>> , 0, 1, 0, 0, 0, 0, 0, 0, 1]>;M := RModule(RSpace(GF(4),6), A);Indecomposab
                                                               ^
User error: Identifier 'A' has not been declared or assigned
>> ,6), A);IndecomposableSummands(M);
                                  ^
User error: Identifier 'M' has not been declared or assigned
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFF = GF(4, 'a')[?7h[?12l[?25h[?25l[?7lsage: F

[?7h[?12l[?25h[?2004l[?7hFinite Field in a of size 2^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7lmagmathis(A, B)[?7h[?12l[?25h[?25l[?7lB^2 == dentity_matrix(F, 6)[?7h[?12l[?25h[?25l[?7lmagmaths(A, B)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7lT)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7lTrue)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B, text=True)

[?7h[?12l[?25h[?2004l[?7h'A := MatrixAlgebra<GF(4),6|[1, a + 1, 0, 0, 0, a, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, a, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1],[1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, a, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1]>;M := RModule(RSpace(GF(4),6), A);IndecomposableSummands(M);'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B, text=True)[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7lmagmathis(A, B)[?7h[?12l[?25h[?25l[?7lB^2 == dentity_matrix(F, 6)[?7h[?12l[?25h[?25l[?7lA*BB*A[?7h[?12l[?25h[?25l[?7l^2identity_matrix(F, 6)[?7h[?12l[?25h[?25l[?7lg =AS.genus()[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lgroup_actionmarices_dR(AS)[?7h[?12l[?25h[?25l[?7lA, B = groupacion_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7lh(AS)[?7h[?12l[?25h[?25l[?7lo(AS)[?7h[?12l[?25h[?25l[?7ll(AS)[?7h[?12l[?25h[?25l[?7lo(AS)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_holo(AS)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lmagmathis(A, B, text=True)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B, text=True)

[?7h[?12l[?25h[?2004l[?7h'A := MatrixAlgebra<GF(4),3|[1, a + 1, 0, 0, 1, 0, 0, 0, 1],[1, 1, 0, 0, 1, 0, 0, 0, 1]>;M := RModule(RSpace(GF(4),3), A);IndecomposableSummands(M);'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B, text=True)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [24], 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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:69, in coordinates(self, threshold, basis)

File <string>:84, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
(1) * dx
(z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(z0 + 1) * dx
(z0*z1 + z1) * dx
(z0^2 - z0 + 1) * dx
(x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx
(x*z0 + x) * dx
(x^2) * dx
(0) * dx
(0) * dx
(x^2) * dx
(x^2 - z0*z1 + z1) * dx
(x^2) * dx
(x^2*z0 + z0^2*z1 + z1^2) * dx
(x*z0 - x) * dx
(x*z0^2 - x*z1) * dx
(x*z0^2 - x*z0 - x*z1 + x) * dx
((x^4 - x^2*z0*z1 + x^2*z1 + z1^2 + z1)/x^2) * dx
---------------------------------------------------------------------------
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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:70, in coordinates(self, threshold, basis)

File <string>:84, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.fct_field[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[(1) * dx,
 (z1) * dx,
 (x^2*z0 + z0^2*z1 + z1^2) * dx,
 (z0) * dx,
 (z0*z1) * dx,
 (z0^2) * dx,
 (x) * dx,
 (-x*z0^2 + x*z1) * dx,
 (x*z0) * dx,
 (x^2) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = f.parent().base_ring().gens()[0][?7h[?12l[?25h[?25l[?7las_reductionAS, AAA)[?7h[?12l[?25h[?25l[?7las_[?7h[?12l[?25h[?25l[?7lreduction(AS, AAA)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7las[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

[?7h[?12l[?25h[?2004l
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd ..
]0;~/Research/2021 De Rham/DeRhamComputation~/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/as_covers/as_cech_class.sage
	modified:   sage/as_covers/as_cover_class.sage
	modified:   sage/as_covers/as_form_class.sage
	modified:   sage/as_covers/group_action_matrices.sage
	modified:   sage/as_covers/tests/group_action_matrices_test.sage
	modified:   sage/init.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/as_reduction.sage
	sage/drafty/better_trace.sage
	sage/drafty/draft4.sage
	sage/drafty/draft5.sage
	sage/drafty/draft6.sage
	sage/drafty/draft8.sage
	sage/drafty/lift_to_de_rham.sage
	sage/drafty/pole_numbers.sage
	superelliptic_arbitrary_field.ipynb

no changes added to commit (use "git add" and/or "git commit -a")
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add sage/as_covers/as_reduction.sage 
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -u
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git commit -m ""a"s" "r"e"d"u"c"t"i"o"n" "("s"r"a"""t"a"r"e")" "p"l"u"s" "m"a"c"i"e"r"z" "d"z"i"a"l"a"n"i"a" "n"a" "b"a"z"i"e" "d"R" "p"r"a"w"i"e" "d"z"i"a"l"a"
[master 6494187] as reduction (stare) plus macierz dzialania na bazie dR prawie dziala
 9 files changed, 1155 insertions(+), 14959 deletions(-)
 rewrite sage/.run.term-0.term (97%)
 create mode 100644 sage/as_covers/as_reduction.sage
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ git commit -m "as reduction (stare) plus macierz dzialania na bazie dR prawie dziala"
add -ucommit -m "as reduction (stare) plus macierz dzialania na bazie dR prawie dziala"
sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
(1) * dx
(1) * dx
(z1) * dx
(z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(z0 + 1) * dx
(z0 + 1) * dx
(z0*z1 + z1) * dx
(z0*z1 + z1) * dx
(z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx
(x) * dx
(x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx
(x*z0 + x) * dx
(x*z0 + x) * dx
(x^2) * dx
(x^2) * dx
(0) * dx
(0) * dx
(0) * dx
(0) * dx
(x^2) * dx
(x^2) * dx
(x^2 - z0*z1 + z1) * dx
(x^2 - z0*z1 + z1) * dx
(x^2) * dx
(x^2) * dx
(x^2*z0 + z0^2*z1 + z1^2) * dx
(x^2*z0 + z0^2*z1 + z1^2) * dx
(x*z0 - x) * dx
(x*z0 - x) * dx
(x*z0^2 - x*z1) * dx
(x*z0^2 - x*z1) * dx
(x*z0^2 - x*z0 - x*z1 + x) * dx
(x*z0^2 - x*z0 - x*z1 + x) * dx
((x^4 - x^2*z0*z1 + x^2*z1 + z1^2 + z1)/x^2) * dx
((x^4 - x^2*z0*z1 + x^2*z1 + z1^2 + z1)/x^2) * dx
---------------------------------------------------------------------------
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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:71, in coordinates(self, threshold, basis)

File <string>:84, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[(1) * dx,
 (z1) * dx,
 (x^2*z0 + z0^2*z1 + z1^2) * dx,
 (z0) * dx,
 (z0*z1) * dx,
 (z0^2) * dx,
 (x) * dx,
 (-x*z0^2 + x*z1) * dx,
 (x*z0) * dx,
 (x^2) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004lWARNING: your terminal doesn't support cursor position requests (CPR).

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
(1) * dx
(1) * dx
(z1) * dx
(z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(z0 + 1) * dx
(z0 + 1) * dx
(z0*z1 + z1) * dx
(z0*z1 + z1) * dx
(z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx
(x) * dx
(x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx
(x*z0 + x) * dx
(x*z0 + x) * dx
(x^2) * dx
(x^2) * dx
(0) * dx
(0) * dx
(0) * dx
(0) * dx
(x^2) * dx
(x^2) * dx
(x^2 - z0*z1 + z1) * dx
(x^2 - z0*z1 + z1) * dx
(x^2) * dx
(x^2) * dx
(x^2*z0 + z0^2*z1 + z1^2) * dx
(x^2*z0 + z0^2*z1 + z1^2) * dx
(x*z0 - x) * dx
(x*z0 - x) * dx
(x*z0^2 - x*z1) * dx
(x*z0^2 - x*z1) * dx
(x*z0^2 - x*z0 - x*z1 + x) * dx
(x*z0^2 - x*z0 - x*z1 + x) * dx
((x^4 - x^2*z0*z1 + x^2*z1 + z1^2 + z1)/x^2) * dx
((x^4 - x^2*z0*z1 + x^2*z1 + z1^2 + z1)/x^2) * dx
---------------------------------------------------------------------------
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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:71, in coordinates(self, threshold, basis)

File <string>:84, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B, text=True)[?7h[?12l[?25h[?25l[?7l()l[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
(1) * dx
(1) * dx
(z1) * dx
(z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(z0 + 1) * dx
(z0 + 1) * dx
(z0*z1 + z1) * dx
(z0*z1 + z1) * dx
(z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx
(x) * dx
(x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx
(x*z0 + x) * dx
(x*z0 + x) * dx
(x^2) * dx
(x^2) * dx
(0) * dx
(0) * dx
(0) * dx
(0) * dx
(x^2) * dx
(x^2) * dx
(x^2 - z0*z1 + z1) * dx
(x^2 - z0*z1 + z1) * dx
(x^2) * dx
(x^2) * dx
(x^2*z0 + z0^2*z1 + z1^2) * dx
(x^2*z0 + z0^2*z1 + z1^2) * dx
(x*z0 - x) * dx
(x*z0 - x) * dx
(x*z0^2 - x*z1) * dx
(x*z0^2 - x*z1) * dx
(x*z0^2 - x*z0 - x*z1 + x) * dx
(x*z0^2 - x*z0 - x*z1 + x) * dx
((x^4 - x^2*z0*z1 + x^2*z1 + z1^2 + z1)/x^2) * dx
((x^4 - x^2*z0*z1 + x^2*z1 + z1^2 + z1)/x^2) * dx
---------------------------------------------------------------------------
TypeError                                 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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:71, in coordinates(self, threshold, basis)

File <string>:84, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: AS.x

[?7h[?12l[?25h[?2004l[?7hx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.x[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: AS.y

[?7h[?12l[?25h[?2004l[?7hy
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.y[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7lsage: AS.z

[?7h[?12l[?25h[?2004l[?7h[z0, z1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
(1) * dx
(1) * dx
(z1) * dx
(z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(z0 + 1) * dx
(z0 + 1) * dx
(z0*z1 + z1) * dx
(z0*z1 + z1) * dx
(z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx
(x) * dx
(x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx
(x*z0 + x) * dx
(x*z0 + x) * dx
(x^2) * dx
(x^2) * dx
(0) * dx
(0) * dx
(0) * dx
(0) * dx
(x^2) * dx
(x^2) * dx
(x^2 - z0*z1 + z1) * dx
(x^2 - z0*z1 + z1) * dx
(x^2) * dx
(x^2) * dx
(x^2*z0 + z0^2*z1 + z1^2) * dx
(x^2*z0 + z0^2*z1 + z1^2) * dx
(x*z0 - x) * dx
(x*z0 - x) * dx
(x*z0^2 - x*z1) * dx
(x*z0^2 - x*z1) * dx
(x*z0^2 - x*z0 - x*z1 + x) * dx
(x*z0^2 - x*z0 - x*z1 + x) * dx
((x^4 - x^2*z0*z1 + x^2*z1 + z1^2 + z1)/x^2) * dx
((x^4 - x^2*z0*z1 + x^2*z1 + z1^2 + z1)/x^2) * dx
---------------------------------------------------------------------------
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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:71, in coordinates(self, threshold, basis)

File <string>:84, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lzmag = AS.magical_element(threshold = 18)[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[1][?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lX[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.x[?7h[?12l[?25h[?25l[?7lS.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: AS.z[1]^2/AS.x*AS.dx

[?7h[?12l[?25h[?2004l[?7h(z1^2/x) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[1]^2/AS.x*AS.dx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[1]^2/AS.x*AS.dx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (AS.z[1]^2/AS.x*AS.dx).valuation()

[?7h[?12l[?25h[?2004l[?7h3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[1]^2/AS.x*AS.dx).valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lAS.z[1]^2/AS.x*AS.dx[?7h[?12l[?25h[?25l[?7l(AS.z[1]^2/AS.x*AS.dx).valuation()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
0
(1) * dx
(1) * dx
0
(z1) * dx
(z1) * dx
0
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
0
(z0 + 1) * dx
(z0 + 1) * dx
0
(z0*z1 + z1) * dx
(z0*z1 + z1) * dx
0
(z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx
0
(x) * dx
(x) * dx
0
(-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx
0
(x*z0 + x) * dx
(x*z0 + x) * dx
0
(x^2) * dx
(x^2) * dx
0
(0) * dx
(0) * dx
0
(0) * dx
(0) * dx
0
(x^2) * dx
(x^2) * dx
0
(x^2 - z0*z1 + z1) * dx
(x^2 - z0*z1 + z1) * dx
0
(x^2) * dx
(x^2) * dx
0
(x^2*z0 + z0^2*z1 + z1^2) * dx
(x^2*z0 + z0^2*z1 + z1^2) * dx
0
(x*z0 - x) * dx
(x*z0 - x) * dx
0
(x*z0^2 - x*z1) * dx
(x*z0^2 - x*z1) * dx
0
(x*z0^2 - x*z0 - x*z1 + x) * dx
(x*z0^2 - x*z0 - x*z1 + x) * dx
(x^2*z1 - z0*z1^2 + z1^2)/x^3
((x^4 - x^2*z0*z1 + x^2*z1 + z1^2 + z1)/x^2) * dx
((x^4 - x^2*z0*z1 + x^2*z1 + z1^2 + z1)/x^2) * dx
---------------------------------------------------------------------------
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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:71, in coordinates(self, threshold, basis)

File <string>:84, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(AS.z[1]^2/AS.x*AS.dx).valuation()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
0
---------------------------------------------------------------------------
AttributeError                            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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:68, in coordinates(self, threshold, basis)

File /ext/sage/9.7/src/sage/misc/functional.py:1388, in numerator(x)
   1386 if isinstance(x, int):
   1387     return x
-> 1388 return x.numerator()

AttributeError: 'as_function' object has no attribute 'numerator'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
(x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2)/x^3
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [11], 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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:77, in coordinates(self, threshold, basis)

File <string>:84, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^2*z1 - z0*z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lAx^2*z1 - z0*z1^2)/x^3[?7h[?12l[?25h[?25l[?7lSx^2*z1 - z0*z1^2)/x^3[?7h[?12l[?25h[?25l[?7l.x^2*z1 - z0*z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz1 - z0*z1^2)/x^3[?7h[?12l[?25h[?25l[?7lSz1 - z0*z1^2)/x^3[?7h[?12l[?25h[?25l[?7l.z1 - z0*z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1 - z0*z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[] - z0*z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz0*z1^2)/x^3[?7h[?12l[?25h[?25l[?7lSz0*z1^2)/x^3[?7h[?12l[?25h[?25l[?7l.z0*z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0*z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]*z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lAz1^2)/x^3[?7h[?12l[?25h[?25l[?7lSz1^2)/x^3[?7h[?12l[?25h[?25l[?7l.z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2)/x^3[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lAx^3[?7h[?12l[?25h[?25l[?7lSx^3[?7h[?12l[?25h[?25l[?7l.x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.x)^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2)/(AS.x)^3

[?7h[?12l[?25h[?2004l[?7h(x^2*z1 - z0*z1^2)/x^3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2)/(AS.x)^3[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2)/(AS.x)^3)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2)/(AS.x)^3).valuation()

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR.<x1,x2,y1,y2> = QQ[][?7h[?12l[?25h[?25l[?7lxy[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: Rxy

[?7h[?12l[?25h[?2004l[?7hMultivariate Polynomial Ring in x, y over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l = Rxy(x^2 + y^3)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lRxy(x^2 + y^3)[?7h[?12l[?25h[?25l[?7lsage: f = Rxy(x^2 + y^3)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = AS.genus()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7lx6[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g = Rxy(x^5 + x*y)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = Rxy(x^5 + x*y)[?7h[?12l[?25h[?25l[?7l.parent()[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.quo_rem(f)

[?7h[?12l[?25h[?2004l[?7h(0, x^5 + x*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx^2*z1 - z0*z1^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1 - z0*z1^2[?7h[?12l[?25h[?25l[?7l[] - z0*z1^2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0*z1^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]*z1^2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: x^2*z[1] - z[0]*z[1]^2

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [18], in <cell line: 1>()
----> 1 x**Integer(2)*z[Integer(1)] - z[Integer(0)]*z[Integer(1)]**Integer(2)

NameError: name 'z' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxy[?7h[?12l[?25h[?25l[?7l.<x1,x2,y1,y2> = QQ[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxy[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lzQ, Rxyz, x, y, z = AS.fct_field[?7h[?12l[?25h[?25l[?7l.<>[?7h[?12l[?25h[?25l[?7lx>[?7h[?12l[?25h[?25l[?7l,>[?7h[?12l[?25h[?25l[?7l >[?7h[?12l[?25h[?25l[?7ly>[?7h[?12l[?25h[?25l[?7l,>[?7h[?12l[?25h[?25l[?7l >[?7h[?12l[?25h[?25l[?7lz>[?7h[?12l[?25h[?25l[?7l0>[?7h[?12l[?25h[?25l[?7l,>[?7h[?12l[?25h[?25l[?7l >[?7h[?12l[?25h[?25l[?7lz>[?7h[?12l[?25h[?25l[?7l1>[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lP[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(),[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: Rxyz.<x, y, z0, z1> = PolynomialRing(GF(3), 4)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx^2*z[1] - z[0]*z[1]^2[?7h[?12l[?25h[?25l[?7l, y = Rxyz.gens()[:2][?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l.g[?7h[?12l[?25h[?25l[?7lens[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: x, y, z0, z1 = Rxyz.gens()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y, z0, z1 = Rxyz.gens()[?7h[?12l[?25h[?25l[?7lRxyz.<x, y, z0, z1> = PolynomialRing(GF(3), 4)[?7h[?12l[?25h[?25l[?7lx^2*z[1]- z[0]*[1]^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[^2[?7h[?12l[?25h[?25l[?7l^2[?7h[?12l[?25h[?25l[?7l^2[?7h[?12l[?25h[?25l[?7l1^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[*z1^2[?7h[?12l[?25h[?25l[?7l*z1^2[?7h[?12l[?25h[?25l[?7l*z1^2[?7h[?12l[?25h[?25l[?7l0*z1^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[ - z0*z1^2[?7h[?12l[?25h[?25l[?7l - z0*z1^2[?7h[?12l[?25h[?25l[?7l - z0*z1^2[?7h[?12l[?25h[?25l[?7l1 - z0*z1^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^2*z1 - z0*z1^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (x^2*z1 - z0*z1^2).quo_rem(x^2)

[?7h[?12l[?25h[?2004l[?7h(z1, -z0*z1^2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^2*z1 - z0*z1^2).quo_rem(x^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
(x^2*z1 - z0*z1^2 + z1^2)/x^3
---------------------------------------------------------------------------
TypeError                                 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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

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

File <string>:84, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^2*z1 - z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((x^2*z1 - z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lAx^2*z1 - z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7lSx^2*z1 - z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l.x^2*z1 - z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz1 - z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7lSz1 - z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l.z1 - z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1 - z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7lp1 - z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l1 - z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[] - z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7lSz0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l.z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7lSz1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l.z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz1^2)/x^3[?7h[?12l[?25h[?25l[?7lSz1^2)/x^3[?7h[?12l[?25h[?25l[?7l.z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2)/x^3[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lAx^3[?7h[?12l[?25h[?25l[?7lSx^3[?7h[?12l[?25h[?25l[?7l.x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2 + AS.z[1]^2)/AS.x^3).valuation()

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2 + AS.z[1]^2)/AS.x^3).valuation()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
0
0 0
0
0 0
0
0 0
0
0 0
0
0 0
0
0 0
0
0 0
0
0 0
0
0 0
0
0 0
0
0 0
0
0 0
0
0 0
0
0 0
0
0 0
0
0 0
0
0 0
0
0 0
0
0 0
(x^2*z1 - z0*z1^2 + z1^2)/x^3
0 0
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [24], 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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:76, in coordinates(self, threshold, basis)

File <string>:84, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
0
! 0 0
0
! 0 0
0
! 0 0
0
! 0 0
0
! 0 0
0
! 0 0
0
! 0 0
0
! 0 0
0
! 0 0
0
! 0 0
0
! 0 0
0
! 0 0
0
! 0 0
0
! 0 0
0
! 0 0
0
! 0 0
0
! 0 0
0
! 0 0
0
! 0 0
(x^2*z1 - z0*z1^2 + z1^2)/x^3
! 0 0
---------------------------------------------------------------------------
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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:76, in coordinates(self, threshold, basis)

File <string>:84, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
? 0
! 0 0
? 0
! 0 0
? 0
! 0 0
? 0
! 0 0
? 0
! 0 0
? 0
! 0 0
? 0
! 0 0
? 0
! 0 0
? 0
! 0 0
? 0
! 0 0
? 0
! 0 0
? 0
! 0 0
? 0
! 0 0
? 0
! 0 0
? 0
! 0 0
? 0
! 0 0
? 0
! 0 0
? 0
! 0 0
? 0
! 0 0
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
! 0 0
---------------------------------------------------------------------------
TypeError                                 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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:76, in coordinates(self, threshold, basis)

File <string>:84, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

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

[?7h[?12l[?25h[?2004lTraceback (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 [27] 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>:8 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>:72
    print('!', self.f.function - rem/f_den, '!!:' quo)
                                            ^
SyntaxError: invalid syntax. Perhaps you forgot a comma?

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

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
! 0 !!: 0
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [28], 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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:76, in coordinates(self, threshold, basis)

File <string>:84, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l((AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2 + AS.z[1]^2)/AS.x^3).valuation()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l((AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2 + AS.z[1]^2)/AS.x^3).valuation()[?7h[?12l[?25h[?25l[?7l()l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2 + AS.z[1]^2)/AS.x^3).valuation()

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

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
q r: 0 x^2*z1 - z0*z1^2 + z1^2
! 0 !!: 0
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [30], 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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:77, in coordinates(self, threshold, basis)

File <string>:84, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [31], 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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:77, in coordinates(self, threshold, basis)

File <string>:77, in coordinates(self, basis)

File <string>:137, in holomorphic_differentials_basis(self, threshold)

File <string>:399, in holomorphic_combinations(S)

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

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l((AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2 + AS.z[1]^2)/AS.x^3).valuation()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
! 0 !!: 0
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [32], 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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:77, in coordinates(self, threshold, basis)

File <string>:84, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

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

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
! 0 !!: 0
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [33], 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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:78, in coordinates(self, threshold, basis)

File <string>:84, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

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

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
! 0 !!: 0
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [34], 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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:79, in coordinates(self, threshold, basis)

File <string>:84, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

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

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

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

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

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

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

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

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

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

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

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
! 0 !!: 0
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [35], 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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:79, in coordinates(self, threshold, basis)

File <string>:84, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
^C^C
KeyboardInterrupt

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

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
! 0 !!: 0
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [37], 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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:79, in coordinates(self, threshold, basis)

File <string>:84, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
! 0 !!: 0
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [38], 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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:79, in coordinates(self, threshold, basis)

File <string>:84, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [39], 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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:56, in coordinates(self, threshold, basis)

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>:56, in <genexpr>(.0)

File <string>:47, in __mul__(self, other)

File <string>:3, in __init__(self, C, g)

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

KeyboardInterrupt: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

[?7h[?12l[?25h[?2004l
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
! 0 !!: 0
---------------------------------------------------------------------------
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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:79, in coordinates(self, threshold, basis)

File <string>:84, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
! 0 !!: 0
---------------------------------------------------------------------------
TypeError                                 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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:79, in coordinates(self, threshold, basis)

File <string>:84, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? 0
0 q r: 0 0
if 0 True
! 0 !!: 0

? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
! 0 !!: 0
---------------------------------------------------------------------------
TypeError                                 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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:79, in coordinates(self, threshold, basis)

File <string>:84, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004lWARNING: your terminal doesn't support cursor position requests (CPR).

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

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
nowe!!!! ( (1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( (z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( (z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( (z0*z1 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( (x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( (x*z0 + x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( (x^2) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( ((-x^4 - z1)/x^2) * dx, z1/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( ((-z1^2)/x^2) * dx, z1^2/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( ((x^2*z1 - z0*z1 - z1)/x^2) * dx, (z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( ((x^4*z0 + x^2*z0^2*z1 + x^4 - x^2*z0*z1 + x^2*z1^2 + x^2*z1 - z0*z1^2 - z1^2)/x^2) * dx, (z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( ((-x^2*z0*z1 - x^2*z1 - z0^2*z1 + z0*z1 - z1)/x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( ((-z0^2*z1^2 + z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( ((-x^4*z0^2 + x^4*z0 + x^4*z1 - x^4 + z1^2)/x^3) * dx, z1^2/x^2 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( ((x^2*z1^2 + z0*z1^2 + z1^2)/x^3) * dx, (z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( ((x^4*z0^2 - x^4*z0 - x^2*z0*z1^2 + x^4 - x^2*z1^2 + z0^2*z1^2 - z0*z1^2 + z1^2)/x^3) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( ((-z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
! 0 !!: 0
---------------------------------------------------------------------------
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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:79, in coordinates(self, threshold, basis)

File <string>:84, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
nowe!!!! ( (1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (1) * dx, 0 )
nowe!!!! ( (z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (z1) * dx, 0 )
nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
nowe!!!! ( (z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (z0 + 1) * dx, 0 )
nowe!!!! ( (z0*z1 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (z0*z1 + z1) * dx, 0 )
nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (z0^2 - z0 + 1) * dx, 0 )
nowe!!!! ( (x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x) * dx, 0 )
nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
nowe!!!! ( (x*z0 + x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x*z0 + x) * dx, 0 )
nowe!!!! ( (x^2) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2) * dx, 0 )
nowe!!!! ( ((-x^4 - z1)/x^2) * dx, z1/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (0) * dx, 0 )
nowe!!!! ( ((-z1^2)/x^2) * dx, z1^2/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (0) * dx, 0 )
nowe!!!! ( ((x^2*z1 - z0*z1 - z1)/x^2) * dx, (z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2) * dx, 0 )
nowe!!!! ( ((x^4*z0 + x^2*z0^2*z1 + x^4 - x^2*z0*z1 + x^2*z1^2 + x^2*z1 - z0*z1^2 - z1^2)/x^2) * dx, (z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2 - z0*z1 + z1) * dx, 0 )
nowe!!!! ( ((-x^2*z0*z1 - x^2*z1 - z0^2*z1 + z0*z1 - z1)/x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2) * dx, 0 )
nowe!!!! ( ((-z0^2*z1^2 + z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 )
nowe!!!! ( ((-x^4*z0^2 + x^4*z0 + x^4*z1 - x^4 + z1^2)/x^3) * dx, z1^2/x^2 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x*z0 - x) * dx, 0 )
nowe!!!! ( ((x^2*z1^2 + z0*z1^2 + z1^2)/x^3) * dx, (z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x*z0^2 - x*z1) * dx, 0 )
nowe!!!! ( ((x^4*z0^2 - x^4*z0 - x^2*z0*z1^2 + x^4 - x^2*z1^2 + z0^2*z1^2 - z0*z1^2 + z1^2)/x^3) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x*z0^2 - x*z0 - x*z1 + x) * dx, 0 )
nowe!!!! ( ((-z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
! 0 !!: 0
selfik ( ((-x^4 - z1^2 - z1)/x^2) * dx, 0 )
---------------------------------------------------------------------------
TypeError                                 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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:80, in coordinates(self, threshold, basis)

File <string>:84, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
nowe!!!! ( (1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (1) * dx, 0 )
nowe!!!! ( (z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (z1) * dx, 0 )
nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
nowe!!!! ( (z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (z0 + 1) * dx, 0 )
nowe!!!! ( (z0*z1 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (z0*z1 + z1) * dx, 0 )
nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (z0^2 - z0 + 1) * dx, 0 )
nowe!!!! ( (x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x) * dx, 0 )
nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
nowe!!!! ( (x*z0 + x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x*z0 + x) * dx, 0 )
nowe!!!! ( (x^2) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2) * dx, 0 )
nowe!!!! ( ((-x^4 - z1)/x^2) * dx, z1/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (0) * dx, 0 )
nowe!!!! ( ((-z1^2)/x^2) * dx, z1^2/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (0) * dx, 0 )
nowe!!!! ( ((x^2*z1 - z0*z1 - z1)/x^2) * dx, (z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2) * dx, 0 )
nowe!!!! ( ((x^4*z0 + x^2*z0^2*z1 + x^4 - x^2*z0*z1 + x^2*z1^2 + x^2*z1 - z0*z1^2 - z1^2)/x^2) * dx, (z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2 - z0*z1 + z1) * dx, 0 )
nowe!!!! ( ((-x^2*z0*z1 - x^2*z1 - z0^2*z1 + z0*z1 - z1)/x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2) * dx, 0 )
nowe!!!! ( ((-z0^2*z1^2 + z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 )
nowe!!!! ( ((-x^4*z0^2 + x^4*z0 + x^4*z1 - x^4 + z1^2)/x^3) * dx, z1^2/x^2 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x*z0 - x) * dx, 0 )
nowe!!!! ( ((x^2*z1^2 + z0*z1^2 + z1^2)/x^3) * dx, (z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x*z0^2 - x*z1) * dx, 0 )
nowe!!!! ( ((x^4*z0^2 - x^4*z0 - x^2*z0*z1^2 + x^4 - x^2*z1^2 + z0^2*z1^2 - z0*z1^2 + z1^2)/x^3) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x*z0^2 - x*z0 - x*z1 + x) * dx, 0 )
nowe!!!! ( ((-z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
! 0 !!: 0
selfik ( ((-x^4 - z1^2 - z1)/x^2) * dx, 0 )
---------------------------------------------------------------------------
TypeError                                 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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:80, in coordinates(self, threshold, basis)

File <string>:84, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
nowe!!!! ( (1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (1) * dx, 0 )
nowe!!!! ( (z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (z1) * dx, 0 )
nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
nowe!!!! ( (z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (z0 + 1) * dx, 0 )
nowe!!!! ( (z0*z1 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (z0*z1 + z1) * dx, 0 )
nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (z0^2 - z0 + 1) * dx, 0 )
nowe!!!! ( (x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x) * dx, 0 )
nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
nowe!!!! ( (x*z0 + x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x*z0 + x) * dx, 0 )
nowe!!!! ( (x^2) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2) * dx, 0 )
nowe!!!! ( ((-x^4 - z1)/x^2) * dx, z1/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (0) * dx, 0 )
nowe!!!! ( ((-z1^2)/x^2) * dx, z1^2/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (0) * dx, 0 )
nowe!!!! ( ((x^2*z1 - z0*z1 - z1)/x^2) * dx, (z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2) * dx, 0 )
nowe!!!! ( ((x^4*z0 + x^2*z0^2*z1 + x^4 - x^2*z0*z1 + x^2*z1^2 + x^2*z1 - z0*z1^2 - z1^2)/x^2) * dx, (z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2 - z0*z1 + z1) * dx, 0 )
nowe!!!! ( ((-x^2*z0*z1 - x^2*z1 - z0^2*z1 + z0*z1 - z1)/x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2) * dx, 0 )
nowe!!!! ( ((-z0^2*z1^2 + z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 )
nowe!!!! ( ((-x^4*z0^2 + x^4*z0 + x^4*z1 - x^4 + z1^2)/x^3) * dx, z1^2/x^2 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x*z0 - x) * dx, 0 )
nowe!!!! ( ((x^2*z1^2 + z0*z1^2 + z1^2)/x^3) * dx, (z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x*z0^2 - x*z1) * dx, 0 )
nowe!!!! ( ((x^4*z0^2 - x^4*z0 - x^2*z0*z1^2 + x^4 - x^2*z1^2 + z0^2*z1^2 - z0*z1^2 + z1^2)/x^3) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x*z0^2 - x*z0 - x*z1 + x) * dx, 0 )
nowe!!!! ( ((-z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
! 0 !!: 0
selfik ( ((-x^4 - z1^2 - z1)/x^2) * dx, 0 )
---------------------------------------------------------------------------
TypeError                                 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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:80, in coordinates(self, threshold, basis)

File <string>:84, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

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

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

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

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

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
nowe!!!! ( (1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (1) * dx, 0 )
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (z1) * dx, 0 )
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (z0 + 1) * dx, 0 )
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0*z1 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (z0*z1 + z1) * dx, 0 )
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (z0^2 - z0 + 1) * dx, 0 )
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x) * dx, 0 )
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x*z0 + x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x*z0 + x) * dx, 0 )
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^4 - z1)/x^2) * dx, z1/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (0) * dx, 0 )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z1^2)/x^2) * dx, z1^2/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (0) * dx, 0 )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^2*z1 - z0*z1 - z1)/x^2) * dx, (z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^4*z0 + x^2*z0^2*z1 + x^4 - x^2*z0*z1 + x^2*z1^2 + x^2*z1 - z0*z1^2 - z1^2)/x^2) * dx, (z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2 - z0*z1 + z1) * dx, 0 )
(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^2*z0*z1 - x^2*z1 - z0^2*z1 + z0*z1 - z1)/x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z0^2*z1^2 + z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 )
(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^4*z0^2 + x^4*z0 + x^4*z1 - x^4 + z1^2)/x^3) * dx, z1^2/x^2 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x*z0 - x) * dx, 0 )
(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^2*z1^2 + z0*z1^2 + z1^2)/x^3) * dx, (z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x*z0^2 - x*z1) * dx, 0 )
(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^4*z0^2 - x^4*z0 - x^2*z0*z1^2 + x^4 - x^2*z1^2 + z0^2*z1^2 - z0*z1^2 + z1^2)/x^3) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x*z0^2 - x*z0 - x*z1 + x) * dx, 0 )
(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
! 0 !!: 0
selfik ( ((-x^4 - z1^2 - z1)/x^2) * dx, 0 )
((-x^4 - z1^2 - z1)/x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
---------------------------------------------------------------------------
TypeError                                 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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:80, in coordinates(self, threshold, basis)

File <string>:85, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
nowe!!!! ( (1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (1) * dx, 0 )
---------------------------------------------------------------------------
AttributeError                            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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:77, in coordinates(self, threshold, basis)

File <string>:133, in diffn(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 'derivative'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
nowe!!!! ( (1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (1) * dx, 0 )
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (z1) * dx, 0 )
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (z0 + 1) * dx, 0 )
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0*z1 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (z0*z1 + z1) * dx, 0 )
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (z0^2 - z0 + 1) * dx, 0 )
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (x) * dx, 0 )
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x*z0 + x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (x*z0 + x) * dx, 0 )
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^4 - z1)/x^2) * dx, z1/x )
? 0
0 q r: 0 0
if 0 True
selfik ( (0) * dx, 0 )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z1^2)/x^2) * dx, z1^2/x )
? 0
0 q r: 0 0
if 0 True
selfik ( (0) * dx, 0 )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^2*z1 - z0*z1 - z1)/x^2) * dx, (z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
selfik ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^4*z0 + x^2*z0^2*z1 + x^4 - x^2*z0*z1 + x^2*z1^2 + x^2*z1 - z0*z1^2 - z1^2)/x^2) * dx, (z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
selfik ( (x^2 - z0*z1 + z1) * dx, 0 )
(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^2*z0*z1 - x^2*z1 - z0^2*z1 + z0*z1 - z1)/x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
selfik ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z0^2*z1^2 + z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
selfik ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 )
(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^4*z0^2 + x^4*z0 + x^4*z1 - x^4 + z1^2)/x^3) * dx, z1^2/x^2 )
? 0
0 q r: 0 0
if 0 True
selfik ( (x*z0 - x) * dx, 0 )
(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^2*z1^2 + z0*z1^2 + z1^2)/x^3) * dx, (z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
selfik ( (x*z0^2 - x*z1) * dx, 0 )
(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^4*z0^2 - x^4*z0 - x^2*z0*z1^2 + x^4 - x^2*z1^2 + z0^2*z1^2 - z0*z1^2 + z1^2)/x^3) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
selfik ( (x*z0^2 - x*z0 - x*z1 + x) * dx, 0 )
(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
selfik ( ((-x^4 - z1^2 - z1)/x^2) * dx, 0 )
((-x^4 - z1^2 - z1)/x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
---------------------------------------------------------------------------
TypeError                                 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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:80, in coordinates(self, threshold, basis)

File <string>:85, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
nowe!!!! ( (1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (1) * dx, 0 )
---------------------------------------------------------------------------
AttributeError                            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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:78, in coordinates(self, threshold, basis)

File <string>:133, in diffn(self)

AttributeError: 'as_function' object has no attribute 'derivative'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l((AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2 + AS.z[1]^2)/AS.x^3).valuation()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
nowe!!!! ( (1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (1) * dx, 0 )
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (z1) * dx, 0 )
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (z0 + 1) * dx, 0 )
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0*z1 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (z0*z1 + z1) * dx, 0 )
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (z0^2 - z0 + 1) * dx, 0 )
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (x) * dx, 0 )
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x*z0 + x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (x*z0 + x) * dx, 0 )
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^4 - z1)/x^2) * dx, z1/x )
? 0
0 q r: 0 0
if 0 True
selfik ( (0) * dx, 0 )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z1^2)/x^2) * dx, z1^2/x )
? 0
0 q r: 0 0
if 0 True
selfik ( (0) * dx, 0 )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^2*z1 - z0*z1 - z1)/x^2) * dx, (z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
selfik ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^4*z0 + x^2*z0^2*z1 + x^4 - x^2*z0*z1 + x^2*z1^2 + x^2*z1 - z0*z1^2 - z1^2)/x^2) * dx, (z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
selfik ( (x^2 - z0*z1 + z1) * dx, 0 )
(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^2*z0*z1 - x^2*z1 - z0^2*z1 + z0*z1 - z1)/x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
selfik ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z0^2*z1^2 + z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
selfik ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 )
(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^4*z0^2 + x^4*z0 + x^4*z1 - x^4 + z1^2)/x^3) * dx, z1^2/x^2 )
? 0
0 q r: 0 0
if 0 True
selfik ( (x*z0 - x) * dx, 0 )
(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^2*z1^2 + z0*z1^2 + z1^2)/x^3) * dx, (z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
selfik ( (x*z0^2 - x*z1) * dx, 0 )
(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^4*z0^2 - x^4*z0 - x^2*z0*z1^2 + x^4 - x^2*z1^2 + z0^2*z1^2 - z0*z1^2 + z1^2)/x^3) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
selfik ( (x*z0^2 - x*z0 - x*z1 + x) * dx, 0 )
(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
selfik ( ((-x^4 - z1^2 - z1)/x^2) * dx, 0 )
((-x^4 - z1^2 - z1)/x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
---------------------------------------------------------------------------
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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:80, in coordinates(self, threshold, basis)

File <string>:85, 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
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[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
nowe!!!! ( (1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (1) * dx, 0 )
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (z1) * dx, 0 )
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (z0 + 1) * dx, 0 )
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0*z1 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (z0*z1 + z1) * dx, 0 )
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (z0^2 - z0 + 1) * dx, 0 )
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (x) * dx, 0 )
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x*z0 + x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (x*z0 + x) * dx, 0 )
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^4 - z1)/x^2) * dx, z1/x )
? 0
0 q r: 0 0
if 0 True
selfik ( (0) * dx, 0 )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z1^2)/x^2) * dx, z1^2/x )
? 0
0 q r: 0 0
if 0 True
selfik ( (0) * dx, 0 )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^2*z1 - z0*z1 - z1)/x^2) * dx, (z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
selfik ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^4*z0 + x^2*z0^2*z1 + x^4 - x^2*z0*z1 + x^2*z1^2 + x^2*z1 - z0*z1^2 - z1^2)/x^2) * dx, (z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
selfik ( (x^2 - z0*z1 + z1) * dx, 0 )
(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^2*z0*z1 - x^2*z1 - z0^2*z1 + z0*z1 - z1)/x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
selfik ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z0^2*z1^2 + z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
selfik ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 )
(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^4*z0^2 + x^4*z0 + x^4*z1 - x^4 + z1^2)/x^3) * dx, z1^2/x^2 )
? 0
0 q r: 0 0
if 0 True
selfik ( (x*z0 - x) * dx, 0 )
(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^2*z1^2 + z0*z1^2 + z1^2)/x^3) * dx, (z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
selfik ( (x*z0^2 - x*z1) * dx, 0 )
(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^4*z0^2 - x^4*z0 - x^2*z0*z1^2 + x^4 - x^2*z1^2 + z0^2*z1^2 - z0*z1^2 + z1^2)/x^3) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
selfik ( (x*z0^2 - x*z0 - x*z1 + x) * dx, 0 )
(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
selfik ( ((-x^4 - z1^2 - z1)/x^2) * dx, 0 )
((-x^4 - z1^2 - z1)/x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
---------------------------------------------------------------------------
TypeError                                 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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:80, in coordinates(self, threshold, basis)

File <string>:85, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l((AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2 + AS.z[1]^2)/AS.x^3).valuation()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l((AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2 + AS.z[1]^2)/AS.x^3).valuation()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l((AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2 + AS.z[1]^2)/AS.x^3).valuation()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
nowe!!!! ( (1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (z1) * dx
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (z0 + 1) * dx
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0*z1 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (z0*z1 + z1) * dx
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x*z0 + x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0 + x) * dx
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^4 - z1)/x^2) * dx, z1/x )
? 0
0 q r: 0 0
if 0 True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z1^2)/x^2) * dx, z1^2/x )
? 0
0 q r: 0 0
if 0 True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^2*z1 - z0*z1 - z1)/x^2) * dx, (z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^4*z0 + x^2*z0^2*z1 + x^4 - x^2*z0*z1 + x^2*z1^2 + x^2*z1 - z0*z1^2 - z1^2)/x^2) * dx, (z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
hol_form (x^2 - z0*z1 + z1) * dx
(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^2*z0*z1 - x^2*z1 - z0^2*z1 + z0*z1 - z1)/x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z0^2*z1^2 + z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
hol_form (x^2*z0 + z0^2*z1 + z1^2) * dx
(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^4*z0^2 + x^4*z0 + x^4*z1 - x^4 + z1^2)/x^3) * dx, z1^2/x^2 )
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0 - x) * dx
(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^2*z1^2 + z0*z1^2 + z1^2)/x^3) * dx, (z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0^2 - x*z1) * dx
(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^4*z0^2 - x^4*z0 - x^2*z0*z1^2 + x^4 - x^2*z1^2 + z0^2*z1^2 - z0*z1^2 + z1^2)/x^3) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0^2 - x*z0 - x*z1 + x) * dx
(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
hol_form ((-x^4 - z1^2 - z1)/x^2) * dx
((-x^4 - z1^2 - z1)/x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [11], 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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:80, in coordinates(self, threshold, basis)

File <string>:85, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[1]^2/AS.x*AS.dx[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7llomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[(1) * dx,
 (z1) * dx,
 (x^2*z0 + z0^2*z1 + z1^2) * dx,
 (z0) * dx,
 (z0*z1) * dx,
 (z0^2) * dx,
 (x) * dx,
 (-x*z0^2 + x*z1) * dx,
 (x*z0) * dx,
 (x^2) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
nowe!!!! ( (1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (z1) * dx
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (z0 + 1) * dx
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0*z1 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (z0*z1 + z1) * dx
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x*z0 + x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0 + x) * dx
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^4 - z1)/x^2) * dx, z1/x )
? 0
0 q r: 0 0
if 0 True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z1^2)/x^2) * dx, z1^2/x )
? 0
0 q r: 0 0
if 0 True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^2*z1 - z0*z1 - z1)/x^2) * dx, (z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^4*z0 + x^2*z0^2*z1 + x^4 - x^2*z0*z1 + x^2*z1^2 + x^2*z1 - z0*z1^2 - z1^2)/x^2) * dx, (z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
hol_form (x^2 - z0*z1 + z1) * dx
(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^2*z0*z1 - x^2*z1 - z0^2*z1 + z0*z1 - z1)/x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z0^2*z1^2 + z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
hol_form (x^2*z0 + z0^2*z1 + z1^2) * dx
(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^4*z0^2 + x^4*z0 + x^4*z1 - x^4 + z1^2)/x^3) * dx, z1^2/x^2 )
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0 - x) * dx
(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^2*z1^2 + z0*z1^2 + z1^2)/x^3) * dx, (z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0^2 - x*z1) * dx
(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^4*z0^2 - x^4*z0 - x^2*z0*z1^2 + x^4 - x^2*z1^2 + z0^2*z1^2 - z0*z1^2 + z1^2)/x^3) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0^2 - x*z0 - x*z1 + x) * dx
(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
hol_form ((-x^4 - z1^2 - z1)/x^2) * dx
((-x^4 - z1^2 - z1)/x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
---------------------------------------------------------------------------
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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:80, in coordinates(self, threshold, basis)

File <string>:85, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = AS.holomorphic_differentials_basis()[1][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l AS.holomorphic_differentials_basis()[1][?7h[?12l[?25h[?25l[?7lsage: om = AS.holomorphic_differentials_basis()[1]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = Rxy(x^2 + y^3)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = Rxy(x^2 + y^3)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lsage: f = AS.cohomology_of s

  sage                             sage_globals                     sageobj                          save_session                     scilab                           
 

  sage0                            sage_input                       sample                           %sc                              %%script                         
 

  sage0_version                    sage_mode                        sandpiles                        scatter_plot                     search_def                       
>

  sage_eval                        sage_wraps                       save                             schonheim                        search_doc                       
 

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







[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_of_structure_sheaf_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: f = AS.cohomology_of_structure_sheaf_basis()[1]

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







 [?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentials_basis()[1][?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lrre_duality_pairing[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.serre_duality_pairing(f)

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





 [?7h[?12l[?25h[?25l[?7lom.serre_duality_pairing(f)[?7h[?12l[?25h[?25l[?7lf = AS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentials_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
nowe!!!! ( (1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (z1) * dx
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (z0 + 1) * dx
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0*z1 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (z0*z1 + z1) * dx
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x*z0 + x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0 + x) * dx
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^4 - z1)/x^2) * dx, z1/x )
? 0
0 q r: 0 0
if 0 True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z1^2)/x^2) * dx, z1^2/x )
? 0
0 q r: 0 0
if 0 True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^2*z1 - z0*z1 - z1)/x^2) * dx, (z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^4*z0 + x^2*z0^2*z1 + x^4 - x^2*z0*z1 + x^2*z1^2 + x^2*z1 - z0*z1^2 - z1^2)/x^2) * dx, (z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
hol_form (x^2 - z0*z1 + z1) * dx
(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^2*z0*z1 - x^2*z1 - z0^2*z1 + z0*z1 - z1)/x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z0^2*z1^2 + z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
hol_form (x^2*z0 + z0^2*z1 + z1^2) * dx
(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^4*z0^2 + x^4*z0 + x^4*z1 - x^4 + z1^2)/x^3) * dx, z1^2/x^2 )
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0 - x) * dx
(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^2*z1^2 + z0*z1^2 + z1^2)/x^3) * dx, (z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0^2 - x*z1) * dx
(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^4*z0^2 - x^4*z0 - x^2*z0*z1^2 + x^4 - x^2*z1^2 + z0^2*z1^2 - z0*z1^2 + z1^2)/x^3) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0^2 - x*z0 - x*z1 + x) * dx
(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
hol_form ((-x^4 - z1^2 - z1)/x^2) * dx
((-x^4 - z1^2 - z1)/x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
---------------------------------------------------------------------------
TypeError                                 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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:80, in coordinates(self, threshold, basis)

File <string>:85, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.serre_duality_pairing(f)[?7h[?12l[?25h[?25l[?7lf = AS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentials_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentials_basis()[1][?7h[?12l[?25h[?25l[?7lsage: om = AS.holomorphic_differentials_basis()[1]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentials_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.serre_duality_pairing(f)[?7h[?12l[?25h[?25l[?7lf = AS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7lsage: f = AS.cohomology_of_structure_sheaf_basis()[1]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentials_basis()[1][?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.serre_duality_pairng(f)[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lerre_duality_pairing(f)[?7h[?12l[?25h[?25l[?7lsage: om.serre_duality_pairing(f)

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = AS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7lori, j in enumerate(lll):[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmology_of_structure_sheaf_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: for f in AS.cohomology_of_structure_sheaf_basis():

....: [?7h[?12l[?25h[?25l[?7lprint(i, j)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lrre_duality_pairing[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:     print(om.serre_duality_pairing(f))

....: [?7h[?12l[?25h[?25l[?7lsage: for f in AS.cohomology_of_structure_sheaf_basis():

....:     print(om.serre_duality_pairing(f))

....: 

[?7h[?12l[?25h[?2004l0
0
0
0
2
0
0
0
0
0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor f in AS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lf in AS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7lsage: for f in AS.cohomology_of_structure_sheaf_basis():

....: [?7h[?12l[?25h[?25l[?7lfor b in [3, 5, 7, 13, 23, 67, 89, 397, 683, 2113]:[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7l....:     for omega in AS.holomorphic_differentials_basis():

....: [?7h[?12l[?25h[?25l[?7lprint(a)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_duality_pairing[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:         print(om.serre_duality_pairing(f))

....: [?7h[?12l[?25h[?25l[?7lsage: for f in AS.cohomology_of_structure_sheaf_basis():

....:     for omega in AS.holomorphic_differentials_basis():

....:         print(om.serre_duality_pairing(f))

....: 

[?7h[?12l[?25h[?2004l0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
2
2
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for f in AS.cohomology_of_structure_sheaf_basis():

....:     for omega in AS.holomorphic_differentials_basis():

....:         print(om.serre_duality_pairing(f))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lif in AS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7li,f in AS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7l f in AS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leAS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7lnAS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7luAS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7lmAS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7leAS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7lrAS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7laAS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7ltAS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7leAS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7lenumerate(AS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()):[?7h[?12l[?25h[?25l[?7l()

[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ljomega in AS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7l,omega in AS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7l omega in AS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leAS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7lnAS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7luAS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7lmAS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7leAS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7lrAS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7laAS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7ltAS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7leAS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7lenumerate(AS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l

()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()):[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l

()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lprin(om.sere_duality_pairing(f))[?7h[?12l[?25h[?25l[?7l(om.sere_duality_pairing(f))[?7h[?12l[?25h[?25l[?7l(om.sere_duality_pairing(f))[?7h[?12l[?25h[?25l[?7l(om.sere_duality_pairing(f))[?7h[?12l[?25h[?25l[?7l(om.sere_duality_pairing(f))[?7h[?12l[?25h[?25l[?7li(om.sere_duality_pairing(f))[?7h[?12l[?25h[?25l[?7lif(om.sere_duality_pairing(f))[?7h[?12l[?25h[?25l[?7l (om.sere_duality_pairing(f))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l![?7h[?12l[?25h[?25l[?7l!=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lL[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l....:         if (om.serre_duality_pairing(f)) != 0:

....: [?7h[?12l[?25h[?25l[?7lprint("Collision")[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lj[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l....:             print(i, j)

....: [?7h[?12l[?25h[?25l[?7lsage: for i, f in enumerate(AS.cohomology_of_structure_sheaf_basis()):

....:     for j, omega in enumerate(AS.holomorphic_differentials_basis()):

....:         if (om.serre_duality_pairing(f)) != 0:

....:             print(i, j)

....: 

[?7h[?12l[?25h[?2004l4 0
4 1
4 2
4 3
4 4
4 5
4 6
4 7
4 8
4 9
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
(0, 0, 2, 0, 0, 0, 0, 0, 0, 0)
(0, 0, 0, 0, 0, 2, 0, 0, 0, 0)
(0, 0, 0, 0, 2, 0, 0, 0, 0, 0)
(0, 0, 0, 2, 0, 0, 0, 0, 0, 0)
(0, 2, 2, 0, 0, 0, 0, 0, 0, 0)
(2, 0, 2, 0, 0, 2, 0, 0, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 1, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 0, 2, 0)
(0, 0, 0, 0, 0, 0, 2, 1, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 0, 0, 2)
(0, 0, 2, 0, 0, 0, 0, 0, 0, 0)
(0, 0, 0, 0, 0, 2, 0, 0, 0, 0)
(0, 0, 0, 0, 2, 0, 0, 0, 0, 0)
(0, 0, 0, 2, 0, 0, 0, 0, 0, 0)
(0, 2, 2, 0, 0, 0, 0, 0, 0, 0)
(2, 0, 2, 0, 0, 2, 0, 0, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 1, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 0, 2, 0)
(0, 0, 0, 0, 0, 0, 2, 1, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 0, 0, 2)
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
nowe!!!! ( (1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (z1) * dx
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (z0 + 1) * dx
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0*z1 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (z0*z1 + z1) * dx
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x*z0 + x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0 + x) * dx
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^4 - z1)/x^2) * dx, z1/x )
? 0
0 q r: 0 0
if 0 True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z1^2)/x^2) * dx, z1^2/x )
? 0
0 q r: 0 0
if 0 True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^2*z1 - z0*z1 - z1)/x^2) * dx, (z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^4*z0 + x^2*z0^2*z1 + x^4 - x^2*z0*z1 + x^2*z1^2 + x^2*z1 - z0*z1^2 - z1^2)/x^2) * dx, (z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
hol_form (x^2 - z0*z1 + z1) * dx
(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^2*z0*z1 - x^2*z1 - z0^2*z1 + z0*z1 - z1)/x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z0^2*z1^2 + z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
hol_form (x^2*z0 + z0^2*z1 + z1^2) * dx
(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^4*z0^2 + x^4*z0 + x^4*z1 - x^4 + z1^2)/x^3) * dx, z1^2/x^2 )
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0 - x) * dx
(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^2*z1^2 + z0*z1^2 + z1^2)/x^3) * dx, (z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0^2 - x*z1) * dx
(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^4*z0^2 - x^4*z0 - x^2*z0*z1^2 + x^4 - x^2*z1^2 + z0^2*z1^2 - z0*z1^2 + z1^2)/x^3) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0^2 - x*z0 - x*z1 + x) * dx
(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
hol_form ((-x^4 - z1^2 - z1)/x^2) * dx
((-x^4 - z1^2 - z1)/x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
---------------------------------------------------------------------------
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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:80, in coordinates(self, threshold, basis)

File <string>:85, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: for i, f in enumerate(AS.cohomology_of_structure_sheaf_basis()):

....:     for j, omega in enumerate(AS.holomorphic_differentials_basis()):

....:         if (om.serre_duality_pairing(f)) != 0:

....:             print(i, j)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l

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

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

()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:             print(i, j)

....: [?7h[?12l[?25h[?25l[?7lsage: for i, f in enumerate(AS.cohomology_of_structure_sheaf_basis()):

....:     for j, omega in enumerate(AS.holomorphic_differentials_basis()):

....:         if (om.serre_duality_pairing(f)) != 0:

....:             print(i, j)

....: 

[?7h[?12l[?25h[?2004l(0, 0, 2, 0, 0, 0, 0, 0, 0, 0)
(0, 0, 0, 0, 0, 2, 0, 0, 0, 0)
(0, 0, 0, 0, 2, 0, 0, 0, 0, 0)
(0, 0, 0, 2, 0, 0, 0, 0, 0, 0)
(0, 2, 2, 0, 0, 0, 0, 0, 0, 0)
(2, 0, 2, 0, 0, 2, 0, 0, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 1, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 0, 2, 0)
(0, 0, 0, 0, 0, 0, 2, 1, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 0, 0, 2)
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [13], in <cell line: 1>()
      1 for i, f in enumerate(AS.cohomology_of_structure_sheaf_basis()):
      2     for j, omega in enumerate(AS.holomorphic_differentials_basis()):
----> 3         if (om.serre_duality_pairing(f)) != Integer(0):
      4             print(i, j)

File <string>:117, in serre_duality_pairing(self, fct)

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>:117, in <genexpr>(.0)

AttributeError: 'NoneType' object has no attribute 'residue'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lcohlogy_of_structure_hef_basis()[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.cohomology_of_structure_sheaf_basis()

[?7h[?12l[?25h[?2004l(0, 0, 2, 0, 0, 0, 0, 0, 0, 0)
(0, 0, 0, 0, 0, 2, 0, 0, 0, 0)
(0, 0, 0, 0, 2, 0, 0, 0, 0, 0)
(0, 0, 0, 2, 0, 0, 0, 0, 0, 0)
(0, 2, 2, 0, 0, 0, 0, 0, 0, 0)
(2, 0, 2, 0, 0, 2, 0, 0, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 1, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 0, 2, 0)
(0, 0, 0, 0, 0, 0, 2, 1, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 0, 0, 2)
[?7h[z1/x,
 z1^2/x,
 z0*z1/x,
 z0*z1^2/x,
 z0^2*z1/x,
 z0^2*z1^2/x,
 z1^2/x^2,
 z0*z1^2/x^2,
 z0^2*z1^2/x^2,
 z0^2*z1^2/x^3]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: AS.cohomology_of_structure_sheaf_basis()[1]

[?7h[?12l[?25h[?2004l(0, 0, 2, 0, 0, 0, 0, 0, 0, 0)
(0, 0, 0, 0, 0, 2, 0, 0, 0, 0)
(0, 0, 0, 0, 2, 0, 0, 0, 0, 0)
(0, 0, 0, 2, 0, 0, 0, 0, 0, 0)
(0, 2, 2, 0, 0, 0, 0, 0, 0, 0)
(2, 0, 2, 0, 0, 2, 0, 0, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 1, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 0, 2, 0)
(0, 0, 0, 0, 0, 0, 2, 1, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 0, 0, 2)
[?7hz1^2/x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l AS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l=AS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l AS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A = AS.cohomology_of_structure_sheaf_basis()[1]

[?7h[?12l[?25h[?2004l(0, 0, 2, 0, 0, 0, 0, 0, 0, 0)
(0, 0, 0, 0, 0, 2, 0, 0, 0, 0)
(0, 0, 0, 0, 2, 0, 0, 0, 0, 0)
(0, 0, 0, 2, 0, 0, 0, 0, 0, 0)
(0, 2, 2, 0, 0, 0, 0, 0, 0, 0)
(2, 0, 2, 0, 0, 2, 0, 0, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 1, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 0, 2, 0)
(0, 0, 0, 0, 0, 0, 2, 1, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 0, 0, 2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.serre_duality_pairing(f)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = AS.holomorphic_dfferentials_basis()[1][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[1][?7h[?12l[?25h[?25l[?7lsage: om = AS.holomorphic_differentials_basis()[1]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentials_basis()[1][?7h[?12l[?25h[?25l[?7lm.serre_duality_pairng(f)[?7h[?12l[?25h[?25l[?7lserre_duality_pairing(f)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lA)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: om.serre_duality_pairing(A)

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.serre_duality_pairing(A)[?7h[?12l[?25h[?25l[?7l = AS.holomorphic_dfferentials_basis()[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l2][?7h[?12l[?25h[?25l[?7lsage: om = AS.holomorphic_differentials_basis()[2]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentials_basis()[2][?7h[?12l[?25h[?25l[?7l.serre_duality_pairng(A)[?7h[?12l[?25h[?25l[?7lsage: om.serre_duality_pairing(A)

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.serre_duality_pairing(A)[?7h[?12l[?25h[?25l[?7l = AS.holomorphic_dfferentials_basis()[2][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l3][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7lsage: om = AS.holomorphic_differentials_basis()[3]

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

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentials_basis()[3][?7h[?12l[?25h[?25l[?7l.serre_duality_pairng(A)[?7h[?12l[?25h[?25l[?7lsage: om.serre_duality_pairing(A)

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.serre_duality_pairing(A)[?7h[?12l[?25h[?25l[?7l = AS.holomorphic_dfferentials_basis()[3][?7h[?12l[?25h[?25l[?7l[];[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lduality_pairing[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om = AS.holomorphic_differentials_basis()[3]; om.serre_duality_pairing(A)

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentials_basis()[3]; om.serre_duality_pairing(A)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l]; om.sere_duality_pairing(A)[?7h[?12l[?25h[?25l[?7l4]; om.sere_duality_pairing(A)[?7h[?12l[?25h[?25l[?7lsage: om = AS.holomorphic_differentials_basis()[4]; om.serre_duality_pairing(A)

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = AS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7lS.cohomlgy_f_strucure_shaf_bsis()[1][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lhlrphic_differential_bsis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[(1) * dx,
 (z1) * dx,
 (x^2*z0 + z0^2*z1 + z1^2) * dx,
 (z0) * dx,
 (z0*z1) * dx,
 (z0^2) * dx,
 (x) * dx,
 (-x*z0^2 + x*z1) * dx,
 (x*z0) * dx,
 (x^2) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentils_basis()[4]; om.serre_duality_pairing(A)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]; om.sere_duality_pairing(A)[?7h[?12l[?25h[?25l[?7l5]; om.sere_duality_pairing(A)[?7h[?12l[?25h[?25l[?7lsage: om = AS.holomorphic_differentials_basis()[5]; om.serre_duality_pairing(A)

[?7h[?12l[?25h[?2004l[?7h2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentials_basis()[5]; om.serre_duality_pairing(A)[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_bsis()[?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentils_basis()[4]; om.serre_duality_pairing(A)[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l.serre_duality_pairng(A)[?7h[?12l[?25h[?25l[?7l = AS.holomorphic_dfferentials_basis()[3][?7h[?12l[?25h[?25l[?7l.serre_duality_pairng(A)[?7h[?12l[?25h[?25l[?7l = AS.holomorphic_dfferentials_basis()[2][?7h[?12l[?25h[?25l[?7l.serre_duality_pairng(A)[?7h[?12l[?25h[?25l[?7l = AS.holomorphic_dfferentials_basis()[1][?7h[?12l[?25h[?25l[?7lA = AS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7lS.cohomlgy_f_strucure_shaf_bsis()[1][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: for i, f in enumerate(AS.cohomology_of_structure_sheaf_basis()):

....:     for j, omega in enumerate(AS.holomorphic_differentials_basis()):

....:         if (om.serre_duality_pairing(f)) != 0:

....:             print(i, j)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')

 

 

 [?7h[?12l[?25h[?25l[?7lfor i, f in enumerate(AS.cohomology_of_structure_sheaf_basis()):

....:     for j, omega in enumerate(AS.holomorphic_differentials_basis()):

....:         if (om.serre_duality_pairing(f)) != 0:

....:             print(i, j)[?7h[?12l[?25h[?25l[?7lload('init.sage')

 

 

 [?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTraceback (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 [27] 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>:8 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>:68
    print('products:' [omega.serre_duality_pairing(self.f) for omega in AS.holomorphic_differentials_basis()])
          ^
SyntaxError: invalid syntax. Perhaps you forgot a comma?

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

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
nowe!!!! ( (1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z1) * dx
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z0 + 1) * dx
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0*z1 + z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z0*z1 + z1) * dx
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x*z0 + x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0 + x) * dx
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^4 - z1)/x^2) * dx, z1/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z1^2)/x^2) * dx, z1^2/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^2*z1 - z0*z1 - z1)/x^2) * dx, (z0*z1 + z1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^4*z0 + x^2*z0^2*z1 + x^4 - x^2*z0*z1 + x^2*z1^2 + x^2*z1 - z0*z1^2 - z1^2)/x^2) * dx, (z0*z1^2 + z1^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2 - z0*z1 + z1) * dx
(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^2*z0*z1 - x^2*z1 - z0^2*z1 + z0*z1 - z1)/x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z0^2*z1^2 + z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2*z0 + z0^2*z1 + z1^2) * dx
(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^4*z0^2 + x^4*z0 + x^4*z1 - x^4 + z1^2)/x^3) * dx, z1^2/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0 - x) * dx
(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^2*z1^2 + z0*z1^2 + z1^2)/x^3) * dx, (z0*z1^2 + z1^2)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0^2 - x*z1) * dx
(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^4*z0^2 - x^4*z0 - x^2*z0*z1^2 + x^4 - x^2*z1^2 + z0^2*z1^2 - z0*z1^2 + z1^2)/x^3) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0^2 - x*z0 - x*z1 + x) * dx
(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
hol_form ((-x^4 - z1^2 - z1)/x^2) * dx
((-x^4 - z1^2 - z1)/x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [28], 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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

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

File <string>:85, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldR = AS.de_rham_basis(threshold = 20)[?7h[?12l[?25h[?25l[?7le_rham_coodinate(AS, dR[0])[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lbasis(AS)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lis(AS)[?7h[?12l[?25h[?25l[?7lsage: de_rham_basis(AS)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [29], in <cell line: 1>()
----> 1 de_rham_basis(AS)

NameError: name 'de_rham_basis' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_basis(AS)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAde_rham_basis()[?7h[?12l[?25h[?25l[?7lSde_rham_basis()[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis()

[?7h[?12l[?25h[?2004lz1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[?7h[( (1) * dx, 0 ),
 ( (z1) * dx, 0 ),
 ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (z0*z1) * dx, 0 ),
 ( (z0^2) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( (-x*z0^2 + x*z1) * dx, 0 ),
 ( (x*z0) * dx, 0 ),
 ( (x^2) * dx, 0 ),
 ( ((-x^4 - z1)/x^2) * dx, z1/x ),
 ( ((-z1^2)/x^2) * dx, z1^2/x ),
 ( ((x^2*z1 - z0*z1)/x^2) * dx, z0*z1/x ),
 ( ((x^4*z0 + x^2*z0^2*z1 + x^2*z1^2 - z0*z1^2)/x^2) * dx, z0*z1^2/x ),
 ( ((-x^2*z0*z1 - z0^2*z1)/x^2) * dx, z0^2*z1/x ),
 ( ((-z0^2*z1^2)/x^2) * dx, z0^2*z1^2/x ),
 ( ((-x^4*z0^2 + x^4*z1 + z1^2)/x^3) * dx, z1^2/x^2 ),
 ( ((x^2*z1^2 + z0*z1^2)/x^3) * dx, z0*z1^2/x^2 ),
 ( ((x^4*z0^2 - x^2*z0*z1^2 + z0^2*z1^2)/x^3) * dx, z0^2*z1^2/x^2 ),
 ( ((-z0*z1^2)/x^2) * dx, z0^2*z1^2/x^3 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lgnus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus()

[?7h[?12l[?25h[?2004l[?7h10
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
nowe!!!! ( (1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z1) * dx
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z0 + 1) * dx
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0*z1 + z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z0*z1 + z1) * dx
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x*z0 + x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0 + x) * dx
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (0) * dx, z1/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z1) * dx, z1^2/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + x^2) * dx, (z0*z1 + z1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0*z1 + x^2*z0 - x^2*z1 + z0^2*z1 + x^2 - z0*z1 + z1) * dx, (z0*z1^2 + z1^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2 - z0*z1 + z1) * dx
(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0^2 - x^2*z0 + x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0^2*z1 + x^2*z0*z1 - x^2*z1 + z0*z1^2 + z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2*z0 + z0^2*z1 + z1^2) * dx
(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z0 - x) * dx, z1^2/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0 - x) * dx
(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0*z1 - x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0^2 - x*z1) * dx
(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2*z1 + x*z0^2 + x*z0*z1 - x*z0 - x*z1 + x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0^2 - x*z0 - x*z1 + x) * dx
(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-z0^2*z1 + z0*z1 - z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
hol_form (z0*z1 - z1) * dx
(z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z1 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z1 + 1) * dx
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z0) * dx
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0*z1 + z0) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z0*z1 + z0) * dx
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0^2) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z0^2) * dx
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z1 + x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (-x*z0^2 + x*z1 + x) * dx
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x*z0) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0) * dx
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (0) * dx, (z1 + 1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 1/x
1/x q r: 0 1
if 1/x True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z1 - x^2) * dx, (z1^2 - z1 + 1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 1/x
1/x q r: 0 1
if 1/x True
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0) * dx, (z0*z1 + z0)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? z0/x
z0/x q r: 0 z0
if z0/x True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0*z1 + z0^2*z1 + z0^2) * dx, (z0*z1^2 - z0*z1 + z0)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? z0/x
z0/x q r: 0 z0
if z0/x True
hol_form (z0^2) * dx
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0^2) * dx, (z0^2*z1 + z0^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (z0^2 - z1)/x
(z0^2 - z1)/x q r: 0 z0^2 - z1
if (z0^2 - z1)/x True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0^2*z1 - x^2*z0^2 + z0*z1^2 - z0*z1 + z0) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (z0^2 - z1)/x
(z0^2 - z1)/x q r: 0 z0^2 - z1
if (z0^2 - z1)/x True
hol_form (-z0*z1 + z0) * dx
(-z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2) * dx, (z1^2 - z1 + 1)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (-z1 + 1)/x^2
(-z1 + 1)/x^2 q r: 0 -z1 + 1
if (-z1 + 1)/x^2 True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0*z1 - x*z0) * dx, (z0*z1^2 - z0*z1 + z0)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (-z0*z1 + z0)/x^2
(-z0*z1 + z0)/x^2 q r: 0 -z0*z1 + z0
if (-z0*z1 + z0)/x^2 True
hol_form (-x*z0) * dx
(-x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2*z1) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (-z0^2*z1 + z0^2 - z1^2)/x^2
(-z0^2*z1 + z0^2 - z1^2)/x^2 q r: 0 -z0^2*z1 + z0^2 - z1^2
if (-z0^2*z1 + z0^2 - z1^2)/x^2 False
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [32], 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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:82, in coordinates(self, threshold, basis)

ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
nowe!!!! ( (1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z1) * dx
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z0 + 1) * dx
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0*z1 + z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z0*z1 + z1) * dx
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x*z0 + x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0 + x) * dx
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (0) * dx, z1/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z1) * dx, z1^2/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + x^2) * dx, (z0*z1 + z1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0*z1 + x^2*z0 - x^2*z1 + z0^2*z1 + x^2 - z0*z1 + z1) * dx, (z0*z1^2 + z1^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2 - z0*z1 + z1) * dx
(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0^2 - x^2*z0 + x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0^2*z1 + x^2*z0*z1 - x^2*z1 + z0*z1^2 + z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2*z0 + z0^2*z1 + z1^2) * dx
(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z0 - x) * dx, z1^2/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0 - x) * dx
(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0*z1 - x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0^2 - x*z1) * dx
(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2*z1 + x*z0^2 + x*z0*z1 - x*z0 - x*z1 + x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0^2 - x*z0 - x*z1 + x) * dx
(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-z0^2*z1 + z0*z1 - z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
hol_form (z0*z1 - z1) * dx
(z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z1 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z1 + 1) * dx
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z0) * dx
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0*z1 + z0) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z0*z1 + z0) * dx
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0^2) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z0^2) * dx
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z1 + x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (-x*z0^2 + x*z1 + x) * dx
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x*z0) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0) * dx
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (0) * dx, (z1 + 1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 1/x
1/x q r: 0 1
if 1/x True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z1 - x^2) * dx, (z1^2 - z1 + 1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 1/x
1/x q r: 0 1
if 1/x True
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0) * dx, (z0*z1 + z0)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? z0/x
z0/x q r: 0 z0
if z0/x True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0*z1 + z0^2*z1 + z0^2) * dx, (z0*z1^2 - z0*z1 + z0)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? z0/x
z0/x q r: 0 z0
if z0/x True
hol_form (z0^2) * dx
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0^2) * dx, (z0^2*z1 + z0^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (z0^2 - z1)/x
(z0^2 - z1)/x q r: 0 z0^2 - z1
if (z0^2 - z1)/x True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0^2*z1 - x^2*z0^2 + z0*z1^2 - z0*z1 + z0) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (z0^2 - z1)/x
(z0^2 - z1)/x q r: 0 z0^2 - z1
if (z0^2 - z1)/x True
hol_form (-z0*z1 + z0) * dx
(-z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2) * dx, (z1^2 - z1 + 1)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (-z1 + 1)/x^2
(-z1 + 1)/x^2 q r: 0 -z1 + 1
if (-z1 + 1)/x^2 True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0*z1 - x*z0) * dx, (z0*z1^2 - z0*z1 + z0)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (-z0*z1 + z0)/x^2
(-z0*z1 + z0)/x^2 q r: 0 -z0*z1 + z0
if (-z0*z1 + z0)/x^2 True
hol_form (-x*z0) * dx
(-x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2*z1) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (-z0^2*z1 + z0^2 - z1^2)/x^2
(-z0^2*z1 + z0^2 - z1^2)/x^2 q r: 0 -z0^2*z1 + z0^2 - z1^2
if (-z0^2*z1 + z0^2 - z1^2)/x^2 False
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [33], 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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:82, in coordinates(self, threshold, basis)

ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lon[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l].group_action[?7h[?12l[?25h[?25l[?7l1].group_action[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[)[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l1])[?7h[?12l[?25h[?25l[?7l,])[?7h[?12l[?25h[?25l[?7l ])[?7h[?12l[?25h[?25l[?7l0])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis()[1].group_action([1, 0])

[?7h[?12l[?25h[?2004l[?7h(z1) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[1].group_action([1, 0])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l0])[?7h[?12l[?25h[?25l[?7l,])[?7h[?12l[?25h[?25l[?7l ])[?7h[?12l[?25h[?25l[?7l1])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis()[1].group_action([0, 1])

[?7h[?12l[?25h[?2004l[?7h(z1 + 1) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[1].group_action([0, 1])[?7h[?12l[?25h[?25l[?7l10[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
nowe!!!! ( (1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (1) * dx
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z1) * dx
hol_form (z1) * dx
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0 + 1) * dx
hol_form (z0 + 1) * dx
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0*z1 + z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0*z1 + z1) * dx
hol_form (z0*z1 + z1) * dx
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0^2 - z0 + 1) * dx
hol_form (z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x) * dx
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (-x*z0^2 + x*z0 + x*z1 - x) * dx
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x*z0 + x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x*z0 + x) * dx
hol_form (x*z0 + x) * dx
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2) * dx
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (0) * dx, z1/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (0) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z1) * dx, z1^2/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (0) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + x^2) * dx, (z0*z1 + z1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2) * dx
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0*z1 + x^2*z0 - x^2*z1 + z0^2*z1 + x^2 - z0*z1 + z1) * dx, (z0*z1^2 + z1^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2 - z0*z1 + z1) * dx
hol_form (x^2 - z0*z1 + z1) * dx
(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0^2 - x^2*z0 + x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2) * dx
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0^2*z1 + x^2*z0*z1 - x^2*z1 + z0*z1^2 + z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2*z0 + z0^2*z1 + z1^2) * dx
hol_form (x^2*z0 + z0^2*z1 + z1^2) * dx
(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z0 - x) * dx, z1^2/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x*z0 - x) * dx
hol_form (x*z0 - x) * dx
(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0*z1 - x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x*z0^2 - x*z1) * dx
hol_form (x*z0^2 - x*z1) * dx
(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2*z1 + x*z0^2 + x*z0*z1 - x*z0 - x*z1 + x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x*z0^2 - x*z0 - x*z1 + x) * dx
hol_form (x*z0^2 - x*z0 - x*z1 + x) * dx
(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-z0^2*z1 + z0*z1 - z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
omega - df ((x^4 - x^2*z0*z1 + x^2*z1 + z1^2 + z1)/x^2) * dx
hol_form (z0*z1 - z1) * dx
(z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (1) * dx
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z1 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z1 + 1) * dx
hol_form (z1 + 1) * dx
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx
hol_form (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0) * dx
hol_form (z0) * dx
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0*z1 + z0) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0*z1 + z0) * dx
hol_form (z0*z1 + z0) * dx
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0^2) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0^2) * dx
hol_form (z0^2) * dx
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x) * dx
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z1 + x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (-x*z0^2 + x*z1 + x) * dx
hol_form (-x*z0^2 + x*z1 + x) * dx
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x*z0) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x*z0) * dx
hol_form (x*z0) * dx
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2) * dx
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (0) * dx, (z1 + 1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 1/x
1/x q r: 0 1
if 1/x True
omega - df (1/x^2) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z1 - x^2) * dx, (z1^2 - z1 + 1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 1/x
1/x q r: 0 1
if 1/x True
omega - df ((-x^4 + 1)/x^2) * dx
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0) * dx, (z0*z1 + z0)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? z0/x
z0/x q r: 0 z0
if z0/x True
omega - df ((-x^2 + z0)/x^2) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0*z1 + z0^2*z1 + z0^2) * dx, (z0*z1^2 - z0*z1 + z0)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? z0/x
z0/x q r: 0 z0
if z0/x True
omega - df ((x^2*z0^2 - x^2 + z0)/x^2) * dx
hol_form (z0^2) * dx
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0^2) * dx, (z0^2*z1 + z0^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (z0^2 - z1)/x
(z0^2 - z1)/x q r: 0 z0^2 - z1
if (z0^2 - z1)/x True
omega - df ((-x^4 + x^2*z0 + z0^2 - z1)/x^2) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0^2*z1 - x^2*z0^2 + z0*z1^2 - z0*z1 + z0) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (z0^2 - z1)/x
(z0^2 - z1)/x q r: 0 z0^2 - z1
if (z0^2 - z1)/x True
omega - df ((-x^4 - x^2*z0*z1 - x^2*z0 + z0^2 - z1)/x^2) * dx
hol_form (-z0*z1 + z0) * dx
(-z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2) * dx, (z1^2 - z1 + 1)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (-z1 + 1)/x^2
(-z1 + 1)/x^2 q r: 0 -z1 + 1
if (-z1 + 1)/x^2 True
omega - df ((-x^4 + z1 - 1)/x^3) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0*z1 - x*z0) * dx, (z0*z1^2 - z0*z1 + z0)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (-z0*z1 + z0)/x^2
(-z0*z1 + z0)/x^2 q r: 0 -z0*z1 + z0
if (-z0*z1 + z0)/x^2 True
omega - df ((x^4*z0 + x^2*z1 - x^2 + z0*z1 - z0)/x^3) * dx
hol_form (-x*z0) * dx
(-x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2*z1) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (-z0^2*z1 + z0^2 - z1^2)/x^2
(-z0^2*z1 + z0^2 - z1^2)/x^2 q r: 0 -z0^2*z1 + z0^2 - z1^2
if (-z0^2*z1 + z0^2 - z1^2)/x^2 False
omega - df ((-x^4*z0^2 + x^4*z1 - x^2*z0*z1 + x^2*z0 + z0^2*z1 - z0^2 + z1^2)/x^3) * dx
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [36], 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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:83, in coordinates(self, threshold, basis)

ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[1].group_action([0, 1])[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis()

[?7h[?12l[?25h[?2004lz1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[?7h[( (1) * dx, 0 ),
 ( (z1) * dx, 0 ),
 ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (z0*z1) * dx, 0 ),
 ( (z0^2) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( (-x*z0^2 + x*z1) * dx, 0 ),
 ( (x*z0) * dx, 0 ),
 ( (x^2) * dx, 0 ),
 ( (0) * dx, z1/x ),
 ( (-x^2*z1) * dx, z1^2/x ),
 ( (x^2*z0) * dx, z0*z1/x ),
 ( (-x^2*z0*z1 + x^2*z0 + z0^2*z1) * dx, z0*z1^2/x ),
 ( (x^2*z0^2) * dx, z0^2*z1/x ),
 ( (-x^2*z0^2*z1 + z0*z1^2) * dx, z0^2*z1^2/x ),
 ( (-x*z0^2) * dx, z1^2/x^2 ),
 ( (-x*z0*z1) * dx, z0*z1^2/x^2 ),
 ( (-x*z0^2*z1 + x*z0^2) * dx, z0^2*z1^2/x^2 ),
 ( (-z0^2*z1) * dx, z0^2*z1^2/x^3 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomAS.de_rham_bais()[?7h[?12l[?25h[?25l[?7l,AS.de_rham_basis()[?7h[?12l[?25h[?25l[?7l AS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lfAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7l AS.de_rham_basis()[?7h[?12l[?25h[?25l[?7l=AS.de_rham_basis()[?7h[?12l[?25h[?25l[?7l AS.de_rham_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l16[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: om, f = AS.de_rham_basis()[16]

[?7h[?12l[?25h[?2004lz1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [38], in <cell line: 1>()
----> 1 om, f = AS.de_rham_basis()[Integer(16)]

TypeError: cannot unpack non-iterable as_cech object
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom, f = AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l= AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7l= AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7l= AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7l= AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7l= AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7l= AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc= AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7lc= AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7l = AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: cc = AS.de_rham_basis()[16]

[?7h[?12l[?25h[?2004lz1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcc = AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[0][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7liffn[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: cc[0] - cc[1].diffn()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [40], in <cell line: 1>()
----> 1 cc[Integer(0)] - cc[Integer(1)].diffn()

TypeError: 'as_cech' object is not subscriptable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcc[0] - cc[1].diffn()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lsage: cc

[?7h[?12l[?25h[?2004l[?7h( (-x*z0^2) * dx, z1^2/x^2 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0] - cc[1].diffn()[?7h[?12l[?25h[?25l[?7l = AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7l[0] - cc[1].diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[ - c[1].difn()[?7h[?12l[?25h[?25l[?7l - c[1].difn()[?7h[?12l[?25h[?25l[?7l - c[1].difn()[?7h[?12l[?25h[?25l[?7l. - c[1].difn()[?7h[?12l[?25h[?25l[?7lom- cc[1].diffn()[?7h[?12l[?25h[?25l[?7le - c[1].difn()[?7h[?12l[?25h[?25l[?7lg - c[1].difn()[?7h[?12l[?25h[?25l[?7la - c[1].difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[1.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7lf.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: cc.omega - cc.f.diffn()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [42], in <cell line: 1>()
----> 1 cc.omega - cc.f.diffn()

AttributeError: 'as_cech' object has no attribute 'omega'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcc.omega - cc.f.diffn()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lsage: cc

[?7h[?12l[?25h[?2004l[?7h( (-x*z0^2) * dx, z1^2/x^2 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcc[?7h[?12l[?25h[?25l[?7l.omega - cc.f.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0 - c.f.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: cc.omega0 - cc.f.diffn()

[?7h[?12l[?25h[?2004l[?7h((-x^4*z0^2 - x^4*z1 - z1^2)/x^3) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcc.omega0 - cc.f.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(c.omega0 - c.f.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (cc.omega0 - cc.f.diffn()).expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2*t^-3 + t + 2*t^9 + t^13 + t^21 + 2*t^25 + t^29 + 2*t^45 + t^49 + 2*t^61 + 2*t^65 + 2*t^69 + t^73 + t^85 + 2*t^93 + t^97 + t^113 + t^121 + t^129 + 2*t^133 + t^137 + t^141 + 2*t^153 + t^157 + 2*t^169 + 2*t^173 + 2*t^177 + t^189 + t^193 + 2*t^201 + 2*t^205 + t^217 + 2*t^221 + 2*t^225 + 2*t^229 + t^237 + t^241 + 2*t^249 + t^265 + 2*t^273 + t^277 + t^289 + 2*t^297 + t^301 + 2*t^309 + t^313 + t^325 + 2*t^333 + t^345 + t^349 + 2*t^353 + t^357 + t^361 + t^365 + t^373 + 2*t^385 + 2*t^389 + t^397 + t^421 + 2*t^433 + t^437 + t^441 + t^445 + t^453 + t^457 + t^461 + t^465 + 2*t^477 + t^481 + 2*t^489 + 2*t^493 + 2*t^501 + 2*t^505 + t^513 + t^517 + 2*t^525 + 2*t^537 + t^541 + 2*t^545 + 2*t^549 + 2*t^561 + t^565 + t^569 + 2*t^573 + t^577 + t^585 + t^589 + 2*t^597 + 2*t^601 + t^609 + t^613 + 2*t^621 + t^625 + 2*t^633 + t^637 + 2*t^645 + 2*t^649 + t^657 + t^661 + 2*t^669 + t^685 + 2*t^689 + 2*t^693 + 2*t^697 + t^705 + t^709 + 2*t^717 + 2*t^721 + t^729 + t^733 + 2*t^741 + 2*t^745 + t^757 + 2*t^765 + 2*t^777 + t^781 + t^785 + 2*t^789 + 2*t^793 + t^805 + 2*t^813 + t^817 + t^829 + 2*t^837 + t^853 + 2*t^861 + t^877 + 2*t^885 + 2*t^897 + t^901 + 2*t^909 + t^913 + t^921 + t^925 + t^929 + 2*t^933 + 2*t^945 + t^949 + 2*t^957 + 2*t^961 + O(t^969)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls.coefficient_matrix()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
omega val 0
z1^2/x
omega val 12
z0*z1/x
omega val 6
z0*z1^2/x
omega val 2
z0^2*z1/x
omega val 0
z0^2*z1^2/x
omega val 0
z1^2/x^2
omega val 1
z0*z1^2/x^2
omega val 3
z0^2*z1^2/x^2
omega val 1
z0^2*z1^2/x^3
omega val 6
nowe!!!! ( (1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (1) * dx
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z1) * dx
hol_form (z1) * dx
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0 + 1) * dx
hol_form (z0 + 1) * dx
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0*z1 + z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0*z1 + z1) * dx
hol_form (z0*z1 + z1) * dx
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0^2 - z0 + 1) * dx
hol_form (z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x) * dx
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (-x*z0^2 + x*z0 + x*z1 - x) * dx
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x*z0 + x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x*z0 + x) * dx
hol_form (x*z0 + x) * dx
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2) * dx
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (0) * dx, z1/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (0) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z1) * dx, z1^2/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (0) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + x^2) * dx, (z0*z1 + z1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2) * dx
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0*z1 + x^2*z0 - x^2*z1 + z0^2*z1 + x^2 - z0*z1 + z1) * dx, (z0*z1^2 + z1^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2 - z0*z1 + z1) * dx
hol_form (x^2 - z0*z1 + z1) * dx
(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0^2 - x^2*z0 + x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2) * dx
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0^2*z1 + x^2*z0*z1 - x^2*z1 + z0*z1^2 + z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2*z0 + z0^2*z1 + z1^2) * dx
hol_form (x^2*z0 + z0^2*z1 + z1^2) * dx
(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z0 - x) * dx, z1^2/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x*z0 - x) * dx
hol_form (x*z0 - x) * dx
(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0*z1 - x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x*z0^2 - x*z1) * dx
hol_form (x*z0^2 - x*z1) * dx
(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2*z1 + x*z0^2 + x*z0*z1 - x*z0 - x*z1 + x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x*z0^2 - x*z0 - x*z1 + x) * dx
hol_form (x*z0^2 - x*z0 - x*z1 + x) * dx
(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-z0^2*z1 + z0*z1 - z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
omega - df ((x^4 - x^2*z0*z1 + x^2*z1 + z1^2 + z1)/x^2) * dx
hol_form (z0*z1 - z1) * dx
(z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (1) * dx
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z1 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z1 + 1) * dx
hol_form (z1 + 1) * dx
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx
hol_form (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0) * dx
hol_form (z0) * dx
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0*z1 + z0) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0*z1 + z0) * dx
hol_form (z0*z1 + z0) * dx
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0^2) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0^2) * dx
hol_form (z0^2) * dx
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x) * dx
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z1 + x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (-x*z0^2 + x*z1 + x) * dx
hol_form (-x*z0^2 + x*z1 + x) * dx
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x*z0) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x*z0) * dx
hol_form (x*z0) * dx
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2) * dx
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (0) * dx, (z1 + 1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 1/x
1/x q r: 0 1
if 1/x True
omega - df (1/x^2) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z1 - x^2) * dx, (z1^2 - z1 + 1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 1/x
1/x q r: 0 1
if 1/x True
omega - df ((-x^4 + 1)/x^2) * dx
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0) * dx, (z0*z1 + z0)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? z0/x
z0/x q r: 0 z0
if z0/x True
omega - df ((-x^2 + z0)/x^2) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0*z1 + z0^2*z1 + z0^2) * dx, (z0*z1^2 - z0*z1 + z0)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? z0/x
z0/x q r: 0 z0
if z0/x True
omega - df ((x^2*z0^2 - x^2 + z0)/x^2) * dx
hol_form (z0^2) * dx
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0^2) * dx, (z0^2*z1 + z0^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (z0^2 - z1)/x
(z0^2 - z1)/x q r: 0 z0^2 - z1
if (z0^2 - z1)/x True
omega - df ((-x^4 + x^2*z0 + z0^2 - z1)/x^2) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0^2*z1 - x^2*z0^2 + z0*z1^2 - z0*z1 + z0) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (z0^2 - z1)/x
(z0^2 - z1)/x q r: 0 z0^2 - z1
if (z0^2 - z1)/x True
omega - df ((-x^4 - x^2*z0*z1 - x^2*z0 + z0^2 - z1)/x^2) * dx
hol_form (-z0*z1 + z0) * dx
(-z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2) * dx, (z1^2 - z1 + 1)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (-z1 + 1)/x^2
(-z1 + 1)/x^2 q r: 0 -z1 + 1
if (-z1 + 1)/x^2 True
omega - df ((-x^4 + z1 - 1)/x^3) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0*z1 - x*z0) * dx, (z0*z1^2 - z0*z1 + z0)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (-z0*z1 + z0)/x^2
(-z0*z1 + z0)/x^2 q r: 0 -z0*z1 + z0
if (-z0*z1 + z0)/x^2 True
omega - df ((x^4*z0 + x^2*z1 - x^2 + z0*z1 - z0)/x^3) * dx
hol_form (-x*z0) * dx
(-x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2*z1) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (-z0^2*z1 + z0^2 - z1^2)/x^2
(-z0^2*z1 + z0^2 - z1^2)/x^2 q r: 0 -z0^2*z1 + z0^2 - z1^2
if (-z0^2*z1 + z0^2 - z1^2)/x^2 False
omega - df ((-x^4*z0^2 + x^4*z1 - x^2*z0*z1 + x^2*z0 + z0^2*z1 - z0^2 + z1^2)/x^3) * dx
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [46], 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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:84, in coordinates(self, threshold, basis)

ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus()

[?7h[?12l[?25h[?2004l[?7h10
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(cc.omega0 - cc.f.diffn()).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
11 10
omega val 0
z1^2/x
11 10
omega val 12
z0*z1/x
11 10
omega val 6
z0*z1^2/x
11 10
omega val 2
z0^2*z1/x
11 10
omega val 0
z0^2*z1^2/x
11 10
omega val 0
z1^2/x^2
11 10
omega val 1
z0*z1^2/x^2
11 10
omega val 3
z0^2*z1^2/x^2
11 10
omega val 1
z0^2*z1^2/x^3
11 10
omega val 6
nowe!!!! ( (1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (1) * dx
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z1) * dx
hol_form (z1) * dx
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0 + 1) * dx
hol_form (z0 + 1) * dx
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0*z1 + z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0*z1 + z1) * dx
hol_form (z0*z1 + z1) * dx
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0^2 - z0 + 1) * dx
hol_form (z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x) * dx
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (-x*z0^2 + x*z0 + x*z1 - x) * dx
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x*z0 + x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x*z0 + x) * dx
hol_form (x*z0 + x) * dx
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2) * dx
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (0) * dx, z1/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (0) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z1) * dx, z1^2/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (0) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + x^2) * dx, (z0*z1 + z1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2) * dx
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0*z1 + x^2*z0 - x^2*z1 + z0^2*z1 + x^2 - z0*z1 + z1) * dx, (z0*z1^2 + z1^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2 - z0*z1 + z1) * dx
hol_form (x^2 - z0*z1 + z1) * dx
(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0^2 - x^2*z0 + x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2) * dx
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0^2*z1 + x^2*z0*z1 - x^2*z1 + z0*z1^2 + z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2*z0 + z0^2*z1 + z1^2) * dx
hol_form (x^2*z0 + z0^2*z1 + z1^2) * dx
(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z0 - x) * dx, z1^2/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x*z0 - x) * dx
hol_form (x*z0 - x) * dx
(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0*z1 - x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x*z0^2 - x*z1) * dx
hol_form (x*z0^2 - x*z1) * dx
(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2*z1 + x*z0^2 + x*z0*z1 - x*z0 - x*z1 + x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x*z0^2 - x*z0 - x*z1 + x) * dx
hol_form (x*z0^2 - x*z0 - x*z1 + x) * dx
(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-z0^2*z1 + z0*z1 - z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
omega - df ((x^4 - x^2*z0*z1 + x^2*z1 + z1^2 + z1)/x^2) * dx
hol_form (z0*z1 - z1) * dx
(z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (1) * dx
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z1 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z1 + 1) * dx
hol_form (z1 + 1) * dx
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx
hol_form (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0) * dx
hol_form (z0) * dx
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0*z1 + z0) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0*z1 + z0) * dx
hol_form (z0*z1 + z0) * dx
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0^2) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0^2) * dx
hol_form (z0^2) * dx
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x) * dx
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z1 + x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (-x*z0^2 + x*z1 + x) * dx
hol_form (-x*z0^2 + x*z1 + x) * dx
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x*z0) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x*z0) * dx
hol_form (x*z0) * dx
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2) * dx
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (0) * dx, (z1 + 1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 1/x
1/x q r: 0 1
if 1/x True
omega - df (1/x^2) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z1 - x^2) * dx, (z1^2 - z1 + 1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 1/x
1/x q r: 0 1
if 1/x True
omega - df ((-x^4 + 1)/x^2) * dx
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0) * dx, (z0*z1 + z0)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? z0/x
z0/x q r: 0 z0
if z0/x True
omega - df ((-x^2 + z0)/x^2) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0*z1 + z0^2*z1 + z0^2) * dx, (z0*z1^2 - z0*z1 + z0)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? z0/x
z0/x q r: 0 z0
if z0/x True
omega - df ((x^2*z0^2 - x^2 + z0)/x^2) * dx
hol_form (z0^2) * dx
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0^2) * dx, (z0^2*z1 + z0^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (z0^2 - z1)/x
(z0^2 - z1)/x q r: 0 z0^2 - z1
if (z0^2 - z1)/x True
omega - df ((-x^4 + x^2*z0 + z0^2 - z1)/x^2) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0^2*z1 - x^2*z0^2 + z0*z1^2 - z0*z1 + z0) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (z0^2 - z1)/x
(z0^2 - z1)/x q r: 0 z0^2 - z1
if (z0^2 - z1)/x True
omega - df ((-x^4 - x^2*z0*z1 - x^2*z0 + z0^2 - z1)/x^2) * dx
hol_form (-z0*z1 + z0) * dx
(-z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2) * dx, (z1^2 - z1 + 1)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (-z1 + 1)/x^2
(-z1 + 1)/x^2 q r: 0 -z1 + 1
if (-z1 + 1)/x^2 True
omega - df ((-x^4 + z1 - 1)/x^3) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0*z1 - x*z0) * dx, (z0*z1^2 - z0*z1 + z0)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (-z0*z1 + z0)/x^2
(-z0*z1 + z0)/x^2 q r: 0 -z0*z1 + z0
if (-z0*z1 + z0)/x^2 True
omega - df ((x^4*z0 + x^2*z1 - x^2 + z0*z1 - z0)/x^3) * dx
hol_form (-x*z0) * dx
(-x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2*z1) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (-z0^2*z1 + z0^2 - z1^2)/x^2
(-z0^2*z1 + z0^2 - z1^2)/x^2 q r: 0 -z0^2*z1 + z0^2 - z1^2
if (-z0^2*z1 + z0^2 - z1^2)/x^2 False
omega - df ((-x^4*z0^2 + x^4*z1 - x^2*z0*z1 + x^2*z0 + z0^2*z1 - z0^2 + z1^2)/x^3) * dx
---------------------------------------------------------------------------
ValueError                                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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:84, in coordinates(self, threshold, basis)

ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
omega val 0
z1^2/x
omega val 12
z0*z1/x
omega val 6
z0*z1^2/x
omega val 2
z0^2*z1/x
omega val 0
z0^2*z1^2/x
omega val 0
z1^2/x^2
omega val 1
z0*z1^2/x^2
omega val 3
z0^2*z1^2/x^2
omega val 1
z0^2*z1^2/x^3
omega val 6
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
---------------------------------------------------------------------------
ValueError                                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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:77, in coordinates(self, threshold, basis)

ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lhomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7lsage: AS.cohomology_of_structure_sheaf_basis()[1]

[?7h[?12l[?25h[?2004l[?7hz1^2/x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i, f in enumerate(AS.cohomology_of_structure_sheaf_basis()):[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: for eta in AS.de_rham_basis():

....: [?7h[?12l[?25h[?25l[?7lprint(om.serre_duality_pairing(f))[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:     print(eta.omega0, eta.omega8.valuation())

....: [?7h[?12l[?25h[?25l[?7lsage: for eta in AS.de_rham_basis():

....:     print(eta.omega0, eta.omega8.valuation())

....: 

[?7h[?12l[?25h[?2004lz1/x
omega val 0
z1^2/x
omega val 12
z0*z1/x
omega val 6
z0*z1^2/x
omega val 2
z0^2*z1/x
omega val 0
z0^2*z1^2/x
omega val 0
z1^2/x^2
omega val 1
z0*z1^2/x^2
omega val 3
z0^2*z1^2/x^2
omega val 1
z0^2*z1^2/x^3
omega val 6
(1) * dx 18
(z1) * dx 6
(x^2*z0 + z0^2*z1 + z1^2) * dx 2
(z0) * dx 12
(z0*z1) * dx 0
(z0^2) * dx 6
(x) * dx 9
(-x*z0^2 + x*z1) * dx 1
(x*z0) * dx 3
(x^2) * dx 0
(0) * dx 0
(x^2*z1) * dx 12
(-x^2*z0) * dx 6
(x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx 2
(-x^2*z0^2) * dx 0
(x^2*z0^2*z1 - z0*z1^2) * dx 0
(x*z0^2) * dx 1
(x*z0*z1) * dx 3
(x*z0^2*z1 - x*z0^2) * dx 1
(z0^2*z1) * dx 6
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for eta in AS.de_rham_basis():

....:     print(eta.omega0, eta.omega8.valuation())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lAS.cohomology_ofstructure_sheaf_basis()[1]

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

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (z1) * dx
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (z0 + 1) * dx
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (z0*z1 + z1) * dx
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (x*z0 + x) * dx
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (-x^2 + z0*z1 - z1) * dx
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (-x^2*z0 - z0^2*z1 - z1^2) * dx
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (-x*z0 + x) * dx
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (-x*z0^2 + x*z1) * dx
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (-z0*z1 + z1) * dx
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (z1 + 1) * dx
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (z0) * dx
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (z0*z1 + z0) * dx
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (z0^2) * dx
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (-x*z0^2 + x*z1 + x) * dx
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (x*z0) * dx
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (-z0^2) * dx
(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (z0*z1 - z0) * dx
(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (x*z0) * dx
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
---------------------------------------------------------------------------
ValueError                                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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:78, in coordinates(self, threshold, basis)

ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lhlrphic_differential_bsis()[1].group_action([0, 1])[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lomorphic_differentials_basis()[1].group_action([0, 1])[?7h[?12l[?25h[?25l[?7l([][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls()[1].group_action([0, 1])[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[(1) * dx,
 (z1) * dx,
 (x^2*z0 + z0^2*z1 + z1^2) * dx,
 (z0) * dx,
 (z0*z1) * dx,
 (z0^2) * dx,
 (x) * dx,
 (-x*z0^2 + x*z1) * dx,
 (x*z0) * dx,
 (x^2) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]

None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
( (1) * dx, 0 )
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (z1) * dx, 0 )
hol_form (z1) * dx
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (z0 + 1) * dx, 0 )
hol_form (z0 + 1) * dx
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (z0*z1 + z1) * dx, 0 )
hol_form (z0*z1 + z1) * dx
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (z0^2 - z0 + 1) * dx, 0 )
hol_form (z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (x) * dx, 0 )
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (x*z0 + x) * dx, 0 )
hol_form (x*z0 + x) * dx
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (x^2) * dx, 0 )
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (0) * dx, 0 )
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (0) * dx, 0 )
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (-x^2) * dx, 0 )
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (-x^2 + z0*z1 - z1) * dx, 0 )
hol_form (-x^2 + z0*z1 - z1) * dx
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (-x^2) * dx, 0 )
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (-x^2*z0 - z0^2*z1 - z1^2) * dx, 0 )
hol_form (-x^2*z0 - z0^2*z1 - z1^2) * dx
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (-x*z0 + x) * dx, 0 )
hol_form (-x*z0 + x) * dx
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (-x*z0^2 + x*z1) * dx, 0 )
hol_form (-x*z0^2 + x*z1) * dx
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (-z0*z1 + z1) * dx, (x^2*z1 - z0*z1^2 + z1^2)/x^3 )
hol_form (-z0*z1 + z1) * dx
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (1) * dx, 0 )
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (z1 + 1) * dx, 0 )
hol_form (z1 + 1) * dx
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 )
hol_form (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (z0) * dx, 0 )
hol_form (z0) * dx
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (z0*z1 + z0) * dx, 0 )
hol_form (z0*z1 + z0) * dx
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (z0^2) * dx, 0 )
hol_form (z0^2) * dx
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (x) * dx, 0 )
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (-x*z0^2 + x*z1 + x) * dx, 0 )
hol_form (-x*z0^2 + x*z1 + x) * dx
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (x*z0) * dx, 0 )
hol_form (x*z0) * dx
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (x^2) * dx, 0 )
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (0) * dx, 1/x )
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (x^2) * dx, 1/x )
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (0) * dx, z0/x )
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (-z0^2) * dx, z0/x )
hol_form (-z0^2) * dx
(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (0) * dx, (z0^2 - z1)/x )
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (z0*z1 - z0) * dx, (z0^2 - z1)/x )
hol_form (z0*z1 - z0) * dx
(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (0) * dx, (-z1 + 1)/x^2 )
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (x*z0) * dx, (-z0*z1 + z0)/x^2 )
hol_form (x*z0) * dx
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (0) * dx, (-z0^2*z1 + z0^2 - z1^2)/x^2 )
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [54], 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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:79, in coordinates(self, threshold, basis)

ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-z0^2*z1 + z0^2 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAx^2[?7h[?12l[?25h[?25l[?7lSx^2[?7h[?12l[?25h[?25l[?7l.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz1^2)/AS.x^2[?7h[?12l[?25h[?25l[?7lSz1^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l.z1^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz0^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7lSz0^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l.z0^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz0^2*z1 + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7lSz0^2*z1 + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l.z0^2*z1 + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0^2*z1 + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2*z1 + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz1 + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7lSz1 + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l.z1 + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1 + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (-AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [55], in <cell line: 1>()
----> 1 (-AS.z[Integer(0)]**Integer(2)*AS.z[Integer(1)] + AS.z[Integer(0)]**Integer(2) - AS.z[Integer(1)]**Integer(2))/AS.x**Integer(2)

TypeError: bad operand type for unary -: 'as_function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-1AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l()*AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((-1)*AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2

[?7h[?12l[?25h[?2004l[?7h(-z0^2*z1 + z0^2 - z1^2)/x^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-1)*AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lsage: (((-1)*AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2).expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-6 + 2*t^2 + 2*t^10 + 2*t^14 + 2*t^18 + t^26 + 2*t^30 + 2*t^38 + 2*t^46 + 2*t^54 + t^58 + t^62 + t^66 + 2*t^78 + 2*t^90 + 2*t^94 + t^98 + 2*t^102 + t^118 + t^122 + 2*t^134 + 2*t^138 + 2*t^142 + 2*t^146 + 2*t^154 + t^158 + 2*t^162 + 2*t^166 + t^170 + 2*t^182 + 2*t^186 + t^190 + 2*t^202 + 2*t^206 + 2*t^218 + t^222 + t^230 + 2*t^234 + t^238 + t^246 + 2*t^250 + 2*t^262 + 2*t^266 + t^278 + 2*t^282 + t^286 + 2*t^298 + t^310 + 2*t^314 + 2*t^318 + t^326 + 2*t^330 + 2*t^334 + t^338 + 2*t^346 + t^350 + t^354 + t^370 + 2*t^374 + t^382 + 2*t^386 + t^390 + 2*t^394 + t^402 + 2*t^410 + 2*t^414 + t^418 + t^422 + t^426 + 2*t^434 + t^446 + 2*t^450 + t^458 + 2*t^462 + t^466 + 2*t^470 + 2*t^474 + 2*t^478 + 2*t^482 + 2*t^486 + t^490 + t^494 + t^498 + 2*t^510 + 2*t^514 + t^522 + 2*t^526 + 2*t^530 + 2*t^538 + 2*t^542 + 2*t^546 + 2*t^554 + 2*t^558 + 2*t^562 + 2*t^574 + 2*t^578 + 2*t^586 + 2*t^590 + 2*t^594 + 2*t^602 + 2*t^606 + 2*t^610 + t^618 + 2*t^622 + 2*t^638 + 2*t^642 + 2*t^650 + 2*t^654 + 2*t^670 + t^682 + 2*t^686 + 2*t^698 + 2*t^702 + t^714 + 2*t^718 + t^730 + 2*t^734 + t^746 + 2*t^750 + t^762 + 2*t^766 + 2*t^770 + t^778 + 2*t^782 + 2*t^786 + 2*t^798 + 2*t^802 + 2*t^814 + t^818 + t^826 + 2*t^830 + 2*t^834 + t^842 + 2*t^846 + 2*t^850 + t^858 + 2*t^862 + 2*t^866 + t^874 + 2*t^878 + 2*t^882 + t^890 + 2*t^894 + 2*t^898 + t^906 + 2*t^910 + t^914 + t^922 + 2*t^926 + t^930 + 2*t^942 + t^946 + 2*t^958 + 2*t^966 + t^970 + t^978 + t^982 + 2*t^986 + O(t^994)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: (((-1)*AS.z[0]^2*AS.z[1] + AS.z[0]^2)/AS.x^2).expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2*t^-6 + 2*t^-2 + 2*t^6 + t^10 + 2*t^14 + t^18 + 2*t^22 + t^30 + 2*t^34 + 2*t^38 + t^46 + 2*t^50 + t^54 + 2*t^58 + t^70 + t^74 + t^82 + t^86 + t^90 + t^98 + 2*t^102 + 2*t^106 + t^114 + t^122 + 2*t^126 + 2*t^130 + t^134 + t^138 + 2*t^146 + t^154 + t^162 + t^166 + t^174 + t^178 + 2*t^182 + t^194 + t^198 + 2*t^206 + t^210 + 2*t^214 + t^222 + t^226 + t^242 + t^246 + t^258 + t^270 + t^274 + 2*t^278 + t^286 + t^290 + t^294 + t^302 + t^306 + 2*t^322 + 2*t^326 + t^330 + 2*t^338 + 2*t^342 + t^346 + t^350 + 2*t^358 + t^362 + 2*t^366 + t^374 + 2*t^378 + 2*t^382 + t^386 + 2*t^394 + t^398 + t^402 + t^406 + 2*t^410 + t^414 + t^418 + t^422 + 2*t^430 + t^434 + t^438 + t^442 + t^446 + 2*t^454 + 2*t^458 + t^462 + 2*t^470 + t^478 + t^486 + t^490 + t^502 + 2*t^506 + 2*t^514 + t^518 + t^534 + t^546 + t^550 + t^554 + t^566 + t^582 + t^586 + t^594 + t^598 + t^602 + t^610 + t^614 + 2*t^618 + t^626 + t^630 + t^642 + t^646 + t^650 + t^662 + 2*t^666 + t^674 + t^678 + t^694 + t^698 + 2*t^706 + t^710 + 2*t^722 + t^726 + 2*t^738 + t^742 + t^754 + t^758 + 2*t^762 + t^770 + t^774 + 2*t^778 + t^790 + 2*t^794 + t^806 + t^810 + 2*t^818 + t^822 + t^826 + 2*t^834 + t^838 + t^842 + 2*t^850 + t^854 + t^858 + 2*t^866 + t^870 + t^874 + 2*t^882 + t^886 + t^890 + t^898 + t^902 + t^914 + t^918 + t^934 + t^950 + 2*t^954 + 2*t^962 + 2*t^966 + 2*t^990 + O(t^994)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] + AS.z[0]^2)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l-1)*AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l-AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Input In [59], 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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:55, in coordinates(self, threshold, basis)

IndexError: list assignment index out of range
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [60], 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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:61, in coordinates(self, threshold, basis)

File <string>:61, in <listcomp>(.0)

File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:493, in sage.modules.free_module_element.vector()
    491     pass
    492 else:
--> 493     v = arg0_vector_(arg1)
    494     if immutable:
    495         v.set_immutable()

TypeError: IntegerMod_int._vector_() takes no arguments (1 given)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [61], 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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:61, in coordinates(self, threshold, basis)

File <string>:61, in <listcomp>(.0)

File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:493, in sage.modules.free_module_element.vector()
    491     pass
    492 else:
--> 493     v = arg0_vector_(arg1)
    494     if immutable:
    495         v.set_immutable()

TypeError: IntegerMod_int._vector_() takes no arguments (1 given)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (1) * dx, 0 ) []
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z1) * dx, 0 ) []
hol_form (z1) * dx
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) []
hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0 + 1) * dx, 0 ) []
hol_form (z0 + 1) * dx
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0*z1 + z1) * dx, 0 ) []
hol_form (z0*z1 + z1) * dx
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0^2 - z0 + 1) * dx, 0 ) []
hol_form (z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x) * dx, 0 ) []
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) []
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x*z0 + x) * dx, 0 ) []
hol_form (x*z0 + x) * dx
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2) * dx, 0 ) []
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, 0 ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, 0 ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2) * dx, 0 ) []
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2 + z0*z1 - z1) * dx, 0 ) []
hol_form (-x^2 + z0*z1 - z1) * dx
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2) * dx, 0 ) []
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2*z0 - z0^2*z1 - z1^2) * dx, 0 ) []
hol_form (-x^2*z0 - z0^2*z1 - z1^2) * dx
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0 + x) * dx, 0 ) []
hol_form (-x*z0 + x) * dx
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z1) * dx, 0 ) []
hol_form (-x*z0^2 + x*z1) * dx
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) []
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-z0*z1 + z1) * dx, (x^2*z1 - z0*z1^2 + z1^2)/x^3 ) []
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [62], 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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:70, in coordinates(self, threshold, basis)

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

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (1) * dx, 0 ) []
---------------------------------------------------------------------------
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()

AttributeError: 'function' object has no attribute 'numerator'

During handling of the above exception, another exception occurred:

TypeError                                 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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:69, in coordinates(self, threshold, basis)

File <string>:14, 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: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 <function denominator at 0x7f71d01e8820>/1 to an element of Fraction Field of Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (1) * dx, 0 ) []
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z1) * dx, 0 ) []
hol_form (z1) * dx
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) []
hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0 + 1) * dx, 0 ) []
hol_form (z0 + 1) * dx
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0*z1 + z1) * dx, 0 ) []
hol_form (z0*z1 + z1) * dx
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0^2 - z0 + 1) * dx, 0 ) []
hol_form (z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x) * dx, 0 ) []
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) []
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x*z0 + x) * dx, 0 ) []
hol_form (x*z0 + x) * dx
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2) * dx, 0 ) []
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, 0 ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, 0 ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2) * dx, 0 ) []
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2 + z0*z1 - z1) * dx, 0 ) []
hol_form (-x^2 + z0*z1 - z1) * dx
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2) * dx, 0 ) []
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2*z0 - z0^2*z1 - z1^2) * dx, 0 ) []
hol_form (-x^2*z0 - z0^2*z1 - z1^2) * dx
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0 + x) * dx, 0 ) []
hol_form (-x*z0 + x) * dx
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z1) * dx, 0 ) []
hol_form (-x*z0^2 + x*z1) * dx
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) []
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-z0*z1 + z1) * dx, (x^2*z1 - z0*z1^2 + z1^2)/x^3 ) []
hol_form (-z0*z1 + z1) * dx
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (1) * dx, 0 ) []
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z1 + 1) * dx, 0 ) []
hol_form (z1 + 1) * dx
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 ) []
hol_form (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0) * dx, 0 ) []
hol_form (z0) * dx
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0*z1 + z0) * dx, 0 ) []
hol_form (z0*z1 + z0) * dx
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0^2) * dx, 0 ) []
hol_form (z0^2) * dx
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x) * dx, 0 ) []
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z1 + x) * dx, 0 ) []
hol_form (-x*z0^2 + x*z1 + x) * dx
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x*z0) * dx, 0 ) []
hol_form (x*z0) * dx
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2) * dx, 0 ) []
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, 1/x ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2) * dx, 1/x ) []
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, z0/x ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-z0^2) * dx, z0/x ) []
hol_form (-z0^2) * dx
(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, (z0^2 - z1)/x ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0*z1 - z0) * dx, (z0^2 - z1)/x ) []
hol_form (z0*z1 - z0) * dx
(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, (-z1 + 1)/x^2 ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x*z0) * dx, (-z0*z1 + z0)/x^2 ) []
hol_form (x*z0) * dx
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, (-z0^2*z1 + z0^2 - z1^2)/x^2 ) []
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [64], 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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:82, in coordinates(self, threshold, basis)

ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] + AS.z[0]^2)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l - AS.z[1]^2)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] + AS.z[0]^2)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (1) * dx, 0 ) []
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z1) * dx, 0 ) []
hol_form (z1) * dx
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) []
hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0 + 1) * dx, 0 ) []
hol_form (z0 + 1) * dx
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0*z1 + z1) * dx, 0 ) []
hol_form (z0*z1 + z1) * dx
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0^2 - z0 + 1) * dx, 0 ) []
hol_form (z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x) * dx, 0 ) []
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) []
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x*z0 + x) * dx, 0 ) []
hol_form (x*z0 + x) * dx
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2) * dx, 0 ) []
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, 0 ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, 0 ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2) * dx, 0 ) []
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2 + z0*z1 - z1) * dx, 0 ) []
hol_form (-x^2 + z0*z1 - z1) * dx
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2) * dx, 0 ) []
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2*z0 - z0^2*z1 - z1^2) * dx, 0 ) []
hol_form (-x^2*z0 - z0^2*z1 - z1^2) * dx
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0 + x) * dx, 0 ) []
hol_form (-x*z0 + x) * dx
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z1) * dx, 0 ) []
hol_form (-x*z0^2 + x*z1) * dx
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) []
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-z0*z1 + z1) * dx, (x^2*z1 - z0*z1^2 + z1^2)/x^3 ) []
hol_form (-z0*z1 + z1) * dx
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (1) * dx, 0 ) []
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z1 + 1) * dx, 0 ) []
hol_form (z1 + 1) * dx
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 ) []
hol_form (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0) * dx, 0 ) []
hol_form (z0) * dx
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0*z1 + z0) * dx, 0 ) []
hol_form (z0*z1 + z0) * dx
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0^2) * dx, 0 ) []
hol_form (z0^2) * dx
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x) * dx, 0 ) []
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z1 + x) * dx, 0 ) []
hol_form (-x*z0^2 + x*z1 + x) * dx
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x*z0) * dx, 0 ) []
hol_form (x*z0) * dx
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2) * dx, 0 ) []
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, 1/x ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2) * dx, 1/x ) []
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, z0/x ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-z0^2) * dx, z0/x ) []
hol_form (-z0^2) * dx
(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, (z0^2 - z1)/x ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0*z1 - z0) * dx, (z0^2 - z1)/x ) []
hol_form (z0*z1 - z0) * dx
(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, (-z1 + 1)/x^2 ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x*z0) * dx, (-z0*z1 + z0)/x^2 ) []
hol_form (x*z0) * dx
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, (-z0^2*z1 + z0^2 - z1^2)/x^2 ) []
( (0) * dx, (-z0^2*z1 - z1^2)/x^2 )
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [65], 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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:83, in coordinates(self, threshold, basis)

ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.quo_rem(f)[?7h[?12l[?25h[?25l[?7lg =[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAx^2[?7h[?12l[?25h[?25l[?7lSx^2[?7h[?12l[?25h[?25l[?7l.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz1^2)/AS.x^2[?7h[?12l[?25h[?25l[?7lSz1^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l.z1^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lAz0^2*z1 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7lSz0^2*z1 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l.z0^2*z1 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0^2*z1 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2*z1 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz1 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7lSz1 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l/z1 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz1 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l.z1 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (-AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [66], in <cell line: 1>()
----> 1 (-AS.z[Integer(0)]**Integer(2)*AS.z[Integer(1)] - AS.z[Integer(1)]**Integer(2))/AS.x**Integer(2)

TypeError: bad operand type for unary -: 'as_function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l()AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-1)AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((-1)AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2

[?7h[?12l[?25h[?2004l  Input In [67]
    ((-Integer(1))AS.z[Integer(0)]**Integer(2)*AS.z[Integer(1)] - AS.z[Integer(1)]**Integer(2))/AS.x**Integer(2)
      ^
SyntaxError: invalid syntax. Perhaps you forgot a comma?

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-1)AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7lsage: ((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2

[?7h[?12l[?25h[?2004l[?7h(-z0^2*z1 - z1^2)/x^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l2.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2.expansion_at_infty()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [69], in <cell line: 1>()
----> 1 ((-Integer(1))*AS.z[Integer(0)]**Integer(2)*AS.z[Integer(1)] - AS.z[Integer(1)]**Integer(2))/AS.x**Integer(2).expansion_at_infty()

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 'expansion_at_infty'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: (((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-6 + 2*t^2 + 2*t^6 + 2*t^10 + 2*t^14 + 2*t^18 + 2*t^22 + t^26 + 2*t^30 + t^38 + 2*t^42 + 2*t^46 + 2*t^54 + t^62 + t^66 + 2*t^74 + t^98 + 2*t^102 + t^106 + t^110 + 2*t^114 + t^118 + 2*t^122 + t^126 + 2*t^130 + 2*t^134 + 2*t^138 + t^146 + 2*t^154 + 2*t^158 + 2*t^162 + 2*t^166 + t^170 + t^174 + 2*t^182 + 2*t^190 + 2*t^198 + 2*t^214 + t^246 + 2*t^254 + 2*t^262 + 2*t^270 + t^278 + t^294 + 2*t^302 + 2*t^310 + t^318 + 2*t^326 + t^330 + t^334 + t^338 + t^342 + t^346 + t^354 + t^358 + 2*t^362 + 2*t^366 + t^370 + t^378 + 2*t^386 + t^390 + 2*t^398 + t^422 + 2*t^426 + t^430 + t^434 + 2*t^438 + t^442 + 2*t^446 + t^450 + 2*t^454 + 2*t^458 + 2*t^462 + t^470 + 2*t^474 + 2*t^478 + t^482 + 2*t^486 + t^490 + t^494 + t^514 + t^522 + t^530 + 2*t^538 + 2*t^546 + 2*t^554 + 2*t^562 + t^570 + 2*t^578 + 2*t^618 + t^626 + t^634 + t^658 + t^666 + t^674 + 2*t^682 + 2*t^762 + 2*t^770 + 2*t^778 + 2*t^786 + t^794 + 2*t^802 + 2*t^810 + t^818 + 2*t^906 + 2*t^914 + 2*t^922 + 2*t^930 + t^938 + 2*t^946 + 2*t^954 + t^962 + 2*t^966 + t^974 + t^978 + t^982 + t^986 + t^990 + O(t^994)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_atinfty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: (((-1)*AS.z[0]^2*AS.z[1])/AS.x^2).expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2*t^-6 + 2*t^-2 + t^6 + t^10 + 2*t^14 + t^18 + t^22 + t^30 + 2*t^34 + t^38 + 2*t^42 + t^46 + 2*t^50 + t^54 + t^58 + t^70 + t^78 + t^82 + t^86 + 2*t^90 + t^94 + t^98 + 2*t^102 + t^110 + 2*t^122 + t^130 + t^134 + t^138 + t^142 + t^146 + t^154 + t^158 + t^162 + t^166 + 2*t^174 + t^178 + 2*t^182 + t^186 + t^190 + t^194 + t^202 + t^210 + t^214 + t^218 + t^226 + 2*t^230 + t^234 + 2*t^238 + t^242 + t^246 + t^250 + 2*t^254 + t^258 + t^266 + t^274 + 2*t^278 + t^282 + t^290 + 2*t^294 + t^298 + t^306 + t^310 + t^314 + 2*t^318 + 2*t^322 + 2*t^334 + 2*t^338 + t^366 + 2*t^374 + t^382 + t^386 + t^406 + 2*t^414 + t^422 + t^426 + 2*t^442 + 2*t^446 + 2*t^450 + t^454 + t^462 + 2*t^466 + t^470 + t^478 + 2*t^482 + t^486 + t^490 + 2*t^498 + t^502 + 2*t^506 + t^510 + t^514 + t^518 + t^526 + 2*t^530 + t^534 + t^542 + t^546 + t^550 + t^554 + t^558 + t^566 + t^570 + t^574 + t^582 + 2*t^586 + t^590 + 2*t^594 + t^598 + 2*t^602 + t^606 + 2*t^610 + t^614 + t^622 + 2*t^626 + t^630 + t^634 + t^638 + 2*t^642 + t^646 + 2*t^650 + t^654 + t^658 + t^662 + t^670 + 2*t^674 + t^678 + t^682 + t^686 + t^694 + 2*t^698 + t^702 + 2*t^706 + t^710 + 2*t^714 + t^718 + 2*t^722 + t^726 + 2*t^730 + t^734 + 2*t^738 + t^742 + 2*t^746 + t^750 + t^754 + t^758 + t^766 + t^770 + t^774 + t^782 + t^790 + t^798 + t^806 + t^814 + 2*t^818 + t^822 + t^830 + t^838 + t^846 + t^854 + t^862 + t^870 + t^878 + t^886 + t^894 + 2*t^898 + t^902 + t^906 + t^910 + 2*t^914 + t^918 + t^922 + t^926 + t^930 + t^934 + t^938 + t^942 + t^946 + t^950 + t^954 + t^958 + 2*t^966 + 2*t^970 + t^974 + 2*t^986 + O(t^994)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1])/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l - AS.z[1]^2)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).diffn()

[?7h[?12l[?25h[?2004l[?7h((x^4*z0^2 - x^4*z1 + x^2*z0*z1 - z0^2*z1 - z1^2)/x^3) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_nty()[?7h[?12l[?25h[?25l[?7l - AS.z[1]^2)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lAS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l-AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] + AS.z[0]^2)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (1) * dx, 0 ) []
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z1) * dx, 0 ) []
hol_form (z1) * dx
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) []
hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0 + 1) * dx, 0 ) []
hol_form (z0 + 1) * dx
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0*z1 + z1) * dx, 0 ) []
hol_form (z0*z1 + z1) * dx
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0^2 - z0 + 1) * dx, 0 ) []
hol_form (z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x) * dx, 0 ) []
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) []
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x*z0 + x) * dx, 0 ) []
hol_form (x*z0 + x) * dx
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2) * dx, 0 ) []
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, 0 ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, 0 ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2) * dx, 0 ) []
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2 + z0*z1 - z1) * dx, 0 ) []
hol_form (-x^2 + z0*z1 - z1) * dx
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2) * dx, 0 ) []
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2*z0 - z0^2*z1 - z1^2) * dx, 0 ) []
hol_form (-x^2*z0 - z0^2*z1 - z1^2) * dx
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0 + x) * dx, 0 ) []
hol_form (-x*z0 + x) * dx
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z1) * dx, 0 ) []
hol_form (-x*z0^2 + x*z1) * dx
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) []
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-z0*z1 + z1) * dx, (x^2*z1 - z0*z1^2 + z1^2)/x^3 ) []
hol_form (-z0*z1 + z1) * dx
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (1) * dx, 0 ) []
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z1 + 1) * dx, 0 ) []
hol_form (z1 + 1) * dx
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 ) []
hol_form (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0) * dx, 0 ) []
hol_form (z0) * dx
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0*z1 + z0) * dx, 0 ) []
hol_form (z0*z1 + z0) * dx
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0^2) * dx, 0 ) []
hol_form (z0^2) * dx
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x) * dx, 0 ) []
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z1 + x) * dx, 0 ) []
hol_form (-x*z0^2 + x*z1 + x) * dx
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x*z0) * dx, 0 ) []
hol_form (x*z0) * dx
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2) * dx, 0 ) []
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, 1/x ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2) * dx, 1/x ) []
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, z0/x ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-z0^2) * dx, z0/x ) []
hol_form (-z0^2) * dx
(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, (z0^2 - z1)/x ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0*z1 - z0) * dx, (z0^2 - z1)/x ) []
hol_form (z0*z1 - z0) * dx
(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, (-z1 + 1)/x^2 ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x*z0) * dx, (-z0*z1 + z0)/x^2 ) []
hol_form (x*z0) * dx
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, (-z0^2*z1 + z0^2 - z1^2)/x^2 ) []
( (0) * dx, (-z0^2*z1 - z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
---------------------------------------------------------------------------
ValueError                                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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:83, in coordinates(self, threshold, basis)

ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_nty()[?7h[?12l[?25h[?25l[?7l - AS.z[1]^2)/AS.x^2).dfn()[?7h[?12l[?25h[?25l[?7lsage: (((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).diffn()

[?7h[?12l[?25h[?2004l[?7h((x^4*z0^2 - x^4*z1 + x^2*z0*z1 - z0^2*z1 - z1^2)/x^3) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (1) * dx, 0 ) []
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z1) * dx, 0 ) []
hol_form (z1) * dx
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) []
hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0 + 1) * dx, 0 ) []
hol_form (z0 + 1) * dx
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0*z1 + z1) * dx, 0 ) []
hol_form (z0*z1 + z1) * dx
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0^2 - z0 + 1) * dx, 0 ) []
hol_form (z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x) * dx, 0 ) []
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) []
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x*z0 + x) * dx, 0 ) []
hol_form (x*z0 + x) * dx
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2) * dx, 0 ) []
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, 0 ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, 0 ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2) * dx, 0 ) []
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2 + z0*z1 - z1) * dx, 0 ) []
hol_form (-x^2 + z0*z1 - z1) * dx
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2) * dx, 0 ) []
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2*z0 - z0^2*z1 - z1^2) * dx, 0 ) []
hol_form (-x^2*z0 - z0^2*z1 - z1^2) * dx
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0 + x) * dx, 0 ) []
hol_form (-x*z0 + x) * dx
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z1) * dx, 0 ) []
hol_form (-x*z0^2 + x*z1) * dx
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) []
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-z0*z1 + z1) * dx, (x^2*z1 - z0*z1^2 + z1^2)/x^3 ) []
hol_form (-z0*z1 + z1) * dx
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (1) * dx, 0 ) []
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z1 + 1) * dx, 0 ) []
hol_form (z1 + 1) * dx
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 ) []
hol_form (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0) * dx, 0 ) []
hol_form (z0) * dx
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0*z1 + z0) * dx, 0 ) []
hol_form (z0*z1 + z0) * dx
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0^2) * dx, 0 ) []
hol_form (z0^2) * dx
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x) * dx, 0 ) []
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z1 + x) * dx, 0 ) []
hol_form (-x*z0^2 + x*z1 + x) * dx
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x*z0) * dx, 0 ) []
hol_form (x*z0) * dx
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2) * dx, 0 ) []
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, 1/x ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2) * dx, 1/x ) []
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, z0/x ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-z0^2) * dx, z0/x ) []
hol_form (-z0^2) * dx
(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, (z0^2 - z1)/x ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0*z1 - z0) * dx, (z0^2 - z1)/x ) []
hol_form (z0*z1 - z0) * dx
(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, (-z1 + 1)/x^2 ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x*z0) * dx, (-z0*z1 + z0)/x^2 ) []
hol_form (x*z0) * dx
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, (-z0^2*z1 + z0^2 - z1^2)/x^2 ) []
( (0) * dx, (-z0^2*z1 - z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
---------------------------------------------------------------------------
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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:85, in coordinates(self, threshold, basis)

ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7lSz0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-ASz0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1ASz0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l()ASz0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l()*ASz0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7lSz1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l.z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[] - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz1^2)/x^2[?7h[?12l[?25h[?25l[?7lSz1^2)/x^2[?7h[?12l[?25h[?25l[?7l.z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2)/x^2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lAx^2[?7h[?12l[?25h[?25l[?7lSx^2[?7h[?12l[?25h[?25l[?7l.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: ((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2.expansion_at_infty()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [2], in <cell line: 1>()
----> 1 ((-Integer(1))*AS.z[Integer(0)]**Integer(2)*AS.z[Integer(1)] - AS.z[Integer(1)]**Integer(2))/AS.x**Integer(2).expansion_at_infty()

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 'expansion_at_infty'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: ((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2

[?7h[?12l[?25h[?2004l[?7h(-z0^2*z1 - z1^2)/x^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2.)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().diffn()[?7h[?12l[?25h[?25l[?7lexpasion_at_infty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).diffn()

[?7h[?12l[?25h[?2004l[?7h((x^4*z0^2 - x^4*z1 + x^2*z0*z1 - z0^2*z1 - z1^2)/x^3) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[(1) * dx,
 (z1) * dx,
 (x^2*z0 + z0^2*z1 + z1^2) * dx,
 (z0) * dx,
 (z0*z1) * dx,
 (z0^2) * dx,
 (x) * dx,
 (-x*z0^2 + x*z1) * dx,
 (x*z0) * dx,
 (x^2) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lv()[?7h[?12l[?25h[?25l[?7la()[?7h[?12l[?25h[?25l[?7ll()[?7h[?12l[?25h[?25l[?7lu()[?7h[?12l[?25h[?25l[?7la()[?7h[?12l[?25h[?25l[?7lt()[?7h[?12l[?25h[?25l[?7li()[?7h[?12l[?25h[?25l[?7lo()[?7h[?12l[?25h[?25l[?7ln()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (((-1)*AS.z[0]^2*AS.z[1])/AS.x^2).valuation()

[?7h[?12l[?25h[?2004l[?7h-6
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1])/AS.x^2).valuation()[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l[- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l[]- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l[- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l()- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l(- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7lsage: ((- AS.z[1]^2)/AS.x^2).diffn()

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

TypeError: bad operand type for unary -: 'as_function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((- AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1 AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l() AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l()* AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (((-1)* AS.z[1]^2)/AS.x^2).diffn()

[?7h[?12l[?25h[?2004l[?7h((-x^4*z1 - z1^2)/x^3) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-1)* AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (((-1)* AS.z[1]^2)/AS.x^2).valuation()

[?7h[?12l[?25h[?2004l[?7h-6
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lsage: p

[?7h[?12l[?25h[?2004l[?7h3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7lf(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l (-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l=(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l (-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7la(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7las(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7las_(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7lf(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7lu(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7ln(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7lc(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7lt(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7li(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7lo(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7ln(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l((-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7lA(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7lS(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l,(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l (-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lxf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lyf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lzf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lQf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l,f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lRf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lxf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lyf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lzf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l,f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lxf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l,f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lyf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l,f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lzf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l=f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lAf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lSf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l.f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lcf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7ltf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l_f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lif = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lef = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7llf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7ldf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l(f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l()f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l();f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: RxyzQ, Rxyz, x, y,z = AS.fct_field(); ff = as_function(AS, (-z0^2*z1 - z1^2)/x^2)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [12], in <cell line: 1>()
----> 1 RxyzQ, Rxyz, x, y,z = AS.fct_field(); ff = as_function(AS, (-z0**Integer(2)*z1 - z1**Integer(2))/x**Integer(2))

TypeError: 'tuple' object is not callable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field(); ff = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(; f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l; f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lsage: RxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-z0^2*z1 - z1^2)/x^2)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [13], in <cell line: 1>()
----> 1 RxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-z0**Integer(2)*z1 - z1**Integer(2))/x**Integer(2))

NameError: name 'z0' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[] - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1^2)/x^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2)/x^2)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*z[1] - z[1]^2)/x^2)[?7h[?12l[?25h[?25l[?7l3*z[1] - z[1]^2)/x^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lz[1]^2)/x^2)[?7h[?12l[?25h[?25l[?7l[z[1]^2)/x^2)[?7h[?12l[?25h[?25l[?7l[]z[1]^2)/x^2)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l0]z[1]^2)/x^2)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[]*z[1]^2)/x^2)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(x^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l*))[?7h[?12l[?25h[?25l[?7lz))[?7h[?12l[?25h[?25l[?7l[))[?7h[?12l[?25h[?25l[?7l0))[?7h[?12l[?25h[?25l[?7l]))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: RxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-z[0]^3*z[1] - z[0]*z[1]^2)/(x^2*z[0]))

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor eta in AS.de_rham_basis():[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor eta in AS.de_rham_basis():[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7las[?7h[?12l[?25h[?25l[?7las_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7las[?7h[?12l[?25h[?25l[?7las_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(),[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fff = as_cech(AS, as_form(AS, 0), ff)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: fff.

 fff.coordinates  fff.group_action

 fff.curve        fff.omega0      

 fff.f            fff.omega8      



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

 fff.coordinates 





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







[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fff.coordinates()

[?7h[?12l[?25h[?2004lz1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, (-z0^2*z1 - z1^2)/x^2 ) []
( (0) * dx, (-z0^2*z1 - z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [16], in <cell line: 1>()
----> 1 fff.coordinates()

File <string>:85, in coordinates(self, threshold, basis)

ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7l = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-z[0]^3*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7lfff = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lfct_field[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7l = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-z[0]^3*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l(z[0]^3*z[1] - z[0]*z[1]^2)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()*z[1] - z[0]*z[1]^2)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l+)*z[1] - z[0]*z[1]^2)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7lx)*z[1] - z[0]*z[1]^2)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l^)*z[1] - z[0]*z[1]^2)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l2)*z[1] - z[0]*z[1]^2)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l[]+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: RxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0]))

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7l = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lsage: fff = as_cech(AS, as_form(AS, 0), ff)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7l = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-z[0]^3*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7l0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l(); ff= as_function(AS, (-z0^2*z1- z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l(((-1)* AS.z[1]^2)/AS.x^2).valuation()[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7l(-1)*AS.z[0]^2*AS.z[1])/AS.x^2).valuation()[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1])/AS.x^2).valuation()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7l(-1)* AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7lvaluation()[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field(); ff = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l; ff =as_function(AS, (-z0^2*z1 -z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l[0]^3*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7lfff = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7lfff = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: fff.coordinates()

[?7h[?12l[?25h[?2004lz1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, (-x^2*z1 - z0*z1^2 - z0*z1)/(x^2*z0) ) []
( (0) * dx, (-x^2*z1 - z0*z1^2)/(x^2*z0) ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [20], in <cell line: 1>()
----> 1 fff.coordinates()

File <string>:85, in coordinates(self, threshold, basis)

ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7l = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: RxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0]))

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]^ - z[0]*z[1]^2)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l2 - z[0]*z[1]^2)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l(()/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l(())/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lz))/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l[))/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l]))/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l1])/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l+))/(x^2*z[0])[?7h[?12l[?25h[?25l[?7lx))/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l^))/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l4))/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l*))[?7h[?12l[?25h[?25l[?7lz))[?7h[?12l[?25h[?25l[?7l[))[?7h[?12l[?25h[?25l[?7l1))[?7h[?12l[?25h[?25l[?7l]))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: RxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1]^2 - z[0]*(z[1]+x^4))/(x^2*z[0]*z[1]))

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1]^2 - z[0]*(z[1]+x^4))/(x^2*z[0]*z[1]))[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7l = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lsage: fff = as_cech(AS, as_form(AS, 0), ff)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lsage: fff.coordinates()

[?7h[?12l[?25h[?2004lz1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, (-x^4*z0 - x^2*z1^2 - z0*z1^2 - z0*z1)/(x^2*z0*z1) ) []
( (0) * dx, (-x^2*z0 - z1^2)/(z0*z1) ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [25], in <cell line: 1>()
----> 1 fff.coordinates()

File <string>:85, in coordinates(self, threshold, basis)

ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd ..
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -u
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git commit -cm "praca nad as_cech coordinate; przed poprawa drugiej czecsci"
[master d77adde] praca nad as_cech coordinate; przed poprawa drugiej czesci
 5 files changed, 11731 insertions(+), 54 deletions(-)
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git push
Username for 'https://git.wmi.amu.edu.pl': jgare  rnek
Password for 'https://jgarnek@git.wmi.amu.edu.pl': 
Enumerating objects: 35, done.
Counting objects:   2% (1/35)
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Counting objects: 100% (35/35), done.
Delta compression using up to 4 threads
Compressing objects:   4% (1/23)
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Compressing objects: 100% (23/23), done.
Writing objects:   4% (1/23)
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Writing objects: 100% (23/23)
Writing objects: 100% (23/23), 66.79 KiB | 250.00 KiB/s, done.
Total 23 (delta 19), reused 0 (delta 0)
remote: . Processing 1 references
remote: Processed 1 references in total
To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git
   c098f37..d77adde  master -> master
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ sacd sage/
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7l = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1]^2 - z[0]*(z[1]+x^4))/(x^2*z[0]*z[1]))[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7l = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7l = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-z[0]^3*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7l0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l(); ff= as_function(AS, (-z0^2*z1- z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l(((-1)* AS.z[1]^2)/AS.x^2).valuation()[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7l(-1)*AS.z[0]^2*AS.z[1])/AS.x^2).valuation()[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7l-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
---------------------------------------------------------------------------
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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:83, in coordinates(self, threshold, basis)

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

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
---------------------------------------------------------------------------
TypeError                                 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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:69, in coordinates(self, threshold, basis)

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 /ext/sage/9.7/src/sage/structure/parent.pyx:989, in sage.structure.parent.Parent.__mul__()
    987         pass
    988 if _mul_ is None:
--> 989     raise TypeError(_LazyString("For implementing multiplication, provide the method '_mul_' for %s resp. %s", (self, x), {}))
    990 if switch:
    991     return _mul_(self, switch_sides=True)

TypeError: For implementing multiplication, provide the method '_mul_' for 10 resp. R Interpreter
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
---------------------------------------------------------------------------
NameError                                 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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:74, in coordinates(self, threshold, basis)

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

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
---------------------------------------------------------------------------
TypeError                                 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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:72, in coordinates(self, threshold, basis)

TypeError: 'function' object cannot be interpreted as an integer
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
---------------------------------------------------------------------------
UnboundLocalError                         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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:79, in coordinates(self, threshold, basis)

UnboundLocalError: local variable 'S' referenced before assignment
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
---------------------------------------------------------------------------
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>: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: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>:30, in group_action_matrices_dR(AS, threshold)

File <string>:10, in group_action_matrices(space, list_of_group_elements, basis)

File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:580, in sage.modules.free_module_element.vector()
    578         sparse = False
    579 
--> 580 v, R = prepare(v, R, degree)
    581 
    582 M = FreeModule(R, len(v), bool(sparse))

File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:678, in sage.modules.free_module_element.prepare()
    676     except TypeError:
    677         pass
--> 678 v = Sequence(v, universe=R, use_sage_types=True)
    679 ring = v.universe()
    680 if not is_Ring(ring):

File /ext/sage/9.7/src/sage/structure/sequence.py:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types)
    230 if universe is None:
    231     orig_x = x
--> 232     x = list(x)  # make a copy even if x is a list, we're going to change it
    234     if len(x) == 0:
    235         from sage.categories.objects import Objects

TypeError: 'NoneType' object is not iterable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 0 0 0 0 0 0 0]
[0 1 1 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 2 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 1 0 0 0 0 0 0]
[0 1 1 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 0]
[0 0 2 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 1 0 0 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0]]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
---------------------------------------------------------------------------
TypeError                                 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>: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: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>:31, in group_action_matrices_dR(AS, threshold)

File <string>:11, in group_action_matrices(space, list_of_group_elements, basis)

File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:580, in sage.modules.free_module_element.vector()
    578         sparse = False
    579 
--> 580 v, R = prepare(v, R, degree)
    581 
    582 M = FreeModule(R, len(v), bool(sparse))

File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:678, in sage.modules.free_module_element.prepare()
    676     except TypeError:
    677         pass
--> 678 v = Sequence(v, universe=R, use_sage_types=True)
    679 ring = v.universe()
    680 if not is_Ring(ring):

File /ext/sage/9.7/src/sage/structure/sequence.py:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types)
    230 if universe is None:
    231     orig_x = x
--> 232     x = list(x)  # make a copy even if x is a list, we're going to change it
    234     if len(x) == 0:
    235         from sage.categories.objects import Objects

TypeError: 'NoneType' object is not iterable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 0 [[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 0 0 [[1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 1 [[1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 0 1 [[1 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 2 [[1 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 0 2 [[1 0 0 0 0 0 0 0 0 0]
[0 1 1 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 2 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 3 [[1 0 0 0 0 0 0 0 0 0]
[0 1 1 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 2 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 0 3 [[1 0 0 1 0 0 0 0 0 0]
[0 1 1 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 0]
[0 0 2 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 4 [[1 0 0 1 0 0 0 0 0 0]
[0 1 1 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 0]
[0 0 2 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 0 4 [[1 0 0 1 0 0 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 5 [[1 0 0 1 0 0 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 0 5 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 6 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 0 6 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 7 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 0 7 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 8 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 0 8 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 9 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 0 9 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
1 0 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 1 0 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
1 1 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 1 1 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
1 2 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 1 2 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
1 3 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 1 3 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
1 4 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 1 4 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
1 5 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 1 5 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
1 6 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 1 6 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
1 7 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 1 7 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
1 8 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 1 8 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0]]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
1 9 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 1 9 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1]]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
0 19 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
---------------------------------------------------------------------------
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>: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: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>:32, in group_action_matrices_dR(AS, threshold)

File <string>:11, in group_action_matrices(space, list_of_group_elements, basis)

File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:580, in sage.modules.free_module_element.vector()
    578         sparse = False
    579 
--> 580 v, R = prepare(v, R, degree)
    581 
    582 M = FreeModule(R, len(v), bool(sparse))

File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:678, in sage.modules.free_module_element.prepare()
    676     except TypeError:
    677         pass
--> 678 v = Sequence(v, universe=R, use_sage_types=True)
    679 ring = v.universe()
    680 if not is_Ring(ring):

File /ext/sage/9.7/src/sage/structure/sequence.py:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types)
    230 if universe is None:
    231     orig_x = x
--> 232     x = list(x)  # make a copy even if x is a list, we're going to change it
    234     if len(x) == 0:
    235         from sage.categories.objects import Objects

TypeError: 'NoneType' object is not iterable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
0 19 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
---------------------------------------------------------------------------
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>: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: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>:32, in group_action_matrices_dR(AS, threshold)

File <string>:11, in group_action_matrices(space, list_of_group_elements, basis)

File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:580, in sage.modules.free_module_element.vector()
    578         sparse = False
    579 
--> 580 v, R = prepare(v, R, degree)
    581 
    582 M = FreeModule(R, len(v), bool(sparse))

File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:678, in sage.modules.free_module_element.prepare()
    676     except TypeError:
    677         pass
--> 678 v = Sequence(v, universe=R, use_sage_types=True)
    679 ring = v.universe()
    680 if not is_Ring(ring):

File /ext/sage/9.7/src/sage/structure/sequence.py:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types)
    230 if universe is None:
    231     orig_x = x
--> 232     x = list(x)  # make a copy even if x is a list, we're going to change it
    234     if len(x) == 0:
    235         from sage.categories.objects import Objects

TypeError: 'NoneType' object is not iterable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
0 19 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
None
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
---------------------------------------------------------------------------
TypeError                                 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>: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: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>:34, in group_action_matrices_dR(AS, threshold)

File <string>:13, in group_action_matrices(space, list_of_group_elements, basis)

File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:580, in sage.modules.free_module_element.vector()
    578         sparse = False
    579 
--> 580 v, R = prepare(v, R, degree)
    581 
    582 M = FreeModule(R, len(v), bool(sparse))

File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:678, in sage.modules.free_module_element.prepare()
    676     except TypeError:
    677         pass
--> 678 v = Sequence(v, universe=R, use_sage_types=True)
    679 ring = v.universe()
    680 if not is_Ring(ring):

File /ext/sage/9.7/src/sage/structure/sequence.py:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types)
    230 if universe is None:
    231     orig_x = x
--> 232     x = list(x)  # make a copy even if x is a list, we're going to change it
    234     if len(x) == 0:
    235         from sage.categories.objects import Objects

TypeError: 'NoneType' object is not iterable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
0 19 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
None
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [11], 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: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>:34, in group_action_matrices_dR(AS, threshold)

File <string>:13, in group_action_matrices(space, list_of_group_elements, basis)

File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:580, in sage.modules.free_module_element.vector()
    578         sparse = False
    579 
--> 580 v, R = prepare(v, R, degree)
    581 
    582 M = FreeModule(R, len(v), bool(sparse))

File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:678, in sage.modules.free_module_element.prepare()
    676     except TypeError:
    677         pass
--> 678 v = Sequence(v, universe=R, use_sage_types=True)
    679 ring = v.universe()
    680 if not is_Ring(ring):

File /ext/sage/9.7/src/sage/structure/sequence.py:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types)
    230 if universe is None:
    231     orig_x = x
--> 232     x = list(x)  # make a copy even if x is a list, we're going to change it
    234     if len(x) == 0:
    235         from sage.categories.objects import Objects

TypeError: 'NoneType' object is not iterable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
[1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
[0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
[1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
[0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
[0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
[0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
0 19 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2*z1) * dx, z0^2*z1^2/x^3 ) ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) None
None
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
---------------------------------------------------------------------------
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>: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: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>:34, in group_action_matrices_dR(AS, threshold)

File <string>:13, in group_action_matrices(space, list_of_group_elements, basis)

File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:580, in sage.modules.free_module_element.vector()
    578         sparse = False
    579 
--> 580 v, R = prepare(v, R, degree)
    581 
    582 M = FreeModule(R, len(v), bool(sparse))

File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:678, in sage.modules.free_module_element.prepare()
    676     except TypeError:
    677         pass
--> 678 v = Sequence(v, universe=R, use_sage_types=True)
    679 ring = v.universe()
    680 if not is_Ring(ring):

File /ext/sage/9.7/src/sage/structure/sequence.py:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types)
    230 if universe is None:
    231     orig_x = x
--> 232     x = list(x)  # make a copy even if x is a list, we're going to change it
    234     if len(x) == 0:
    235         from sage.categories.objects import Objects

TypeError: 'NoneType' object is not iterable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
mm: 0 19 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2*z1) * dx, z0^2*z1^2/x^3 ) ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) None
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [13], 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: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>:31, in group_action_matrices_dR(AS, threshold)

File <string>:11, in group_action_matrices(space, list_of_group_elements, basis)

File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:580, in sage.modules.free_module_element.vector()
    578         sparse = False
    579 
--> 580 v, R = prepare(v, R, degree)
    581 
    582 M = FreeModule(R, len(v), bool(sparse))

File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:678, in sage.modules.free_module_element.prepare()
    676     except TypeError:
    677         pass
--> 678 v = Sequence(v, universe=R, use_sage_types=True)
    679 ring = v.universe()
    680 if not is_Ring(ring):

File /ext/sage/9.7/src/sage/structure/sequence.py:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types)
    230 if universe is None:
    231     orig_x = x
--> 232     x = list(x)  # make a copy even if x is a list, we're going to change it
    234     if len(x) == 0:
    235         from sage.categories.objects import Objects

TypeError: 'NoneType' object is not iterable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

nowe: ( (1) * dx, 0 )
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
nowe: ( (z1) * dx, 0 )
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
nowe: ( (z0 + 1) * dx, 0 )
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
nowe: ( (z0*z1 + z1) * dx, 0 )
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
nowe: ( (z0^2 - z0 + 1) * dx, 0 )
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
nowe: ( (x) * dx, 0 )
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
nowe: ( (x*z0 + x) * dx, 0 )
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
nowe: ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
nowe: ( (0) * dx, z1/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
nowe: ( (x^2*z1) * dx, z1^2/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x )
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 )
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
mm: 0 19 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2*z1) * dx, z0^2*z1^2/x^3 ) ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) None
---------------------------------------------------------------------------
TypeError                                 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>: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: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>:31, in group_action_matrices_dR(AS, threshold)

File <string>:11, in group_action_matrices(space, list_of_group_elements, basis)

File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:580, in sage.modules.free_module_element.vector()
    578         sparse = False
    579 
--> 580 v, R = prepare(v, R, degree)
    581 
    582 M = FreeModule(R, len(v), bool(sparse))

File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:678, in sage.modules.free_module_element.prepare()
    676     except TypeError:
    677         pass
--> 678 v = Sequence(v, universe=R, use_sage_types=True)
    679 ring = v.universe()
    680 if not is_Ring(ring):

File /ext/sage/9.7/src/sage/structure/sequence.py:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types)
    230 if universe is None:
    231     orig_x = x
--> 232     x = list(x)  # make a copy even if x is a list, we're going to change it
    234     if len(x) == 0:
    235         from sage.categories.objects import Objects

TypeError: 'NoneType' object is not iterable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

( (1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (1) * dx, 0 )
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z1) * dx, 0 )
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
( (z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0 + 1) * dx, 0 )
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
( (z0*z1 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0*z1 + z1) * dx, 0 )
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
( (z0^2 - z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0^2 - z0 + 1) * dx, 0 )
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
( (x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x) * dx, 0 )
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (x*z0 + x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x*z0 + x) * dx, 0 )
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
( (x^2) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
( (0) * dx, z1/x ) <class '__main__.as_cech'>
nowe: ( (0) * dx, z1/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z1) * dx, z1^2/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z1) * dx, z1^2/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x )
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 )
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) <class '__main__.as_cech'>
nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
mm: 0 19 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2*z1) * dx, z0^2*z1^2/x^3 ) ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) None
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [15], 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: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>:32, in group_action_matrices_dR(AS, threshold)

File <string>:12, in group_action_matrices(space, list_of_group_elements, basis)

File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:580, in sage.modules.free_module_element.vector()
    578         sparse = False
    579 
--> 580 v, R = prepare(v, R, degree)
    581 
    582 M = FreeModule(R, len(v), bool(sparse))

File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:678, in sage.modules.free_module_element.prepare()
    676     except TypeError:
    677         pass
--> 678 v = Sequence(v, universe=R, use_sage_types=True)
    679 ring = v.universe()
    680 if not is_Ring(ring):

File /ext/sage/9.7/src/sage/structure/sequence.py:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types)
    230 if universe is None:
    231     orig_x = x
--> 232     x = list(x)  # make a copy even if x is a list, we're going to change it
    234     if len(x) == 0:
    235         from sage.categories.objects import Objects

TypeError: 'NoneType' object is not iterable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

( (1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (1) * dx, 0 )
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z1) * dx, 0 )
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
( (z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0 + 1) * dx, 0 )
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
( (z0*z1 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0*z1 + z1) * dx, 0 )
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
( (z0^2 - z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0^2 - z0 + 1) * dx, 0 )
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
( (x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x) * dx, 0 )
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (x*z0 + x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x*z0 + x) * dx, 0 )
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
( (x^2) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
( (0) * dx, z1/x ) <class '__main__.as_cech'>
nowe: ( (0) * dx, z1/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z1) * dx, z1^2/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z1) * dx, z1^2/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x )
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 )
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) <class '__main__.as_cech'>
nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
333:
mm: 0 19 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2*z1) * dx, z0^2*z1^2/x^3 ) ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) None
---------------------------------------------------------------------------
TypeError                                 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>: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: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>:32, in group_action_matrices_dR(AS, threshold)

File <string>:12, in group_action_matrices(space, list_of_group_elements, basis)

File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:580, in sage.modules.free_module_element.vector()
    578         sparse = False
    579 
--> 580 v, R = prepare(v, R, degree)
    581 
    582 M = FreeModule(R, len(v), bool(sparse))

File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:678, in sage.modules.free_module_element.prepare()
    676     except TypeError:
    677         pass
--> 678 v = Sequence(v, universe=R, use_sage_types=True)
    679 ring = v.universe()
    680 if not is_Ring(ring):

File /ext/sage/9.7/src/sage/structure/sequence.py:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types)
    230 if universe is None:
    231     orig_x = x
--> 232     x = list(x)  # make a copy even if x is a list, we're going to change it
    234     if len(x) == 0:
    235         from sage.categories.objects import Objects

TypeError: 'NoneType' object is not iterable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

( (1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (1) * dx, 0 )
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z1) * dx, 0 )
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
( (z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0 + 1) * dx, 0 )
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
( (z0*z1 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0*z1 + z1) * dx, 0 )
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
( (z0^2 - z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0^2 - z0 + 1) * dx, 0 )
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
( (x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x) * dx, 0 )
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (x*z0 + x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x*z0 + x) * dx, 0 )
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
( (x^2) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
( (0) * dx, z1/x ) <class '__main__.as_cech'>
nowe: ( (0) * dx, z1/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z1) * dx, z1^2/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z1) * dx, z1^2/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x )
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 )
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) <class '__main__.as_cech'>
nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Input In [17], 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: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>:32, in group_action_matrices_dR(AS, threshold)

File <string>:10, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:80, in coordinates(self, threshold, basis)

File <string>:155, in holomorphic_combinations_fcts(S, pole_order)

IndexError: list index out of range
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

( (1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (1) * dx, 0 )
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z1) * dx, 0 )
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
( (z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0 + 1) * dx, 0 )
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
( (z0*z1 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0*z1 + z1) * dx, 0 )
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
( (z0^2 - z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0^2 - z0 + 1) * dx, 0 )
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
( (x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x) * dx, 0 )
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (x*z0 + x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x*z0 + x) * dx, 0 )
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
( (x^2) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
( (0) * dx, z1/x ) <class '__main__.as_cech'>
nowe: ( (0) * dx, z1/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z1) * dx, z1^2/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z1) * dx, z1^2/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x )
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 )
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) <class '__main__.as_cech'>
nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
A0: 0
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Input In [18], 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: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>:32, in group_action_matrices_dR(AS, threshold)

File <string>:10, in group_action_matrices(space, list_of_group_elements, basis)

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

File <string>:155, in holomorphic_combinations_fcts(S, pole_order)

IndexError: list index out of range
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

( (1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (1) * dx, 0 )
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z1) * dx, 0 )
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
( (z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0 + 1) * dx, 0 )
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
( (z0*z1 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0*z1 + z1) * dx, 0 )
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
( (z0^2 - z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0^2 - z0 + 1) * dx, 0 )
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
( (x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x) * dx, 0 )
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (x*z0 + x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x*z0 + x) * dx, 0 )
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
( (x^2) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
( (0) * dx, z1/x ) <class '__main__.as_cech'>
nowe: ( (0) * dx, z1/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z1) * dx, z1^2/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z1) * dx, z1^2/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x )
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 )
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) <class '__main__.as_cech'>
nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
10 1 [[0, 1, 2], [0, 1, 2]]
A0: 0
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Input In [19], 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: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>:32, in group_action_matrices_dR(AS, threshold)

File <string>:10, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:82, in coordinates(self, threshold, basis)

File <string>:155, in holomorphic_combinations_fcts(S, pole_order)

IndexError: list index out of range
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

( (1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (1) * dx, 0 )
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z1) * dx, 0 )
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
( (z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0 + 1) * dx, 0 )
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
( (z0*z1 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0*z1 + z1) * dx, 0 )
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
( (z0^2 - z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0^2 - z0 + 1) * dx, 0 )
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
( (x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x) * dx, 0 )
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (x*z0 + x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x*z0 + x) * dx, 0 )
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
( (x^2) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
( (0) * dx, z1/x ) <class '__main__.as_cech'>
nowe: ( (0) * dx, z1/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z1) * dx, z1^2/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z1) * dx, z1^2/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x )
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 )
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) <class '__main__.as_cech'>
nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
10 1 [[0, 1, 2], [0, 1, 2]]
A0: 0
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Input In [20], 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: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>:32, in group_action_matrices_dR(AS, threshold)

File <string>:10, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:83, in coordinates(self, threshold, basis)

File <string>:155, in holomorphic_combinations_fcts(S, pole_order)

IndexError: list index out of range
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lrint(len(AS1.at_most_poles(M, threshold=20)))[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lsage: product

[?7h[?12l[?25h[?2004l[?7h<function symbolic_prod at 0x7f38b8be4e50>
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7lor eta in AS.de_rham_basis():[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: for k in product(*pr):

....: [?7h[?12l[?25h[?25l[?7lprint(eta.omega0, eta.omega8.valuation())[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lnt(eta.omega0, eta.omega8.valuation())[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l....:     print(k)

....: [?7h[?12l[?25h[?25l[?7lsage: for k in product(*pr):

....:     print(k)

....: 

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [22], in <cell line: 1>()
----> 1 for k in product(*pr):
      2     print(k)

NameError: name 'pr' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for k in product(*pr):

....:     print(k)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lproduct

 [?7h[?12l[?25h[?25l[?7lloa('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

( (1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (1) * dx, 0 )
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z1) * dx, 0 )
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
( (z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0 + 1) * dx, 0 )
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
( (z0*z1 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0*z1 + z1) * dx, 0 )
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
( (z0^2 - z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0^2 - z0 + 1) * dx, 0 )
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
( (x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x) * dx, 0 )
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (x*z0 + x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x*z0 + x) * dx, 0 )
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
( (x^2) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
( (0) * dx, z1/x ) <class '__main__.as_cech'>
nowe: ( (0) * dx, z1/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z1) * dx, z1^2/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z1) * dx, z1^2/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x )
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 )
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) <class '__main__.as_cech'>
nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
10 1 [[0, 1, 2], [0, 1, 2]]
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A0: 90
A: 1
B: 2
333:
mm: 0 19 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2*z1) * dx, z0^2*z1^2/x^3 ) ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) None
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [23], 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: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>:32, in group_action_matrices_dR(AS, threshold)

File <string>:12, in group_action_matrices(space, list_of_group_elements, basis)

File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:580, in sage.modules.free_module_element.vector()
    578         sparse = False
    579 
--> 580 v, R = prepare(v, R, degree)
    581 
    582 M = FreeModule(R, len(v), bool(sparse))

File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:678, in sage.modules.free_module_element.prepare()
    676     except TypeError:
    677         pass
--> 678 v = Sequence(v, universe=R, use_sage_types=True)
    679 ring = v.universe()
    680 if not is_Ring(ring):

File /ext/sage/9.7/src/sage/structure/sequence.py:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types)
    230 if universe is None:
    231     orig_x = x
--> 232     x = list(x)  # make a copy even if x is a list, we're going to change it
    234     if len(x) == 0:
    235         from sage.categories.objects import Objects

TypeError: 'NoneType' object is not iterable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

( (1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (1) * dx, 0 )
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z1) * dx, 0 )
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
( (z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0 + 1) * dx, 0 )
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
( (z0*z1 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0*z1 + z1) * dx, 0 )
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
( (z0^2 - z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0^2 - z0 + 1) * dx, 0 )
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
( (x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x) * dx, 0 )
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (x*z0 + x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x*z0 + x) * dx, 0 )
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
( (x^2) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
( (0) * dx, z1/x ) <class '__main__.as_cech'>
nowe: ( (0) * dx, z1/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z1) * dx, z1^2/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z1) * dx, z1^2/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x )
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 )
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) <class '__main__.as_cech'>
nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [24], 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: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>:32, in group_action_matrices_dR(AS, threshold)

File <string>:10, in group_action_matrices(space, list_of_group_elements, basis)

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

TypeError: unsupported operand type(s) for -: 'sage.rings.fraction_field_element.FractionFieldElement' and 'as_function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

( (1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (1) * dx, 0 )
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z1) * dx, 0 )
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
( (z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0 + 1) * dx, 0 )
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
( (z0*z1 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0*z1 + z1) * dx, 0 )
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
( (z0^2 - z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0^2 - z0 + 1) * dx, 0 )
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
( (x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x) * dx, 0 )
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (x*z0 + x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x*z0 + x) * dx, 0 )
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
( (x^2) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
( (0) * dx, z1/x ) <class '__main__.as_cech'>
nowe: ( (0) * dx, z1/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z1) * dx, z1^2/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z1) * dx, z1^2/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x )
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 )
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) <class '__main__.as_cech'>
nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
---------------------------------------------------------------------------
NameError                                 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>: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: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>:32, in group_action_matrices_dR(AS, threshold)

File <string>:10, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:88, in coordinates(self, threshold, basis)

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

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

( (1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (1) * dx, 0 )
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z1) * dx, 0 )
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
( (z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0 + 1) * dx, 0 )
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
( (z0*z1 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0*z1 + z1) * dx, 0 )
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
( (z0^2 - z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0^2 - z0 + 1) * dx, 0 )
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
( (x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x) * dx, 0 )
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (x*z0 + x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x*z0 + x) * dx, 0 )
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
( (x^2) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
( (0) * dx, z1/x ) <class '__main__.as_cech'>
nowe: ( (0) * dx, z1/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z1) * dx, z1^2/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z1) * dx, z1^2/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x )
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 )
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) <class '__main__.as_cech'>
nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
nowe: ( (-z0*z1 + z1) * dx, 0 )
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0]
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: [2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0]
nowe: ( (-z0*z1 + z1) * dx, 0 )
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0]
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 19 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2*z1) * dx, z0^2*z1^2/x^3 ) ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) [2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0]
---------------------------------------------------------------------------
IndexError                                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>: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: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>:32, in group_action_matrices_dR(AS, threshold)

File <string>:12, in group_action_matrices(space, list_of_group_elements, basis)

File /ext/sage/9.7/src/sage/matrix/matrix0.pyx:1504, in sage.matrix.matrix0.Matrix.__setitem__()
   1502         raise IndexError("value does not have the right number of columns")
   1503     elif single_col and row_list_len != len(value_list):
-> 1504         raise IndexError("value does not have the right number of rows")
   1505 else:
   1506     if row_list_len != len(value_list):

IndexError: value does not have the right number of rows
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

( (1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (1) * dx, 0 )
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) (1, 0, 0, 0, 0, 0, 0, 0, 0, 0)
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Input In [27], 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: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>:32, in group_action_matrices_dR(AS, threshold)

File <string>:12, in group_action_matrices(space, list_of_group_elements, basis)

File /ext/sage/9.7/src/sage/matrix/matrix0.pyx:1504, in sage.matrix.matrix0.Matrix.__setitem__()
   1502         raise IndexError("value does not have the right number of columns")
   1503     elif single_col and row_list_len != len(value_list):
-> 1504         raise IndexError("value does not have the right number of rows")
   1505 else:
   1506     if row_list_len != len(value_list):

IndexError: value does not have the right number of rows
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

( (1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (1) * dx, 0 )
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (1, 0, 0, 0, 0, 0, 0, 0, 0, 0)
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Input In [28], 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: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>:32, in group_action_matrices_dR(AS, threshold)

File <string>:12, in group_action_matrices(space, list_of_group_elements, basis)

File /ext/sage/9.7/src/sage/matrix/matrix0.pyx:1504, in sage.matrix.matrix0.Matrix.__setitem__()
   1502         raise IndexError("value does not have the right number of columns")
   1503     elif single_col and row_list_len != len(value_list):
-> 1504         raise IndexError("value does not have the right number of rows")
   1505 else:
   1506     if row_list_len != len(value_list):

IndexError: value does not have the right number of rows
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

( (1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [29], 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: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>:32, in group_action_matrices_dR(AS, threshold)

File <string>:10, in group_action_matrices(space, list_of_group_elements, basis)

File <string>:94, in coordinates(self, threshold, basis)

File /ext/sage/9.7/src/sage/structure/element.pyx:1233, in sage.structure.element.Element.__add__()
   1231 # Left and right are Sage elements => use coercion model
   1232 if BOTH_ARE_ELEMENT(cl):
-> 1233     return coercion_model.bin_op(left, right, add)
   1234 
   1235 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 +: 'Vector space of dimension 10 over Finite Field of size 3' and 'Vector space of dimension 20 over Finite Field of size 3'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

( (1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 1, 1, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0 + 1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (z0*z1 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0*z1 + z1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (z0^2 - z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0^2 - z0 + 1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (1, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x*z0 + x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x*z0 + x) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x^2) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (0) * dx, z1/x ) <class '__main__.as_cech'>
nowe: ( (0) * dx, z1/x )
cc: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x^2*z1) * dx, z1^2/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z1) * dx, z1^2/x )
cc: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0)
( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x )
cc: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0] 20
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0)
( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x )
cc: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0] 20
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 2, 0, 0, 1, 0, 0, 0, 0, 2, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0)
( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
cc: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0] 20
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0)
( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
cc: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0] 20
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0)
( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 )
cc: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0] 20
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0)
( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
cc: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0] 20
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0)
( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
cc: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0] 20
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0)
( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) <class '__main__.as_cech'>
nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
cc: [2, 0, 0, 0, 0, 0, 0, 0, 0, 1] 20
nowe: ( (-z0*z1 + z1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0]
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1)
nowe: ( (-z0*z1 + z1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0]
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1)
( (1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (z1 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z1 + 1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 1, 0, 0, 0, 0]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (1, 2, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (z0) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (z0*z1 + z0) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0*z1 + z0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (z0^2) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (-x*z0^2 + x*z1 + x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (-x*z0^2 + x*z1 + x) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x*z0) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x*z0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x^2) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (0) * dx, (z1 + 1)/x ) <class '__main__.as_cech'>
nowe: ( (0) * dx, (z1 + 1)/x )
cc: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
nowe: ( (0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0)
nowe: ( (0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x^2*z1 + x^2) * dx, (z1^2 - z1 + 1)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z1 + x^2) * dx, (z1^2 - z1 + 1)/x )
cc: [2, 1, 0, 0, 0, 0, 0, 0, 0, 0] 20
nowe: ( (x^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0)
nowe: ( (x^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0)
( (-x^2*z0) * dx, (z0*z1 + z0)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0) * dx, (z0*z1 + z0)/x )
cc: [0, 0, 1, 0, 0, 0, 0, 0, 0, 0] 20
nowe: ( (0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0)
nowe: ( (0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0)
( (x^2*z0*z1 - z0^2*z1 - z0^2) * dx, (z0*z1^2 - z0*z1 + z0)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0*z1 - z0^2*z1 - z0^2) * dx, (z0*z1^2 - z0*z1 + z0)/x )
cc: [0, 0, 2, 1, 0, 0, 0, 0, 0, 0] 20
nowe: ( (-z0^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0]
(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0)
nowe: ( (-z0^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0]
(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0)
( (-x^2*z0^2) * dx, (z0^2*z1 + z0^2)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0^2) * dx, (z0^2*z1 + z0^2)/x )
cc: [1, 0, 0, 0, 1, 0, 0, 0, 0, 0] 20
nowe: ( (0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0)
nowe: ( (0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0)
( (x^2*z0^2*z1 + x^2*z0^2 - z0*z1^2 + z0*z1 - z0) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0^2*z1 + x^2*z0^2 - z0*z1^2 + z0*z1 - z0) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x )
cc: [1, 0, 0, 0, 2, 1, 0, 0, 0, 0] 20
nowe: ( (z0*z1 - z0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0]
(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 0)
nowe: ( (z0*z1 - z0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0]
(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 0)
( (x*z0^2) * dx, (z1^2 - z1 + 1)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2) * dx, (z1^2 - z1 + 1)/x^2 )
cc: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0] 20
nowe: ( (0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0)
nowe: ( (0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0)
( (x*z0*z1 + x*z0) * dx, (z0*z1^2 - z0*z1 + z0)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0*z1 + x*z0) * dx, (z0*z1^2 - z0*z1 + z0)/x^2 )
cc: [0, 0, 0, 0, 0, 0, 0, 1, 0, 0] 20
nowe: ( (x*z0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0)
nowe: ( (x*z0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0)
( (x*z0^2*z1) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2*z1) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^2 )
cc: [0, 0, 0, 0, 0, 0, 1, 0, 1, 0] 20
nowe: ( (0) * dx, z0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(-x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0]
(-x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0)
nowe: ( (0) * dx, z0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(-x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0]
(-x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0)
( (z0^2*z1 + z0^2) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^3 ) <class '__main__.as_cech'>
nowe: ( (z0^2*z1 + z0^2) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^3 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 1] 20
nowe: ( (z0^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1)
nowe: ( (z0^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1)
[
RModule of dimension 6 over GF(3),
RModule of dimension 14 over GF(3)
]
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [30], 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: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>

TypeError: 'text' is an invalid keyword argument for print()
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

( (1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 1, 1, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0 + 1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (z0*z1 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0*z1 + z1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (z0^2 - z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0^2 - z0 + 1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (1, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x*z0 + x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x*z0 + x) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x^2) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (0) * dx, z1/x ) <class '__main__.as_cech'>
nowe: ( (0) * dx, z1/x )
cc: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x^2*z1) * dx, z1^2/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z1) * dx, z1^2/x )
cc: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0)
( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x )
cc: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0] 20
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0)
( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x )
cc: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0] 20
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 2, 0, 0, 1, 0, 0, 0, 0, 2, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0)
( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
cc: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0] 20
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0)
( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
cc: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0] 20
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0)
( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 )
cc: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0] 20
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0)
( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
cc: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0] 20
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0)
( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
cc: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0] 20
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0)
( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) <class '__main__.as_cech'>
nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
cc: [2, 0, 0, 0, 0, 0, 0, 0, 0, 1] 20
nowe: ( (-z0*z1 + z1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0]
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1)
nowe: ( (-z0*z1 + z1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0]
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1)
( (1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (z1 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z1 + 1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 1, 0, 0, 0, 0]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (1, 2, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (z0) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (z0*z1 + z0) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0*z1 + z0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (z0^2) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (-x*z0^2 + x*z1 + x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (-x*z0^2 + x*z1 + x) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x*z0) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x*z0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x^2) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (0) * dx, (z1 + 1)/x ) <class '__main__.as_cech'>
nowe: ( (0) * dx, (z1 + 1)/x )
cc: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
nowe: ( (0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0)
nowe: ( (0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x^2*z1 + x^2) * dx, (z1^2 - z1 + 1)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z1 + x^2) * dx, (z1^2 - z1 + 1)/x )
cc: [2, 1, 0, 0, 0, 0, 0, 0, 0, 0] 20
nowe: ( (x^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0)
nowe: ( (x^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0)
( (-x^2*z0) * dx, (z0*z1 + z0)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0) * dx, (z0*z1 + z0)/x )
cc: [0, 0, 1, 0, 0, 0, 0, 0, 0, 0] 20
nowe: ( (0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0)
nowe: ( (0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0)
( (x^2*z0*z1 - z0^2*z1 - z0^2) * dx, (z0*z1^2 - z0*z1 + z0)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0*z1 - z0^2*z1 - z0^2) * dx, (z0*z1^2 - z0*z1 + z0)/x )
cc: [0, 0, 2, 1, 0, 0, 0, 0, 0, 0] 20
nowe: ( (-z0^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0]
(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0)
nowe: ( (-z0^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0]
(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0)
( (-x^2*z0^2) * dx, (z0^2*z1 + z0^2)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0^2) * dx, (z0^2*z1 + z0^2)/x )
cc: [1, 0, 0, 0, 1, 0, 0, 0, 0, 0] 20
nowe: ( (0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0)
nowe: ( (0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0)
( (x^2*z0^2*z1 + x^2*z0^2 - z0*z1^2 + z0*z1 - z0) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0^2*z1 + x^2*z0^2 - z0*z1^2 + z0*z1 - z0) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x )
cc: [1, 0, 0, 0, 2, 1, 0, 0, 0, 0] 20
nowe: ( (z0*z1 - z0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0]
(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 0)
nowe: ( (z0*z1 - z0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0]
(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 0)
( (x*z0^2) * dx, (z1^2 - z1 + 1)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2) * dx, (z1^2 - z1 + 1)/x^2 )
cc: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0] 20
nowe: ( (0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0)
nowe: ( (0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0)
( (x*z0*z1 + x*z0) * dx, (z0*z1^2 - z0*z1 + z0)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0*z1 + x*z0) * dx, (z0*z1^2 - z0*z1 + z0)/x^2 )
cc: [0, 0, 0, 0, 0, 0, 0, 1, 0, 0] 20
nowe: ( (x*z0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0)
nowe: ( (x*z0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0)
( (x*z0^2*z1) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2*z1) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^2 )
cc: [0, 0, 0, 0, 0, 0, 1, 0, 1, 0] 20
nowe: ( (0) * dx, z0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(-x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0]
(-x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0)
nowe: ( (0) * dx, z0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(-x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0]
(-x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0)
( (z0^2*z1 + z0^2) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^3 ) <class '__main__.as_cech'>
nowe: ( (z0^2*z1 + z0^2) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^3 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 1] 20
nowe: ( (z0^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1)
nowe: ( (z0^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1)
[
RModule of dimension 6 over GF(3),
RModule of dimension 14 over GF(3)
]
None
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4

(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 6 over GF(3),
RModule of dimension 14 over GF(3)
]
None
[?2004h[?25l[?7lsage: [?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ git add -u
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ git commit -m ""o"b"l"i"c"z"e""a"n"i"e" "d"z"i"a"l"a"n"i"a" "n"a" "d"R" "c"h"y"b"a" "d"z"i"a"l"a"
[master f7a04c6] obliczanie dzialania na dR chyba dziala
 3 files changed, 7256 insertions(+), 23 deletions(-)
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^3
z1^2 - z1 = x^5

(1) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(x*z0 + x + z1) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(x*z0 + z1 + 1) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(2),
RModule of dimension 4 over GF(2)
]
(1) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(x*z0 + x + z1) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(x*z0 + z1 + 1) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A

[?7h[?12l[?25h[?2004l[?7h[1 0 1 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 1 0 1 0 0 0 0 0 1]
[0 0 0 0 1 0 0 0 1 0]
[0 0 0 0 0 1 0 1 0 0]
[0 0 0 0 0 0 1 0 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l^2 == identity_matrix(F, 6)[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l.coefficient_matrix()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.dimensions()

[?7h[?12l[?25h[?2004l[?7h(10, 10)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.dimensions()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus()

[?7h[?12l[?25h[?2004l[?7h5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7l.dimenions()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l.dimensions()[?7h[?12l[?25h[?25l[?7lS.genu()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7l^2 == identity_matrix(F, 6)[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lid[?7h[?12l[?25h[?25l[?7lide[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A^p == identity_matrix(10)

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA^p == identity_matrix(10)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^p = identity_matrix(10)[?7h[?12l[?25h[?25l[?7lB^p = identity_matrix(10)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B^p == identity_matrix(10)

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA^p == identity_matrix(10)[?7h[?12l[?25h[?25l[?7l*BB*A[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l== B*A[?7h[?12l[?25h[?25l[?7lsage: A*B == B*A

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA*B == B*A[?7h[?12l[?25h[?25l[?7lB^pidentity_matrix(10)[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS.genus()[?7h[?12l[?25h[?25l[?7l.dimenions()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^7
z1^2 - z1 = x^5

(1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x*z1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x^2*z1 + x*z0 + x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x^3) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x*z1 + x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x^2*z1 + x^2 + x*z0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x^3) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
[
RModule of dimension 1 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 4 over GF(2)
]
(1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x*z1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x^2*z1 + x*z0 + x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x^3) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x^3) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x*z1 + x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x^2*z1 + x^2 + x*z0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x^3) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x^3) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^7
z1^2 - z1 = x^9

(1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^2*z0 + x^2 + x*z1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^3*z0 + x^3 + x^2*z1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^3) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^4) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^5) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^2*z0 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^3*z0 + x^2*z1 + x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^3) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^4) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^5) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
[
RModule of dimension 1 over GF(2),
RModule of dimension 1 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 6 over GF(2)
]
(1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^2*z0 + x^2 + x*z1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^3*z0 + x^3 + x^2*z1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^3) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^4) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^5) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^5 + x^4) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^4) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^3 + x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^2*z0 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^3*z0 + x^2*z1 + x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^3) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^4) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^5) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^5) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^3) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lA*B == B*A[?7h[?12l[?25h[?25l[?7lB^pidentity_matrix(10)[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS.genus()[?7h[?12l[?25h[?25l[?7l.dimenions()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lsage: A

[?7h[?12l[?25h[?2004l[?7h22 x 22 dense matrix over Finite Field of size 2 (use the '.str()' method to see the entries)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^11
z1^2 - z1 = x^9

[
RModule of dimension 1 over GF(2),
RModule of dimension 1 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 6 over GF(2)
]
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [11], 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: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>:29, in group_action_matrices_dR(AS, threshold)

File <string>:378, in de_rham_basis(self, threshold)

File <string>:366, in lift_to_de_rham(self, fct, threshold)

ValueError: Increase threshold!
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^11
z1^2 - z1 = x^9

[
RModule of dimension 1 over GF(2),
RModule of dimension 1 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 6 over GF(2)
]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 5 with the equation:
 z^5 - z = x^3
---------------------------------------------------------------------------
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>: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: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>:14, in <module>

ValueError: not enough values to unpack (expected 2, got 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 5 with the equation:
 z^5 - z = x^3
---------------------------------------------------------------------------
TypeError                                 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>: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: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 /ext/sage/9.7/src/sage/matrix/special.py:922, in identity_matrix(ring, n, sparse)
    920     n = ring
    921     ring = ZZ
--> 922 return matrix_space.MatrixSpace(ring, n, n, sparse)(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/matrix/matrix_space.py:561, in MatrixSpace.__classcall__(cls, base_ring, nrows, ncols, sparse, implementation, **kwds)
    516 """
    517 Normalize the arguments to call the ``__init__`` constructor.
    518 
   (...)
    558     False
    559 """
    560 if base_ring not in _Rings:
--> 561     raise TypeError("base_ring (=%s) must be a ring"%base_ring)
    562 nrows = int(nrows)
    563 if ncols is None:

TypeError: base_ring (=8) must be a ring
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 5 with the equation:
 z^5 - z = x^3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l.dimensions()[?7h[?12l[?25h[?25l[?7lj[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l.dimensions()[?7h[?12l[?25h[?25l[?7lj[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.jordan_form()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [4], in <cell line: 1>()
----> 1 A.jordan_form()

AttributeError: 'list' object has no attribute 'jordan_form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_form()[?7h[?12l[?25h[?25l[?7lsage: A

[?7h[?12l[?25h[?2004l[?7h[
[1 1 1 0 0 0 0 3]
[0 1 2 0 0 0 0 4]
[0 0 1 0 0 0 0 4]
[0 0 0 1 4 1 3 0]
[0 0 0 0 1 3 1 0]
[0 0 0 0 0 1 4 0]
[0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 1]
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l = AS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: A = A[0]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = A[0][?7h[?12l[?25h[?25l[?7l.jordan_form()[?7h[?12l[?25h[?25l[?7lj[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldan_form()[?7h[?12l[?25h[?25l[?7lan_form()[?7h[?12l[?25h[?25l[?7lsage: A.jordan_form()

[?7h[?12l[?25h[?2004l[?7h[1 1 0 0|0 0 0 0]
[0 1 1 0|0 0 0 0]
[0 0 1 1|0 0 0 0]
[0 0 0 1|0 0 0 0]
[-------+-------]
[0 0 0 0|1 1 0 0]
[0 0 0 0|0 1 1 0]
[0 0 0 0|0 0 1 1]
[0 0 0 0|0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_form()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lb()[?7h[?12l[?25h[?25l[?7ll()[?7h[?12l[?25h[?25l[?7lo()[?7h[?12l[?25h[?25l[?7lc()[?7h[?12l[?25h[?25l[?7lk()[?7h[?12l[?25h[?25l[?7ls()[?7h[?12l[?25h[?25l[?7lsage: A.jordan_blocks()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [8], in <cell line: 1>()
----> 1 A.jordan_blocks()

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.matrix.matrix_modn_dense_float.Matrix_modn_dense_float' object has no attribute 'jordan_blocks'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_blocks()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lsage: A.jordan_blocks()

  A.C                                 A.QR                                A.add_multiple_of_row               A.adjoint_classical                  

  A.H                                 A.T                                 A.add_to_entry                      A.adjugate                           

  A.LLL_gram                          A.act_on_polynomial                 A.additive_order                    A.anticommutator                    >

  A.LU                                A.add_multiple_of_column            A.adjoint                           A.antitranspose                      

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

 A.C                                







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

 A.C                                 A.QR                               [?7h[?12l[?25h[?25l[?7lC

 A.C                                 A.QR                               [?7h[?12l[?25h[?25l[?7l









[?7h[?12l[?25h[?25l[?7ljordan_blocks()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_blocks()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: A.jordan_blocks()[0]

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [9], in <cell line: 1>()
----> 1 A.jordan_blocks()[Integer(0)]

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.matrix.matrix_modn_dense_float.Matrix_modn_dense_float' object has no attribute 'jordan_blocks'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_blocks()[0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[0][?7h[?12l[?25h[?25l[?7l()[0][?7h[?12l[?25h[?25l[?7l()[0][?7h[?12l[?25h[?25l[?7l()[0][?7h[?12l[?25h[?25l[?7l()[0][?7h[?12l[?25h[?25l[?7l()[0][?7h[?12l[?25h[?25l[?7lf()[0][?7h[?12l[?25h[?25l[?7lo()[0][?7h[?12l[?25h[?25l[?7lr()[0][?7h[?12l[?25h[?25l[?7lm()[0][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A.jordan_form()[0]

[?7h[?12l[?25h[?2004l[?7h(1, 1, 0, 0, 0, 0, 0, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_form()[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm()[0][?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lsage: A.jordan_form(sub

 subdivide=  

 subfactorial

 subsets     



 [?7h[?12l[?25h[?25l[?7ldivide=

 subdivide=  





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







[?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lTrue[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.jordan_form(subdivide=True)

[?7h[?12l[?25h[?2004l[?7h[1 1 0 0|0 0 0 0]
[0 1 1 0|0 0 0 0]
[0 0 1 1|0 0 0 0]
[0 0 0 1|0 0 0 0]
[-------+-------]
[0 0 0 0|1 1 0 0]
[0 0 0 0|0 1 1 0]
[0 0 0 0|0 0 1 1]
[0 0 0 0|0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_form(subdivide=True)[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: A.jordan_form(subdivide=True)[0]

[?7h[?12l[?25h[?2004l[?7h(1, 1, 0, 0, 0, 0, 0, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_form(subdivide=True)[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.jordan_form(subdivide=True)

[?7h[?12l[?25h[?2004l[?7h[1 1 0 0|0 0 0 0]
[0 1 1 0|0 0 0 0]
[0 0 1 1|0 0 0 0]
[0 0 0 1|0 0 0 0]
[-------+-------]
[0 0 0 0|1 1 0 0]
[0 0 0 0|0 1 1 0]
[0 0 0 0|0 0 1 1]
[0 0 0 0|0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_form(subdivide=True)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_form(subdivide=True)[?7h[?12l[?25h[?25l[?7l()[0][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.jordan_form(subdivide=True)

[?7h[?12l[?25h[?2004l[?7h[1 1 0 0|0 0 0 0]
[0 1 1 0|0 0 0 0]
[0 0 1 1|0 0 0 0]
[0 0 0 1|0 0 0 0]
[-------+-------]
[0 0 0 0|1 1 0 0]
[0 0 0 0|0 1 1 0]
[0 0 0 0|0 0 1 1]
[0 0 0 0|0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_form(subdivide=True)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltA.jordan_form(subdivide=True)[?7h[?12l[?25h[?25l[?7lyA.jordan_form(subdivide=True)[?7h[?12l[?25h[?25l[?7lpA.jordan_form(subdivide=True)[?7h[?12l[?25h[?25l[?7leA.jordan_form(subdivide=True)[?7h[?12l[?25h[?25l[?7ltype(A.jordan_form(subdivide=True)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: type(A.jordan_form(subdivide=True))

[?7h[?12l[?25h[?2004l[?7h<class 'sage.matrix.matrix_modn_dense_float.Matrix_modn_dense_float'>
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(A.jordan_form(subdivide=True))[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: type(A.jordan_form(subdivide=True))[0]

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [16], in <cell line: 1>()
----> 1 type(A.jordan_form(subdivide=True))[Integer(0)]

TypeError: 'sage.misc.inherit_comparison.InheritComparisonMetaclass' object is not subscriptable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(A.jordan_form(subdivide=True))[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lTru[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: type(A.jordan_form(

  base_ring=                                   subdivide=                                   AA                                            

  check_input=                                 transformation=                              AS                                            

  eigenvalues=                                 %%!                                          AbelianGroup                                 >

  sparse=                                      A                                            AbelianGroupMorphism                          

 [?7h[?12l[?25h[?25l[?7lbase_ring=

 base_ring=                                  







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

 base_ring=                                   subdivide=                                  [?7h[?12l[?25h[?25l[?7lAA

 subdivide=                                   AA                                          [?7h[?12l[?25h[?25l[?7lbelianGroupWithValues

 subdivdeAA        belianGroupWithValues

 transformaion=AS             belianVariety

<%%!         AbelianGroupdditiveAbelianGroup

 A      belianGroupMorphismdditiveAbelianGroupWrapper[?7h[?12l[?25h[?25l[?7ldditiveAbelianGroupWrapperElement

AA        belianGroupWithValuesdditiveAbelianGroupWrapperElement

AS             belianVarietydditiveMagmas

AbelianGroupdditiveAbelianGroupffneCryptosystem  

belianGroupMorphismdditiveAbelianGroupWrapperffneGroup                [?7h[?12l[?25h[?25l[?7lbelianGroupWithValues

 AbelianGroupWithValues                       AdditiveAbelianGroupWrapperElement          [?7h[?12l[?25h[?25l[?7ldditiveAbelianGroupWrapperElement

 AbelianGroupWithValues                       AdditiveAbelianGroupWrapperElement          [?7h[?12l[?25h[?25l[?7lffneHypersurface

belianGroupWithValuesdditiveAbelianGroupWrapperElementffneHypersurface                

belianVarietydditiveMagmasffneNilTeperleyLiebTypeA

dditiveAbelianGroupffneCryptosystem  PermutationGroup

dditiveAbelianGroupWrapperffneGroup                Space[?7h[?12l[?25h[?25l[?7lToricVaiety

dditiveAbelianGroupWrapperElementffneHypersurface                ToricVaiety

dditiveMagmasffneNilTeperleyLiebTypeAWeylGroups           

ffneCryptosystem  PermutationGrouplarmInterrup        

ffneGroup                Spacelgebra    [?7h[?12l[?25h[?25l[?7llgebraIdeals

ffneHypersurface                ToricVaietylgebraIdeals     

ffneNilTeperleyLiebTypeAWeylGroups           lgebraModules  

PermutationGrouplarmInterrup        gebraicField

Spacelgebra    icNumber[?7h[?12l[?25h[?25l[?7licReal

ToricVaietylgebraIdeals     icReal

WeylGroups           lgebraModules  icRealField

larmInterrup        gebraicFields      

lgebra    icNumbersWithBasis[?7h[?12l[?25h[?25l[?7llCusps

lgebraIdeals     icReallCusps     

lgebraModules  icRealFieldlExactCovers    

gebraicFields      phabet

icNumbersWithBasisphabeticString[?7h[?12l[?25h[?25l[?7lternatingGroup

icReallCusps     ternatingGroup

icRealFieldlExactCovers    ternaingSignMatrices

s      phabetternaingSignMatrix

sWithBasisphabeticStringrithmEror  [?7h[?12l[?25h[?25l[?7llCusps

 AllCusps                                     AlternatingGroup                            [?7h[?12l[?25h[?25l[?7lternatingGroup

 AllCusps                                     AlternatingGroup                            [?7h[?12l[?25h[?25l[?7lrithmecSubgroup_Permutation

lCusps     ternatingGrouprithmecSubgroup_Permutation

lExactCovers    ternaingSignMatricesrrangemets           

phabetternaingSignMatrixrinGroup           

phabeticStringrithmEror  ssertionEror [?7h[?12l[?25h[?25l[?7lssionGroupS

ternatingGrouprithmecSubgroup_PermutationssionGroupS                  

ternaingSignMatricesrrangemets           ssionGroupU

ternaingSignMatrixrinGroup           symptoticRing

rithmEror  ssertionEror tkinModulaCorrespondenceDatabase[?7h[?12l[?25h[?25l[?7lrithmeticSubgroup_Permutation

 ArithmeticSubgroup_Permutation               AssionGroupS                                [?7h[?12l[?25h[?25l[?7llternangGroup

 AlternatingGroup                             ArithmeticSubgroup_Permutation              [?7h[?12l[?25h[?25l[?7lrithmecSubgroup_Permutation

 AlternatingGroup                             ArithmeticSubgroup_Permutation              [?7h[?12l[?25h[?25l[?7lssionGroupS

 ArithmeticSubgroup_Permutation               AssionGroupS                                [?7h[?12l[?25h[?25l[?7ltknModularPolynomialDatabase

rithmecSubgroup_PermutationssionGroupS                  tknModularPolynomialDatabase

rrangemets           ssionGroupUttributeError

rinGroup           symptoticRingugentedLatticeDiagramFilling

ssertionEror tkinModulaCorrespondenceDatabaseutomaton                         [?7h[?12l[?25h[?25l[?7lxiom

ssionGroupS                  tknModularPolynomialDatabasexiom                         

ssionGroupUttributeErrorBackslashOperator

symptoticRingugentedLatticeDiagramFillingBaseExcption                 

tkinModulaCorrespondenceDatabaseutomaton                         BaxterPermutations[?7h[?12l[?25h[?25l[?7lBerkovich_Cp_Affine

tknModularPolynomialDatabasexiom                         Berkovich_Cp_Affine

ttributeErrorBackslashOperatorerovic_Cp_Prjective

ugentedLatticeDiagramFillingBaseExcption                 esel       

utomaton                         BaxterPermutationsezoutianQadraticForm[?7h[?12l[?25h[?25l[?7lialgebras

xiom                         Berkovich_Cp_Affineialgebras         

BackslashOperatorerovic_Cp_PrjectiveialgebrasWithBasis    

BaseExcption                 esel       imodules

BaxterPermutationsezoutianQadraticForminaryQF              [?7h[?12l[?25h[?25l[?7lnaryQF_reduced_representatives

Berkovich_Cp_Affineialgebras         naryQF_reduced_representatives

erovic_Cp_PrjectiveialgebrasWithBasis    naryRecurrenceSequence

esel       imodulesnaryStrings

ezoutianQadraticForminaryQF              Tree[?7h[?12l[?25h[?25l[?7lTrees

ialgebras         naryQF_reduced_representativesTrees                     

ialgebrasWithBasis    naryRecurrenceSequenceptiteGaph          

imodulesnaryStringstset       

inaryQF              TreelockDesign[?7h[?12l[?25h[?25l[?7lBlockingIOError

naryQF_reduced_representativesTrees                     lockingIOError

naryRecurrenceSequenceptiteGaph          ooleanPolynomialRing

naryStringstset       raidGroup

TreelockDesignranchingRule[?7h[?12l[?25h[?25l[?7lBrandtModule

Trees                     lockingIOErrorrandtModule   

ptiteGaph          ooleanPolynomialRingraurAlgebra        

tset       raidGroupokenPipeError

lockDesignranchingRuleuhatTitsQuotient[?7h[?12l[?25h[?25l[?7lBufferError

lockingIOErrorrandtModule   ufferError 

ooleanPolynomialRingraurAlgebra        ytesWarning 

raidGroupokenPipeErrorCBF            

ranchingRuleuhatTitsQuotientCC                [?7h[?12l[?25h[?25l[?7lCDF

randtModule   ufferError CDF        

raurAlgebra        ytesWarning CFiniteSequence

okenPipeErrorCBF            FiniteSequences

uhatTitsQuotientCC                IF[?7h[?12l[?25h[?25l[?7lL

ufferError CDF        L

ytesWarning CFiniteSequencePRFanoToricVariety

CBF            FiniteSequencesRT             

CC                IFRT_basis[?7h[?12l[?25h[?25l[?7lRT_list

CDF        LRT_list

CFiniteSequencePRFanoToricVarietyRT_vects        

FiniteSequencesRT             _super

IFRT_basisachedFunction[?7h[?12l[?25h[?25l[?7lallableSymbolicExpressionRing

LRT_listallableSymbolicExpressionRing

PRFanoToricVarietyRT_vects        artanMatix

RT             _superartanType

RT_basisachedFunctiontegory      [?7h[?12l[?25h[?25l[?7lhainComplex

RT_listallableSymbolicExpressionRinghainComplex                  

RT_vects        artanMatixhainCompleMorphism

_superartanTypehainComlexes

achedFunctiontegory      hi     [?7h[?12l[?25h[?25l[?7lChildProcessError

allableSymbolicExpressionRinghainComplex                  ildProcessError

artanMatixhainCompleMorphismi                  

artanTypehainComlexeslssFunction 

tegory      hi     lassicalCrystals[?7h[?12l[?25h[?25l[?7lClassicalModularPolynomialDatabase

hainComplex                  ildProcessErrorlassicalModularPolynomialDatabase

hainCompleMorphismi                  liffordAlgebra

hainComlexeslssFunction uterAlgebra

hi     lassicalCrystalsuterComplex   [?7h[?12l[?25h[?25l[?7luterQuiver

ildProcessErrorlassicalModularPolynomialDatabaseuterQuiver                     

i                  liffordAlgebrausteSeed    

lssFunction uterAlgebraoalgbras    

lassicalCrystalsuterComplex   oalgbrasWithBasis[?7h[?12l[?25h[?25l[?7lolor

lassicalModularPolynomialDatabaseuterQuiver                     olor        

liffordAlgebrausteSeed    olordPrmutations

uterAlgebraoalgbras    mbinations

uterComplex   oalgbrasWithBasismbinatorialCls [?7h[?12l[?25h[?25l[?7lmbinatorialFreeModule

uterQuiver                     olor        mbinatorialFreeModule

usteSeed    olordPrmutationsmbinatoialObject

oalgbras    mbinationsorialPolyhedron

oalgbrasWithBasismbinatorialCls Species[?7h[?12l[?25h[?25l[?7lmutiveAdditiveGroups

olor        mbinatorialFreeModulemutiveAdditiveGroups

olordPrmutationsmbinatoialObjectmutiveAdditiveMonoids

mbinationsorialPolyhedronmutiveAdditivSemigroups

mbinatorialCls SpeciesmutiveAgebraElement[?7h[?12l[?25h[?25l[?7llgebraIdeals

mbinatorialFreeModulemutiveAdditiveGroupslgebraIdeals 

mbinatoialObjectmutiveAdditiveMonoidslgebras       

orialPolyhedronmutiveAdditivSemigroupsRing              

SpeciesmutiveAgebraElementRingElement   [?7h[?12l[?25h[?25l[?7lRingIdeals

mutiveAdditiveGroupslgebraIdeals RingIdeals   

mutiveAdditiveMonoidslgebras       Rings   

mutiveAdditivSemigroupsRing              pleteDiscreteValuationFields

mutiveAgebraElementRingElement   pleteDiscreteValuaionRings[?7h[?12l[?25h[?25l[?7lAlgebraIdeals

 CommutativeAlgebraIdeals                     CommutativeRingIdeals                       [?7h[?12l[?25h[?25l[?7ldditiveGroups

 CommutativeAdditiveGroups                    CommutativeAlgebraIdeals                    [?7h[?12l[?25h[?25l[?7lbinorialFreeModule

binorialFreeModule  dditiveGroupsAlgebraIdeals

binorialObject       dditiveMonoidsAlgebras

binorialPolyhdron      AdditiveSemigroupsmutativeRing                

binoriaSpecies     AlgebraElementmutativeRingElemen        [?7h[?12l[?25h[?25l[?7llor

lor                  binorialFreeModule  dditiveGroups

loredPemutationsbinorialObject       dditiveMonoids

ions           binorialPolyhdron      AdditiveSemigroups

Class  binoriaSpecies     AlgebraElement[?7h[?12l[?25h[?25l[?7llusterQuiver

lusterQuiverlor                  binorialFreeModule  

lustrSed        loredPemutationsbinorialObject       

algebras  ions           binorialPolyhdron      

algebrasWithBisClass  binoriaSpecies     [?7h[?12l[?25h[?25l[?7lasicalModularPolynomialDatabase

asicalModularPolynomialDatabaselusterQuiverlor                  

iffodAlgebralustrSed        loredPemutations

lustrAlgebraalgebras  ions           

lustrComplex     algebrasWithBisClass  [?7h[?12l[?25h[?25l[?7lChildProcessError

hildProcessError                 asicalModularPolynomialDatabaselusterQuiver

i             iffodAlgebralustrSed        

asFunction lustrAlgebraalgebras  

asicalCrystalslustrComplex     algebrasWithBis[?7h[?12l[?25h[?25l[?7lChainComplex

ainComplex     hildProcessError                 asicalModularPolynomialDatabase

hainComplexMorphismi             iffodAlgebra

hinComplexesasFunction lustrAlgebra

hi              asicalCrystalslustrComplex     [?7h[?12l[?25h[?25l[?7lallableSymbolicExpressionRing

allableSymbolicExpressionRingainComplex     hildProcessError                 

artanMatri        hainComplexMorphismi             

artanTye    hinComplexesasFunction 

ategoryhi              asicalCrystals[?7h[?12l[?25h[?25l[?7lRT_list

RT_list                      allableSymbolicExpressionRingainComplex     

RT_vectos artanMatri        hainComplexMorphism

_super   artanTye    hinComplexes

chedFunctionategoryhi              [?7h[?12l[?25h[?25l[?7lLF

LF     RT_list                      allableSymbolicExpressionRing

PRFanoTicVarietyRT_vectos artanMatri        

RT    _super   artanTye    

RT_basis     chedFunctionategory[?7h[?12l[?25h[?25l[?7lD

DLF     RT_list                      

FiniteSequence    PRFanoTicVarietyRT_vectos 

FiniteSequencesRT    _super   

IF      RT_basis     chedFunction[?7h[?12l[?25h[?25l[?7lBufferError

BufferErrorDLF     

BytesWarning   FiniteSequence    PRFanoTicVariety

BF             FiniteSequencesRT    

C IF      RT_basis     [?7h[?12l[?25h[?25l[?7lBrandtModule

randtModuleBufferErrorD

rauerAlgebraBytesWarning   FiniteSequence    

BrokenPipeErrorBF             FiniteSequences

BruhatTitsQuotientC IF      [?7h[?12l[?25h[?25l[?7lBlockingIOError

lockingIOErrorrandtModuleBufferError

oolanPolynomialRingrauerAlgebraBytesWarning   

aidGroup     BrokenPipeErrorBF             

anchingRule     BruhatTitsQuotientC [?7h[?12l[?25h[?25l[?7lBlockingIOErro









[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lvision([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: type(A.jordan_form().subdivision())

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [17], in <cell line: 1>()
----> 1 type(A.jordan_form().subdivision())

File /ext/sage/9.7/src/sage/matrix/matrix2.pyx:8845, in sage.matrix.matrix2.Matrix.subdivision()
   8843         self._subdivisions = (l_row, l_col)
   8844 
-> 8845 def subdivision(self, i, j):
   8846     """
   8847     Returns an immutable copy of the (i,j)th submatrix of self,

TypeError: subdivision() takes exactly 2 positional arguments (0 given)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(A.jordan_form().subdivision())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7li))[?7h[?12l[?25h[?25l[?7l,))[?7h[?12l[?25h[?25l[?7l ))[?7h[?12l[?25h[?25l[?7li))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, i)[?7h[?12l[?25h[?25l[?7l1, i)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l1))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: type(A.jordan_form().subdivision(1, 1))

[?7h[?12l[?25h[?2004l[?7h<class 'sage.matrix.matrix_modn_dense_float.Matrix_modn_dense_float'>
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(A.jordan_form().subdivision(1, 1))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7ltyp(A.jordan_form().subdivision(1, 1))[?7h[?12l[?25h[?25l[?7l(A.jordan_form().subdivision(1, 1))[?7h[?12l[?25h[?25l[?7l(A.jordan_form().subdivision(1, 1))[?7h[?12l[?25h[?25l[?7l(A.jordan_form().subdivision(1, 1))[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls(A.jordan_form().subdivision(1, 1))[?7h[?12l[?25h[?25l[?7lt(A.jordan_form().subdivision(1, 1))[?7h[?12l[?25h[?25l[?7lstr(A.jordan_form().subdivision(1, 1))[?7h[?12l[?25h[?25l[?7lsage: str(A.jordan_form().subdivision(1, 1))

[?7h[?12l[?25h[?2004l[?7h'[1 1 0 0]\n[0 1 1 0]\n[0 0 1 1]\n[0 0 0 1]'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 2^2 with the equation:
 z^2 - z = x^3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 2^2 with the equations:
z0^2 - z0 = x^3
z1^2 - z1 = a*x^3

/ext/sage/9.7/src/sage/rings/polynomial/polynomial_singular_interface.py:372:
********************************************************************************
Denominators of fraction field elements are sometimes dropped without warning.
This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696.
********************************************************************************
>> A := MatrixAlgebra<GF(4),6|[1, a + 1, 0, 0, 0, a, 0, 1, 0, 0, 0, 0, 0, 0, 1
                                  ^
User error: Identifier 'a' has not been declared or assigned
>> , 0, 1, 0, 0, 0, 0, 0, 0, 1]>;M := RModule(RSpace(GF(4),6), A);Indecomposab
                                                               ^
User error: Identifier 'A' has not been declared or assigned
>> ,6), A);IndecomposableSummands(M);
                                  ^
User error: Identifier 'M' has not been declared or assigned
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 2^2 with the equations:
z0^2 - z0 = x^3
z1^2 - z1 = a*x^3

---------------------------------------------------------------------------
NameError                                 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>: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: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>

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

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 2^2 with the equations:
z0^2 - z0 = x^3
z1^2 - z1 = a*x^3

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_form(subdivide=True)[?7h[?12l[?25h[?25l[?7lS.genus()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_form(subdivide=True)[?7h[?12l[?25h[?25l[?7lsage: A

[?7h[?12l[?25h[?2004l[?7h[    1 a + 1     0     0     0     a]
[    0     1     0     0     0     0]
[    0     0     1     0     a     0]
[    0     0     0     1     1     0]
[    0     0     0     0     1     0]
[    0     0     0     0     0     1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB^p == identity_matrix(10)[?7h[?12l[?25h[?25l[?7lsage: B

[?7h[?12l[?25h[?2004l[?7h[1 1 0 0 0 1]
[0 1 0 0 0 0]
[0 0 1 0 1 0]
[0 0 0 1 a 0]
[0 0 0 0 1 0]
[0 0 0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B, text=True)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lgmathis(A, B, text=True)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B, text=True)

[?7h[?12l[?25h[?2004l[?7h'A := MatrixAlgebra<GF(4),6|[1, a + 1, 0, 0, 0, a, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, a, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1],[1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, a, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1]>;M := RModule(RSpace(GF(4),6), A);IndecomposableSummands(M);'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS.genus()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus()

[?7h[?12l[?25h[?2004l[?7h3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lmagmathis(A, B, text=True)[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^3
z1^2 - z1 = x^13

[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lare_equivalent_matrix(A1, A2, q)[?7h[?12l[?25h[?25l[?7lsage: q = 5

....: p = q.factor()[0][0]

....: n = 2

....: A1 = matrix(ZZ, [[1, 3], [3, 4]])

....: A2 = matrix(ZZ, [[2, 3], [2, 2]])

....: print((identity_matrix(n) + A1.transpose()*A1).determinant()%p)

....: print((identity_matrix(n) + A2.transpose()*A2).determinant()%p)[?7h[?12l[?25h[?25l[?7lare_equivalent_matrix(A1, A2, q)

 

 

 

 

 

 [?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llista_np = [2*i+1 for i in range(q//2)][?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^5

[
RModule of dimension 6 over GF(3),
RModule of dimension 6 over GF(3),
RModule of dimension 14 over GF(3)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA2 = matrix(ZZ, [[2, 3], [2, 2]])[?7h[?12l[?25h[?25l[?7lS.genus()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lmagical_element()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lgical_element()[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element()

[?7h[?12l[?25h[?2004l[?7h[x^4*z0 + x^3*z1 + z0^2*z1^2]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lare_equivalent_matrix(A1, A2, q)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lno  20 -th root; divide by 2
---------------------------------------------------------------------------
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>: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: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>:44, in __init__(self, C, list_of_fcts, prec)

ValueError: not enough values to unpack (expected 4, got 2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lno  14 -th root; divide by 2
---------------------------------------------------------------------------
ValueError                                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>: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: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>:44, in __init__(self, C, list_of_fcts, prec)

ValueError: not enough values to unpack (expected 4, got 2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^5
z1^3 - z1 = x^11

I haven't found all forms.
---------------------------------------------------------------------------
NameError                                 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>: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: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>:29, in group_action_matrices_dR(AS, threshold)

File <string>:145, in holomorphic_differentials_basis(self, threshold)

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

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^5
z1^3 - z1 = x^11

I haven't found all forms.
---------------------------------------------------------------------------
NameError                                 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>: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: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>:29, in group_action_matrices_dR(AS, threshold)

File <string>:145, in holomorphic_differentials_basis(self, threshold)

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

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^5
z1^3 - z1 = x^11

I haven't found all forms.
---------------------------------------------------------------------------
NameError                                 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>: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: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>:29, in group_action_matrices_dR(AS, threshold)

File <string>:145, in holomorphic_differentials_basis(self, threshold)

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

[?7h[?12l[?25h[?2004lno  20 -th root; divide by 2
---------------------------------------------------------------------------
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>: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: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>:44, in __init__(self, C, list_of_fcts, prec)

ValueError: not enough values to unpack (expected 4, got 2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = 2*x^8

[
RModule of dimension 6 over GF(3),
RModule of dimension 6 over GF(3),
RModule of dimension 6 over GF(3),
RModule of dimension 6 over GF(3),
RModule of dimension 6 over GF(3),
RModule of dimension 14 over GF(3)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = 2*x^11

[
RModule of dimension 6 over GF(3),
RModule of dimension 6 over GF(3),
RModule of dimension 6 over GF(3),
RModule of dimension 6 over GF(3),
RModule of dimension 6 over GF(3),
RModule of dimension 6 over GF(3),
RModule of dimension 6 over GF(3),
RModule of dimension 6 over GF(3),
RModule of dimension 14 over GF(3)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

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

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 5 with the equations:
z0^5 - z0 = x^2
z1^5 - z1 = x^7




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

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

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 5 with the equations:
z0^5 - z0 = x^2
z1^5 - z1 = x^7

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.magical_element()[?7h[?12l[?25h[?25l[?7lmagical_element()[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element()

[?7h[?12l[?25h[?2004l[?7h[x^6*z0^3 + x^5*z0^2*z1 + z0^4*z1^4 + x^4*z0*z1^2 + x^3*z1^3]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rhmbasis()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( (z1) * dx, 0 ),
 ( (z1^2) * dx, 0 ),
 ( (z1^3) * dx, 0 ),
 ( (2*x^4*z0^4 - 2*x^3*z0^3*z1 - x^2*z0^2*z1^2 + z1^4) * dx, 0 ),
 ( (z0) * dx, 0 ),
 ( (z0*z1) * dx, 0 ),
 ( (z0*z1^2) * dx, 0 ),
 ( (z0*z1^3) * dx, 0 ),
 ( (x^3*z0^4*z1 + x^2*z0^3*z1^2 + x^6 + x*z0^2*z1^3 + z0*z1^4) * dx, 0 ),
 ( (z0^2) * dx, 0 ),
 ( (z0^2*z1) * dx, 0 ),
 ( (z0^2*z1^2) * dx, 0 ),
 ( (-x^5 + z0^2*z1^3) * dx, 0 ),
 ( (z0^3) * dx, 0 ),
 ( (z0^3*z1) * dx, 0 ),
 ( (z0^3*z1^2) * dx, 0 ),
 ( (2*x^5*z0 + z0^3*z1^3 + 2*x^4*z1) * dx, 0 ),
 ( (z0^4) * dx, 0 ),
 ( (z0^4*z1) * dx, 0 ),
 ( (z0^4*z1^2) * dx, 0 ),
 ( (-x^5*z0^2 + z0^4*z1^3 - 2*x^4*z0*z1 + 2*x^3*z1^2) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( (x*z1) * dx, 0 ),
 ( (x*z1^2) * dx, 0 ),
 ( (-x^4*z0^3 + x*z1^3) * dx, 0 ),
 ( (x*z0) * dx, 0 ),
 ( (x*z0*z1) * dx, 0 ),
 ( (x*z0*z1^2) * dx, 0 ),
 ( (-x^4*z0^4 - 2*x^3*z0^3*z1 + 2*x^2*z0^2*z1^2 + x*z0*z1^3) * dx, 0 ),
 ( (x*z0^2) * dx, 0 ),
 ( (x*z0^2*z1) * dx, 0 ),
 ( (x*z0^2*z1^2) * dx, 0 ),
 ( (x*z0^3) * dx, 0 ),
 ( (x*z0^3*z1) * dx, 0 ),
 ( (x*z0^3*z1^2 - x^5) * dx, 0 ),
 ( (x*z0^4) * dx, 0 ),
 ( (x*z0^4*z1) * dx, 0 ),
 ( (x*z0^4*z1^2 + x^5*z0 - 2*x^4*z1) * dx, 0 ),
 ( (x^2) * dx, 0 ),
 ( (x^2*z1) * dx, 0 ),
 ( (x^2*z1^2) * dx, 0 ),
 ( (x^2*z0) * dx, 0 ),
 ( (x^2*z0*z1) * dx, 0 ),
 ( (-x^4*z0^3 + x^2*z0*z1^2) * dx, 0 ),
 ( (x^2*z0^2) * dx, 0 ),
 ( (x^2*z0^2*z1) * dx, 0 ),
 ( (x^2*z0^3) * dx, 0 ),
 ( (x^2*z0^3*z1) * dx, 0 ),
 ( (x^2*z0^4) * dx, 0 ),
 ( (x^2*z0^4*z1 - x^5) * dx, 0 ),
 ( (x^3) * dx, 0 ),
 ( (x^3*z1) * dx, 0 ),
 ( (x^3*z0) * dx, 0 ),
 ( (x^3*z0*z1) * dx, 0 ),
 ( (x^3*z0^2) * dx, 0 ),
 ( (-x^4*z0^3 + x^3*z0^2*z1) * dx, 0 ),
 ( (x^3*z0^3) * dx, 0 ),
 ( (x^3*z0^4) * dx, 0 ),
 ( (x^4) * dx, 0 ),
 ( (x^4*z0) * dx, 0 ),
 ( (x^4*z0^2) * dx, 0 ),
 ( (-2*x^5) * dx, z1/x ),
 ( (x^5*z1) * dx, z1^2/x ),
 ( (-x^5*z1^2) * dx, z1^3/x ),
 ( (2*x^5*z1^3) * dx, z1^4/x ),
 ( (-2*x^5*z0) * dx, z0*z1/x ),
 ( (x^5*z0*z1) * dx, z0*z1^2/x ),
 ( (-x^5*z0*z1^2) * dx, z0*z1^3/x ),
 ( (2*x^5*z0*z1^3 - x^4*z0^4 + x^3*z0^3*z1 - 2*x^2*z0^2*z1^2) * dx, z0*z1^4/x ),
 ( (-2*x^5*z0^2) * dx, z0^2*z1/x ),
 ( (x^5*z0^2*z1) * dx, z0^2*z1^2/x ),
 ( (-x^5*z0^2*z1^2) * dx, z0^2*z1^3/x ),
 ( (2*x^5*z0^2*z1^3 - x^3*z0^4*z1 - x^2*z0^3*z1^2 - x^6 - x*z0^2*z1^3) * dx, z0^2*z1^4/x ),
 ( (0) * dx, z0^3/x ),
 ( (-2*x^5*z0^3) * dx, z0^3*z1/x ),
 ( (x^5*z0^3*z1) * dx, z0^3*z1^2/x ),
 ( (-x^5*z0^3*z1^2 - x^5) * dx, z0^3*z1^3/x ),
 ( (2*x^5*z0^3*z1^3 - z0^2*z1^4) * dx, z0^3*z1^4/x ),
 ( (0) * dx, z0^4/x ),
 ( (-2*x^5*z0^4) * dx, z0^4*z1/x ),
 ( (x^5*z0^4*z1) * dx, z0^4*z1^2/x ),
 ( (-x^5*z0^4*z1^2 + x^5*z0 + x^4*z1) * dx, z0^4*z1^3/x ),
 ( (2*x^5*z0^4*z1^3 - x^4*z0^3 + 2*z0^3*z1^4) * dx, z0^4*z1^4/x ),
 ( (x^4*z1) * dx, z1^2/x^2 ),
 ( (-x^4*z1^2) * dx, z1^3/x^2 ),
 ( (2*x^4*z1^3) * dx, z1^4/x^2 ),
 ( (x^4*z0*z1) * dx, z0*z1^2/x^2 ),
 ( (-x^4*z0*z1^2) * dx, z0*z1^3/x^2 ),
 ( (2*x^4*z0*z1^3) * dx, z0*z1^4/x^2 ),
 ( (x^4*z0^2*z1) * dx, z0^2*z1^2/x^2 ),
 ( (-x^4*z0^2*z1^2) * dx, z0^2*z1^3/x^2 ),
 ( (2*x^4*z0^2*z1^3 + x^5) * dx, z0^2*z1^4/x^2 ),
 ( (-2*x^4*z0^3) * dx, z0^3*z1/x^2 ),
 ( (x^4*z0^3*z1) * dx, z0^3*z1^2/x^2 ),
 ( (-x^4*z0^3*z1^2) * dx, z0^3*z1^3/x^2 ),
 ( (2*x^4*z0^3*z1^3 - 2*x^5*z0 + x^4*z1) * dx, z0^3*z1^4/x^2 ),
 ( (-2*x^4*z0^4) * dx, z0^4*z1/x^2 ),
 ( (x^4*z0^4*z1) * dx, z0^4*z1^2/x^2 ),
 ( (-x^4*z0^4*z1^2) * dx, z0^4*z1^3/x^2 ),
 ( (2*x^4*z0^4*z1^3 + x^5*z0^2 - x^4*z0*z1 + 2*x^3*z1^2) * dx, z0^4*z1^4/x^2 ),
 ( (-x^3*z1^2) * dx, z1^3/x^3 ),
 ( (2*x^3*z1^3) * dx, z1^4/x^3 ),
 ( (-x^3*z0*z1^2) * dx, z0*z1^3/x^3 ),
 ( (2*x^3*z0*z1^3) * dx, z0*z1^4/x^3 ),
 ( (-x^3*z0^2*z1^2) * dx, z0^2*z1^3/x^3 ),
 ( (2*x^3*z0^2*z1^3) * dx, z0^2*z1^4/x^3 ),
 ( (x^3*z0^3*z1) * dx, z0^3*z1^2/x^3 ),
 ( (-x^3*z0^3*z1^2) * dx, z0^3*z1^3/x^3 ),
 ( (2*x^3*z0^3*z1^3) * dx, z0^3*z1^4/x^3 ),
 ( (x^3*z0^4*z1) * dx, z0^4*z1^2/x^3 ),
 ( (-x^3*z0^4*z1^2) * dx, z0^4*z1^3/x^3 ),
 ( (2*x^3*z0^4*z1^3) * dx, z0^4*z1^4/x^3 ),
 ( (2*x^2*z1^3) * dx, z1^4/x^4 ),
 ( (2*x^2*z0*z1^3) * dx, z0*z1^4/x^4 ),
 ( (-x^2*z0^2*z1^2) * dx, z0^2*z1^3/x^4 ),
 ( (2*x^2*z0^2*z1^3) * dx, z0^2*z1^4/x^4 ),
 ( (-x^2*z0^3*z1^2) * dx, z0^3*z1^3/x^4 ),
 ( (2*x^2*z0^3*z1^3) * dx, z0^3*z1^4/x^4 ),
 ( (-x^2*z0^4*z1^2) * dx, z0^4*z1^3/x^4 ),
 ( (2*x^2*z0^4*z1^3) * dx, z0^4*z1^4/x^4 ),
 ( (2*x*z0^2*z1^3) * dx, z0^2*z1^4/x^5 ),
 ( (2*x*z0^3*z1^3) * dx, z0^3*z1^4/x^5 ),
 ( (2*x*z0^4*z1^3) * dx, z0^4*z1^4/x^5 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7l, B = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l_(AS)[?7h[?12l[?25h[?25l[?7ld(AS)[?7h[?12l[?25h[?25l[?7lr(AS)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7lR(AS)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l();[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_dR(AS); magma

 magma     

 magma_free

 magmathis 



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

 magma     





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

 magma     

 magma_free[?7h[?12l[?25h[?25l[?7lthis



 magma_free

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







[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_dR(AS); magmathis(A, B)

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

^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[24;1R^[[25;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R

^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[24;1R^[[25;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

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

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

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

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

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

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

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

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [1;3S[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^3
z1^2 - z1 = x^5

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_dR(AS); magmathis(A, B)[?7h[?12l[?25h[?25l[?7lS.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ljumps[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lsage: AS.jumps

[?7h[?12l[?25h[?2004l[?7h[[3, 7]]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.jumps[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lraification_jumps()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lfication_jumps()[?7h[?12l[?25h[?25l[?7lsage: AS.ramification_jumps()

[?7h[?12l[?25h[?2004l[?7h[3, 7]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.ramification_jumps()[?7h[?12l[?25h[?25l[?7ljups[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^3
z1^2 - z1 = x^7

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.ramification_jumps()[?7h[?12l[?25h[?25l[?7ljups[?7h[?12l[?25h[?25l[?7lsage: AS.jumps

[?7h[?12l[?25h[?2004l[?7h[[3, 11]]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.jumps[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l1 3 [[3, 11]] 1 5
^C---------------------------------------------------------------------------
KeyboardInterrupt                         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>: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: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>:44, in __init__(self, C, list_of_fcts, prec)

File <string>:134, in artin_schreier_transform(power_series, prec)

File <string>:12, in new_reverse(power_series, prec)

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1831, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
   1829 if x:
   1830     raise ValueError("must not specify %s keyword and positional argument" % name)
-> 1831 a = self(kwds[name])
   1832 del kwds[name]
   1833 try:

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1852, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
   1850         x = x[0]
   1851 
-> 1852     return self.__u(*x)*(x[0]**self.__n)
   1853 
   1854 def __pari__(self):

File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:365, in sage.rings.power_series_poly.PowerSeries_poly.__call__()
    363         x[0] = a
    364         x = tuple(x)
--> 365     return self.__f(x)
    366 
    367 def _unsafe_mutate(self, i, value):

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:898, in sage.rings.polynomial.polynomial_element.Polynomial.__call__()
    896             return result
    897         pol._compiled = CompiledPolynomialFunction(pol.list())
--> 898     return pol._compiled.eval(a)
    899 
    900 def compose_trunc(self, Polynomial other, long n):

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:125, in sage.rings.polynomial.polynomial_compiled.CompiledPolynomialFunction.eval()
    123 cdef object temp
    124 try:
--> 125     pd_eval(self._dag, x, self._coeffs)  #see further down
    126     temp = self._dag.value               #for an explanation
    127     pd_clean(self._dag)                  #of these 3 lines

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
    352     if pd.value is None:
--> 353         pd.eval(vars, coeffs)
    354     pd.hits += 1
    355 

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
    505 
    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507         pd_eval(self.left, vars, coeffs)
    508         pd_eval(self.right, vars, coeffs)
    509         self.value = self.left.value * self.right.value + coeffs[self.index]

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
    352     if pd.value is None:
--> 353         pd.eval(vars, coeffs)
    354     pd.hits += 1
    355 

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
    505 
    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507         pd_eval(self.left, vars, coeffs)
    508         pd_eval(self.right, vars, coeffs)
    509         self.value = self.left.value * self.right.value + coeffs[self.index]

    [... skipping similar frames: sage.rings.polynomial.polynomial_compiled.pd_eval at line 353 (96 times), sage.rings.polynomial.polynomial_compiled.abc_pd.eval at line 507 (95 times)]

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
    505 
    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507         pd_eval(self.left, vars, coeffs)
    508         pd_eval(self.right, vars, coeffs)
    509         self.value = self.left.value * self.right.value + coeffs[self.index]

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
    352     if pd.value is None:
--> 353         pd.eval(vars, coeffs)
    354     pd.hits += 1
    355 

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:509, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
    507 pd_eval(self.left, vars, coeffs)
    508 pd_eval(self.right, vars, coeffs)
--> 509 self.value = self.left.value * self.right.value + coeffs[self.index]
    510 pd_clean(self.left)
    511 pd_clean(self.right)

File /ext/sage/9.7/src/sage/structure/element.pyx:1233, in sage.structure.element.Element.__add__()
   1231 # Left and right are Sage elements => use coercion model
   1232 if BOTH_ARE_ELEMENT(cl):
-> 1233     return coercion_model.bin_op(left, right, add)
   1234 
   1235 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:1230, in sage.structure.element.Element.__add__()
   1228 cdef int cl = classify_elements(left, right)
   1229 if HAVE_SAME_PARENT(cl):
-> 1230     return (<Element>left)._add_(right)
   1231 # Left and right are Sage elements => use coercion model
   1232 if BOTH_ARE_ELEMENT(cl):

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:764, in sage.rings.laurent_series_ring_element.LaurentSeries._add_()
    762 elif self.__n > right.__n:
    763     m = right.__n
--> 764     f1 = self.__u << self.__n - m
    765     f2 = right.__u
    766 else:

File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:583, in sage.rings.power_series_poly.PowerSeries_poly.__lshift__()
    581 """
    582 if n:
--> 583     return PowerSeries_poly(self._parent, self.__f << n, self._prec + n)
    584 else:
    585     return self

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

[?7h[?12l[?25h[?2004l1 3 [[3, 11]] 1 5
1 5 [[3, 11]] 1 9
1 7 [[3, 11]] 1 13
1 9 [[3, 11]] 1 17
1 11 [[3, 11]] 1 21
1 13 [[3, 11]] 1 25
3 5 [[3, 11]] 3 7
3 7 [[3, 11]] 3 11
3 9 [[3, 11]] 3 15
3 11 [[3, 11]] 3 19
3 13 [[3, 11]] 3 23
5 7 [[3, 11]] 5 9
5 9 [[3, 11]] 5 13
5 11 [[3, 11]] 5 17
5 13 [[3, 11]] 5 21
7 9 [[3, 11]] 7 11
7 11 [[3, 11]] 7 15
7 13 [[3, 11]] 7 19
9 11 [[3, 11]] 9 13
9 13 [[3, 11]] 9 17
11 13 [[3, 11]] 11 15
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l1 3 [[1, 5]] 1 5
1 5 [[1, 9]] 1 9
1 7 [[1, 13]] 1 13
1 9 [[1, 17]] 1 17
1 11 [[1, 21]] 1 21
1 13 [[1, 25]] 1 25
3 5 [[3, 7]] 3 7
3 7 [[3, 11]] 3 11
3 9 [[3, 15]] 3 15
3 11 [[3, 19]] 3 19
3 13 [[3, 23]] 3 23
5 7 [[5, 9]] 5 9
5 9 [[5, 13]] 5 13
5 11 [[5, 17]] 5 17
5 13 [[5, 21]] 5 21
7 9 [[7, 11]] 7 11
7 11 [[7, 15]] 7 15
7 13 [[7, 19]] 7 19
9 11 [[9, 13]] 9 13
9 13 [[9, 17]] 9 17
11 13 [[11, 15]] 11 15
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.jumps[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^11
z1^2 - z1 = x^13

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.jumps[?7h[?12l[?25h[?25l[?7lraification_jumps()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lfication_jumps()[?7h[?12l[?25h[?25l[?7lsage: AS.ramification_jumps()

[?7h[?12l[?25h[?2004l[?7h[11, 15]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.ramification_jumps()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lonent_of_different_prim()[?7h[?12l[?25h[?25l[?7lsage: AS.exponent_of_different_prim()

[?7h[?12l[?25h[?2004l[?7h37
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l1 3 [[1, 5]] 1 5
3 7
1 5 [[1, 9]] 1 9
7 11
1 7 [[1, 13]] 1 13
11 15
1 9 [[1, 17]] 1 17
15 19
1 11 [[1, 21]] 1 21
19 23
1 13 [[1, 25]] 1 25
23 27
3 5 [[3, 7]] 3 7
9 13
3 7 [[3, 11]] 3 11
13 17
3 9 [[3, 15]] 3 15
17 21
3 11 [[3, 19]] 3 19
21 25
3 13 [[3, 23]] 3 23
25 29
5 7 [[5, 9]] 5 9
15 19
5 9 [[5, 13]] 5 13
19 23
5 11 [[5, 17]] 5 17
23 27
5 13 [[5, 21]] 5 21
27 31
7 9 [[7, 11]] 7 11
21 25
7 11 [[7, 15]] 7 15
25 29
7 13 [[7, 19]] 7 19
29 33
9 11 [[9, 13]] 9 13
27 31
9 13 [[9, 17]] 9 17
31 35
11 13 [[11, 15]] 11 15
33 37
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l1 3 [[1, 5]] 1 5
7 7
1 5 [[1, 9]] 1 9
11 11
1 7 [[1, 13]] 1 13
15 15
1 9 [[1, 17]] 1 17
19 19
1 11 [[1, 21]] 1 21
23 23
1 13 [[1, 25]] 1 25
27 27
3 5 [[3, 7]] 3 7
13 13
3 7 [[3, 11]] 3 11
17 17
3 9 [[3, 15]] 3 15
21 21
3 11 [[3, 19]] 3 19
25 25
3 13 [[3, 23]] 3 23
29 29
5 7 [[5, 9]] 5 9
19 19
5 9 [[5, 13]] 5 13
23 23
5 11 [[5, 17]] 5 17
27 27
5 13 [[5, 21]] 5 21
31 31
7 9 [[7, 11]] 7 11
25 25
7 11 [[7, 15]] 7 15
29 29
7 13 [[7, 19]] 7 19
33 33
9 11 [[9, 13]] 9 13
31 31
9 13 [[9, 17]] 9 17
35 35
11 13 [[11, 15]] 11 15
37 37
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lzmag = AS.magical_element(threshold = 18)[0][?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7l.jorda_form(subdivide=True)[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[1]^2/AS.x*AS.dx[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]*[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: AS.z[0]*AS.z[1]

[?7h[?12l[?25h[?2004l[?7hz0*z1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[0]*AS.z[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]*AS.z[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]*AS.z[1]).norm()

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

AttributeError: 'as_function' object has no attribute 'norm'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprint((identity_matrix(n) + A2.transpose()*A2).determinant()%p)[?7h[?12l[?25h[?25l[?7l = q.factor()[0][0][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[0]*AS.z[1][?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lmagical_element()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lal_element()[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element()

[?7h[?12l[?25h[?2004l[?7h[]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7lh)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7lh)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7ll)[?7h[?12l[?25h[?25l[?7ld)[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element(threshold=20)

[?7h[?12l[?25h[?2004l[?7h[x^12 + z0*z1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lare_equivalent_matrix(A1, A2, q)[?7h[?12l[?25h[?25l[?7lsage: a

[?7h[?12l[?25h[?2004l[?7h13
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lsage: b

[?7h[?12l[?25h[?2004l[?7h13
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]*AS.z[1]).norm()[?7h[?12l[?25h[?25l[?7la^8 + a^7 + a^5 + a^3 + a^2)^2[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: (a+b)/2

[?7h[?12l[?25h[?2004l[?7h13
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element(threshold=20)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^11
z1^2 - z1 = x^13

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a+b)/2[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: (11+13)/2

[?7h[?12l[?25h[?2004l[?7h12
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l1 3 [[1, 5]] 1 5
7 7
1 5 [[1, 9]] 1 9
11 11
1 7 [[1, 13]] 1 13
15 15
1 9 [[1, 17]] 1 17
19 19
1 11 [[1, 21]] 1 21
23 23
1 13 [[1, 25]] 1 25
27 27
3 5 [[3, 7]] 3 7
13 13
3 7 [[3, 11]] 3 11
17 17
3 9 [[3, 15]] 3 15
21 21
3 11 [[3, 19]] 3 19
25 25
3 13 [[3, 23]] 3 23
29 29
5 7 [[5, 9]] 5 9
19 19
5 9 [[5, 13]] 5 13
23 23
5 11 [[5, 17]] 5 17
27 27
5 13 [[5, 21]] 5 21
31 31
7 9 [[7, 11]] 7 11
25 25
7 11 [[7, 15]] 7 15
29 29
7 13 [[7, 19]] 7 19
33 33
9 11 [[9, 13]] 9 13
31 31
9 13 [[9, 17]] 9 17
35 35
11 13 [[11, 15]] 11 15
37 37
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.magical_element(threshold=20)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lgical_element(threshold=20)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element()

[?7h[?12l[?25h[?2004l[?7h[(a + 1)*x^3 + z0*z1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l16.factor()[0][0][?7h[?12l[?25h[?25l[?7l/(a^13 + a^12 + a^11 + a^9 + a^8 + a^4 + a^3 + a)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: 1/(a+1)

[?7h[?12l[?25h[?2004l[?7ha
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[x^6*z0 + x^5*z1 + x^4*z0 + x^4*z2 + z0*z1*z2]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[x^7*z0 + x^6*z1 + x^5*z0 + x^4*z2 + z0*z1*z2]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[x^7*z0 + x^6*z0 + x^6*z1 + x^5*z0 + x^5*z1 + x^4*z2 + z0*z1*z2]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l/ext/sage/9.7/src/sage/rings/polynomial/polynomial_singular_interface.py:372:
********************************************************************************
Denominators of fraction field elements are sometimes dropped without warning.
This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696.
********************************************************************************
>> A := MatrixAlgebra<GF(4),6|[1, a + 1, 0, 0, 0, a, 0, 1, 0, 0, 0, 0, 0, 0, 1
                                  ^
User error: Identifier 'a' has not been declared or assigned
>> , 0, 1, 0, 0, 0, 0, 0, 0, 1]>;M := RModule(RSpace(GF(4),6), A);Indecomposab
                                                               ^
User error: Identifier 'A' has not been declared or assigned
>> ,6), A);IndecomposableSummands(M);
                                  ^
User error: Identifier 'M' has not been declared or assigned
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

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

[?7h[?12l[?25h[?2004l[
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 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>: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: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>

TypeError: group_action_matrices_holo() got an unexpected keyword argument 'threshold'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[
RModule of dimension 1 over GF(2^2),
RModule of dimension 2 over GF(2^2)
]
[
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[
RModule of dimension 1 over GF(2^2),
RModule of dimension 2 over GF(2^2),
RModule of dimension 3 over GF(2^2)
]
[
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[
RModule of dimension 1 over GF(2^2),
RModule of dimension 1 over GF(2^2),
RModule of dimension 2 over GF(2^2),
RModule of dimension 2 over GF(2^2),
RModule of dimension 3 over GF(2^2)
]
[
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[
RModule of dimension 1 over GF(2^2),
RModule of dimension 2 over GF(2^2)
]
[
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[
RModule of dimension 1 over GF(2^2),
RModule of dimension 2 over GF(2^2)
]
F<a> := GF(4);A := MatrixAlgebra<GF(4),6|[1, a + 1, 0, 0, 0, a, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, a, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1],[1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, a, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1]>;M := RModule(RSpace(GF(4),6), A);IndecomposableSummands(M);
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[
RModule of dimension 1 over GF(2),
RModule of dimension 4 over GF(2)
]
F<a> := GF(4);A := MatrixAlgebra<GF(2),10|[1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],[1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]>;M := RModule(RSpace(GF(2),10), A);IndecomposableSummands(M);
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[
RModule of dimension 1 over GF(2),
RModule of dimension 4 over GF(2)
]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[
RModule of dimension 1 over GF(2),
RModule of dimension 4 over GF(2)
]
A := MatrixAlgebra<GF(2),10|[1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],[1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]>;M := RModule(RSpace(GF(2),10), A);IndecomposableSummands(M);
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004lWARNING: your terminal doesn't support cursor position requests (CPR).

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

[?7h[?12l[?25h[?2004l[
RModule of dimension 1 over GF(2),
RModule of dimension 4 over GF(2)
]
^C^C
KeyboardInterrupt

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

[?7h[?12l[?25h[?2004l1 3 [[1, 5]] 1 5
7 7
1 5 [[1, 9]] 1 9
11 11
1 7 [[1, 13]] 1 13
15 15
^C---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zz_pex.pyx:280, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.__call__()
    279 try:
--> 280     if a.parent() is not K:
    281         a = K.coerce(a)

AttributeError: 'tuple' object has no attribute 'parent'

During handling of the above exception, another exception occurred:

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>: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: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>:44, in __init__(self, C, list_of_fcts, prec)

File <string>:134, in artin_schreier_transform(power_series, prec)

File <string>:12, in new_reverse(power_series, prec)

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1831, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
   1829 if x:
   1830     raise ValueError("must not specify %s keyword and positional argument" % name)
-> 1831 a = self(kwds[name])
   1832 del kwds[name]
   1833 try:

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1852, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
   1850         x = x[0]
   1851 
-> 1852     return self.__u(*x)*(x[0]**self.__n)
   1853 
   1854 def __pari__(self):

File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:365, in sage.rings.power_series_poly.PowerSeries_poly.__call__()
    363         x[0] = a
    364         x = tuple(x)
--> 365     return self.__f(x)
    366 
    367 def _unsafe_mutate(self, i, value):

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zz_pex.pyx:283, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.__call__()
    281         a = K.coerce(a)
    282 except (TypeError, AttributeError, NotImplementedError):
--> 283     return Polynomial.__call__(self, a)
    284 
    285 _a = self._parent._modulus.ZZ_pE(list(a.polynomial()))

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:898, in sage.rings.polynomial.polynomial_element.Polynomial.__call__()
    896             return result
    897         pol._compiled = CompiledPolynomialFunction(pol.list())
--> 898     return pol._compiled.eval(a)
    899 
    900 def compose_trunc(self, Polynomial other, long n):

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:125, in sage.rings.polynomial.polynomial_compiled.CompiledPolynomialFunction.eval()
    123 cdef object temp
    124 try:
--> 125     pd_eval(self._dag, x, self._coeffs)  #see further down
    126     temp = self._dag.value               #for an explanation
    127     pd_clean(self._dag)                  #of these 3 lines

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
    352     if pd.value is None:
--> 353         pd.eval(vars, coeffs)
    354     pd.hits += 1
    355 

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
    505 
    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507         pd_eval(self.left, vars, coeffs)
    508         pd_eval(self.right, vars, coeffs)
    509         self.value = self.left.value * self.right.value + coeffs[self.index]

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
    352     if pd.value is None:
--> 353         pd.eval(vars, coeffs)
    354     pd.hits += 1
    355 

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
    505 
    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507         pd_eval(self.left, vars, coeffs)
    508         pd_eval(self.right, vars, coeffs)
    509         self.value = self.left.value * self.right.value + coeffs[self.index]

    [... skipping similar frames: sage.rings.polynomial.polynomial_compiled.pd_eval at line 353 (10 times), sage.rings.polynomial.polynomial_compiled.abc_pd.eval at line 507 (9 times)]

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
    505 
    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507         pd_eval(self.left, vars, coeffs)
    508         pd_eval(self.right, vars, coeffs)
    509         self.value = self.left.value * self.right.value + coeffs[self.index]

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
    352     if pd.value is None:
--> 353         pd.eval(vars, coeffs)
    354     pd.hits += 1
    355 

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:509, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
    507 pd_eval(self.left, vars, coeffs)
    508 pd_eval(self.right, vars, coeffs)
--> 509 self.value = self.left.value * self.right.value + coeffs[self.index]
    510 pd_clean(self.left)
    511 pd_clean(self.right)

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:912, in sage.rings.laurent_series_ring_element.LaurentSeries._mul_()
    910 """
    911 cdef LaurentSeries right = <LaurentSeries>right_r
--> 912 return type(self)(self._parent,
    913                   self.__u * right.__u,
    914                   self.__n + right.__n)

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:165, in sage.rings.laurent_series_ring_element.LaurentSeries.__init__()
    163         self.__u = f
    164 else:
--> 165     val = f.valuation()
    166     if val is infinity:
    167         self.__n = 0

File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:134, in sage.rings.power_series_poly.PowerSeries_poly.valuation()
    132         return self._prec
    133 
--> 134     return self.__f.valuation()
    135 
    136 def degree(self):

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:9215, in sage.rings.polynomial.polynomial_element.Polynomial.valuation()
   9213 if p is None:
   9214     for k from 0 <= k <= self.degree():
-> 9215         if self.get_unsafe(k):
   9216             return ZZ(k)
   9217 if isinstance(p, Polynomial):

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zz_pex.pyx:179, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.get_unsafe()
    177     self._parent._modulus.restore()
    178     cdef ZZ_pE_c c_pE = ZZ_pEX_coeff(self.x, i)
--> 179     return self._parent._base(ZZ_pE_c_to_list(c_pE))
    180 
    181 cpdef list list(self, bint copy=True):

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/finite_field_givaro.py:229, in FiniteField_givaro._element_constructor_(self, e)
    211     """
    212     Return a random element of ``self``.
    213 
   (...)
    225         True
    226     """
    227     return self._cache.random_element()
--> 229 def _element_constructor_(self, e):
    230     """
    231     Coerces several data types to ``self``.
    232 
   (...)
    368         2*a4^3 + 2*a4^2 + 1
    369     """
    370     return self._cache.element_from_data(e)

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

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

[?7h[?12l[?25h[?2004l1 2 [[1, 4]] 1 4
7 14
1 4 [[1, 10]] 1 10
13 26
^C---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zz_pex.pyx:280, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.__call__()
    279 try:
--> 280     if a.parent() is not K:
    281         a = K.coerce(a)

AttributeError: 'tuple' object has no attribute 'parent'

During handling of the above exception, another exception occurred:

KeyboardInterrupt                         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>: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: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>:44, in __init__(self, C, list_of_fcts, prec)

File <string>:134, in artin_schreier_transform(power_series, prec)

File <string>:12, in new_reverse(power_series, prec)

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1831, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
   1829 if x:
   1830     raise ValueError("must not specify %s keyword and positional argument" % name)
-> 1831 a = self(kwds[name])
   1832 del kwds[name]
   1833 try:

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1852, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
   1850         x = x[0]
   1851 
-> 1852     return self.__u(*x)*(x[0]**self.__n)
   1853 
   1854 def __pari__(self):

File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:365, in sage.rings.power_series_poly.PowerSeries_poly.__call__()
    363         x[0] = a
    364         x = tuple(x)
--> 365     return self.__f(x)
    366 
    367 def _unsafe_mutate(self, i, value):

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zz_pex.pyx:283, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.__call__()
    281         a = K.coerce(a)
    282 except (TypeError, AttributeError, NotImplementedError):
--> 283     return Polynomial.__call__(self, a)
    284 
    285 _a = self._parent._modulus.ZZ_pE(list(a.polynomial()))

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:898, in sage.rings.polynomial.polynomial_element.Polynomial.__call__()
    896             return result
    897         pol._compiled = CompiledPolynomialFunction(pol.list())
--> 898     return pol._compiled.eval(a)
    899 
    900 def compose_trunc(self, Polynomial other, long n):

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:125, in sage.rings.polynomial.polynomial_compiled.CompiledPolynomialFunction.eval()
    123 cdef object temp
    124 try:
--> 125     pd_eval(self._dag, x, self._coeffs)  #see further down
    126     temp = self._dag.value               #for an explanation
    127     pd_clean(self._dag)                  #of these 3 lines

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
    352     if pd.value is None:
--> 353         pd.eval(vars, coeffs)
    354     pd.hits += 1
    355 

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
    505 
    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507         pd_eval(self.left, vars, coeffs)
    508         pd_eval(self.right, vars, coeffs)
    509         self.value = self.left.value * self.right.value + coeffs[self.index]

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
    352     if pd.value is None:
--> 353         pd.eval(vars, coeffs)
    354     pd.hits += 1
    355 

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
    505 
    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507         pd_eval(self.left, vars, coeffs)
    508         pd_eval(self.right, vars, coeffs)
    509         self.value = self.left.value * self.right.value + coeffs[self.index]

    [... skipping similar frames: sage.rings.polynomial.polynomial_compiled.pd_eval at line 353 (13 times), sage.rings.polynomial.polynomial_compiled.abc_pd.eval at line 507 (12 times)]

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
    505 
    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507         pd_eval(self.left, vars, coeffs)
    508         pd_eval(self.right, vars, coeffs)
    509         self.value = self.left.value * self.right.value + coeffs[self.index]

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
    352     if pd.value is None:
--> 353         pd.eval(vars, coeffs)
    354     pd.hits += 1
    355 

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:509, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
    507 pd_eval(self.left, vars, coeffs)
    508 pd_eval(self.right, vars, coeffs)
--> 509 self.value = self.left.value * self.right.value + coeffs[self.index]
    510 pd_clean(self.left)
    511 pd_clean(self.right)

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:539, in sage.rings.power_series_poly.PowerSeries_poly._mul_()
    537     19*w^10 + 323*w^11 + O(w^12)
    538 """
--> 539 prec = self._mul_prec(right_r)
    540 return PowerSeries_poly(self._parent,
    541                         self.__f * (<PowerSeries_poly>right_r).__f,

File /ext/sage/9.7/src/sage/rings/power_series_ring_element.pyx:949, in sage.rings.power_series_ring_element.PowerSeries._mul_prec()
    947         prec = sp + right.valuation()
    948     else:
--> 949         prec = min(rp + self.valuation(), sp + right.valuation())
    950 # endif
    951 return prec

File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:131, in sage.rings.power_series_poly.PowerSeries_poly.valuation()
    129     +Infinity
    130 """
--> 131 if self.__f == 0:
    132     return self._prec
    133 

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/categories/map.pyx:1692, in sage.categories.map.FormalCompositeMap._call_()
   1690 """
   1691 for f in self.__list:
-> 1692     x = f._call_(x)
   1693 return x
   1694 

File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:153, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    151 argument is assumed to be bound to the codomain).
    152 """
--> 153 cpdef Element _call_(self, x):
    154     cdef Parent C = self._codomain
    155     try:

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/finite_field_givaro.py:229, in FiniteField_givaro._element_constructor_(self, e)
    211     """
    212     Return a random element of ``self``.
    213 
   (...)
    225         True
    226     """
    227     return self._cache.random_element()
--> 229 def _element_constructor_(self, e):
    230     """
    231     Coerces several data types to ``self``.
    232 
   (...)
    368         2*a4^3 + 2*a4^2 + 1
    369     """
    370     return self._cache.element_from_data(e)

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

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

[?7h[?12l[?25h[?2004lTraceback (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 [4] 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>:28
    print((p-_sage_const_1 )*(a+p*b, AS.exponent_of_different_prim())
         ^
SyntaxError: '(' was never closed

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

[?7h[?12l[?25h[?2004l1 2 [[1, 4]] 1 4
14 14
1 4 [[1, 10]] 1 10
26 26
1 5 [[1, 13]] 1 13
32 32
1 7 [[1, 19]] 1 19
44 44
1 8 [[1, 22]] 1 22
50 50
1 10 [[1, 28]] 1 28
62 62
1 11 [[1, 31]] 1 31
68 68
^C---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zz_pex.pyx:280, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.__call__()
    279 try:
--> 280     if a.parent() is not K:
    281         a = K.coerce(a)

AttributeError: 'tuple' object has no attribute 'parent'

During handling of the above exception, another exception occurred:

KeyboardInterrupt                         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>: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: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>:44, in __init__(self, C, list_of_fcts, prec)

File <string>:134, in artin_schreier_transform(power_series, prec)

File <string>:12, in new_reverse(power_series, prec)

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1831, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
   1829 if x:
   1830     raise ValueError("must not specify %s keyword and positional argument" % name)
-> 1831 a = self(kwds[name])
   1832 del kwds[name]
   1833 try:

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1852, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
   1850         x = x[0]
   1851 
-> 1852     return self.__u(*x)*(x[0]**self.__n)
   1853 
   1854 def __pari__(self):

File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:365, in sage.rings.power_series_poly.PowerSeries_poly.__call__()
    363         x[0] = a
    364         x = tuple(x)
--> 365     return self.__f(x)
    366 
    367 def _unsafe_mutate(self, i, value):

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zz_pex.pyx:283, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.__call__()
    281         a = K.coerce(a)
    282 except (TypeError, AttributeError, NotImplementedError):
--> 283     return Polynomial.__call__(self, a)
    284 
    285 _a = self._parent._modulus.ZZ_pE(list(a.polynomial()))

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:898, in sage.rings.polynomial.polynomial_element.Polynomial.__call__()
    896             return result
    897         pol._compiled = CompiledPolynomialFunction(pol.list())
--> 898     return pol._compiled.eval(a)
    899 
    900 def compose_trunc(self, Polynomial other, long n):

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:125, in sage.rings.polynomial.polynomial_compiled.CompiledPolynomialFunction.eval()
    123 cdef object temp
    124 try:
--> 125     pd_eval(self._dag, x, self._coeffs)  #see further down
    126     temp = self._dag.value               #for an explanation
    127     pd_clean(self._dag)                  #of these 3 lines

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
    352     if pd.value is None:
--> 353         pd.eval(vars, coeffs)
    354     pd.hits += 1
    355 

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
    505 
    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507         pd_eval(self.left, vars, coeffs)
    508         pd_eval(self.right, vars, coeffs)
    509         self.value = self.left.value * self.right.value + coeffs[self.index]

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
    352     if pd.value is None:
--> 353         pd.eval(vars, coeffs)
    354     pd.hits += 1
    355 

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
    505 
    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507         pd_eval(self.left, vars, coeffs)
    508         pd_eval(self.right, vars, coeffs)
    509         self.value = self.left.value * self.right.value + coeffs[self.index]

    [... skipping similar frames: sage.rings.polynomial.polynomial_compiled.pd_eval at line 353 (5 times), sage.rings.polynomial.polynomial_compiled.abc_pd.eval at line 507 (4 times)]

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
    505 
    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507         pd_eval(self.left, vars, coeffs)
    508         pd_eval(self.right, vars, coeffs)
    509         self.value = self.left.value * self.right.value + coeffs[self.index]

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
    352     if pd.value is None:
--> 353         pd.eval(vars, coeffs)
    354     pd.hits += 1
    355 

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:509, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
    507 pd_eval(self.left, vars, coeffs)
    508 pd_eval(self.right, vars, coeffs)
--> 509 self.value = self.left.value * self.right.value + coeffs[self.index]
    510 pd_clean(self.left)
    511 pd_clean(self.right)

File /ext/sage/9.7/src/sage/structure/element.pyx:1233, in sage.structure.element.Element.__add__()
   1231 # Left and right are Sage elements => use coercion model
   1232 if BOTH_ARE_ELEMENT(cl):
-> 1233     return coercion_model.bin_op(left, right, add)
   1234 
   1235 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/categories/morphism.pyx:601, in sage.categories.morphism.SetMorphism._call_()
    599         3
    600     """
--> 601     return self._function(x)
    602 
    603 cpdef Element _call_with_args(self, x, args=(), kwds={}):

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:919, in sage.rings.laurent_series_ring_element.LaurentSeries._lmul_()
    917     return type(self)(self._parent, self.__u._rmul_(c), self.__n)
    918 
--> 919 cpdef _lmul_(self, Element c):
    920     return type(self)(self._parent, self.__u._lmul_(c), self.__n)
    921 

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:920, in sage.rings.laurent_series_ring_element.LaurentSeries._lmul_()
    918 
    919     cpdef _lmul_(self, Element c):
--> 920         return type(self)(self._parent, self.__u._lmul_(c), self.__n)
    921 
    922     def __pow__(_self, r, dummy):

File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:569, in sage.rings.power_series_poly.PowerSeries_poly._lmul_()
    567         2 + 6*t^4 + O(t^120)
    568     """
--> 569     return PowerSeries_poly(self._parent, c * self.__f, self._prec, check=False)
    570 
    571 def __lshift__(PowerSeries_poly self, n):

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:1194, in sage.structure.coerce.CoercionModel.bin_op()
   1192 if action is not None:
   1193     if (<Action>action)._is_left:
-> 1194         return (<Action>action)._act_(x, y)
   1195     else:
   1196         return (<Action>action)._act_(y, x)

File /ext/sage/9.7/src/sage/structure/coerce_actions.pyx:612, in sage.structure.coerce_actions.LeftModuleAction._act_()
    610 if self.extended_base is not None:
    611     a = <ModuleElement?>self.extended_base(a)
--> 612 return (<ModuleElement>a)._rmul_(<Element>g)  # g * a
    613 
    614 

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:400, in sage.rings.polynomial.polynomial_element.Polynomial._rmul_()
    398     if not right:
    399         return self._parent.zero()
--> 400     return self * self._parent(right)
    401 
    402 def subs(self, *x, **kwds):

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/polynomial/polynomial_element.pyx:12221, in sage.rings.polynomial.polynomial_element.PolynomialBaseringInjection._call_()
  12219         Univariate Polynomial Ring in x over Integer Ring
  12220     """
> 12221     return self._new_constant_poly_(x, self._codomain)
  12222 
  12223 cpdef Element _call_with_args(self, x, args=(), kwds={}):

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:5449, in sage.rings.polynomial.polynomial_element.Polynomial._new_constant_poly()
   5447     return self.get_unsafe(0)
   5448 
-> 5449 cpdef Polynomial _new_constant_poly(self, a, Parent P):
   5450     """
   5451     Create a new constant polynomial from a in P, which MUST be an

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:5463, in sage.rings.polynomial.polynomial_element.Polynomial._new_constant_poly()
   5461     """
   5462     t = type(self)
-> 5463     return t(P, [a] if a else [], check=False)
   5464 
   5465 def is_monic(self):

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zz_pex.pyx:151, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.__init__()
    149     # not do K.coerce(e) but K(e).
    150     e = K(e)
--> 151     d = parent._modulus.ZZ_pE(list(e.polynomial()))
    152     ZZ_pEX_SetCoeff(self.x, i, d.x)
    153 return

File /ext/sage/9.7/src/sage/libs/ntl/ntl_ZZ_pEContext.pyx:149, in sage.libs.ntl.ntl_ZZ_pEContext.ntl_ZZ_pEContext_class.ZZ_pE()
    147     [4 3]
    148 """
--> 149 from .ntl_ZZ_pE import ntl_ZZ_pE
    150 return ntl_ZZ_pE(v,modulus=self)
    151 

File <frozen importlib._bootstrap>:404, in parent(self)

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

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

[?7h[?12l[?25h[?2004l1 2 [[1, 6]] 1 6
44 44
1 3 [[1, 11]] 1 11
64 64
1 4 [[1, 16]] 1 16
84 84
1 6 [[1, 26]] 1 26
124 124
1 7 [[1, 31]] 1 31
144 144
no  36 -th root; divide by 2
---------------------------------------------------------------------------
ValueError                                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>: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: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>:44, in __init__(self, C, list_of_fcts, prec)

ValueError: not enough values to unpack (expected 4, got 2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 5^2 with the equations:
z0^5 - z0 = x
z1^5 - z1 = x^7

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 5^2 with the equations:
z0^5 - z0 = x
z1^5 - z1 = x^7

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.magical_element()[?7h[?12l[?25h[?25l[?7lz[0]*AS.z[1][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0]*AS.z[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[]^*AS.z[1][?7h[?12l[?25h[?25l[?7l(*AS.z[1][?7h[?12l[?25h[?25l[?7l()*AS.z[1][?7h[?12l[?25h[?25l[?7l()p*AS.z[1][?7h[?12l[?25h[?25l[?7l-*AS.z[1][?7h[?12l[?25h[?25l[?7l*AS.z[1][?7h[?12l[?25h[?25l[?7l()*AS.z[1][?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)*AS.z[1][?7h[?12l[?25h[?25l[?7l-)*AS.z[1][?7h[?12l[?25h[?25l[?7l1)*AS.z[1][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lno  8 -th root; divide by 2
---------------------------------------------------------------------------
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>: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: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>:37, in <module>

File <string>:44, in __init__(self, C, list_of_fcts, prec)

ValueError: not enough values to unpack (expected 4, got 2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 5 with the equations:
z0^5 - z0 = x^3
z1^5 - z1 = 3*x^4

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.magical_element()[?7h[?12l[?25h[?25l[?7lz[0]*AS.z[1][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]*AS.z[1][?7h[?12l[?25h[?25l[?7l[]^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.z[0]^(p-1)*AS.z[1]^(p-1)

[?7h[?12l[?25h[?2004l[?7hz0^4*z1^4
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[0]^(p-1)*AS.z[1]^(p-1)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.z[0]^(p-1)*AS.z[1]^(p-1).valuation()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [13], in <cell line: 1>()
----> 1 AS.z[Integer(0)]**(p-Integer(1))*AS.z[Integer(1)]**(p-Integer(1)).valuation()

TypeError: Integer.valuation() takes exactly one argument (0 given)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[0]^(p-1)*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[]()[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[]()[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]^(p-1)*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()).valuation()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]^(p-1)*AS.z[1]^(p-1)).valuation()

[?7h[?12l[?25h[?2004l[?7h-140
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l4*Q[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[0]^(p-1)*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lmagical_element()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lcal_element()[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element()

[?7h[?12l[?25h[?2004l[?7h[z0^4*z1^4 + 2*x^3*z0^3*z1 - 2*x^2*z0^2*z1^3 + x^5*z0 - x^4*z1^2]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lonent_of_different_prim()[?7h[?12l[?25h[?25l[?7lsage: AS.exponent_of_different_prim()

[?7h[?12l[?25h[?2004l[?7h92
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[0]^(p-1)*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]^3*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lA)[?7h[?12l[?25h[?25l[?7lS)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lz)[?7h[?12l[?25h[?25l[?7l[)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]^3*AS.z[1]).valuation()

[?7h[?12l[?25h[?2004l[?7h-65
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]^3*AS.z[1]).valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l^).valuation()[?7h[?12l[?25h[?25l[?7l3).valuation()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*AS.z[1]^3).valuation()[?7h[?12l[?25h[?25l[?7l2*AS.z[1]^3).valuation()[?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]^2*AS.z[1]^3).valuation()

[?7h[?12l[?25h[?2004l[?7h-90
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lno  18 -th root; divide by 3
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [19], 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: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>:37, in <module>

File <string>:44, in __init__(self, C, list_of_fcts, prec)

ValueError: not enough values to unpack (expected 4, got 2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l\[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l\[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(AS.z[0]^2*AS.z[1]^3).valuation()[?7h[?12l[?25h[?25l[?7l3).valuation()[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim[?7h[?12l[?25h[?25l[?7lsage: AS.exponent_of_different_prim()

[?7h[?12l[?25h[?2004l[?7h132
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lmagical_element()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lcal_element()[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element()

[?7h[?12l[?25h[?2004l[?7h[x^6*z0^2 - x^3*z0^3*z1^2 + z0^4*z1^4 - 2*x^6*z1 + 2*x^3*z0*z1^3]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]^2*AS.z[1]^3).valuation()[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.z[0]^2*AS.z[1]^3).valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*AS.z[1]^3).valuation()[?7h[?12l[?25h[?25l[?7l3*AS.z[1]^3).valuation()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l2).valuation()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]^3*AS.z[1]^2).valuation()

[?7h[?12l[?25h[?2004l[?7h-105
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]^3*AS.z[1]^2).valuation()[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7lexponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.magical_element()[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element()

[?7h[?12l[?25h[?2004l[?7h[]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7lh)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7lh)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7ll)[?7h[?12l[?25h[?25l[?7ld)[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element(threshold=20)

[?7h[?12l[?25h[?2004l[?7h[x^8 + x^6*z0*z1 + x^4*z0^2*z1^2 + x^2*z0^3*z1^3 + z0^4*z1^4]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element(threshold=20)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(AS.z[0]^3*AS.z[1]^2).valuation()[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7lexponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lsage: AS.exponent_of_different_prim()

[?7h[?12l[?25h[?2004l[?7h152
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lmagical_element(threshold=20)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(AS.z[0]^3*AS.z[1]^2).valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l3).valuation()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]^3*AS.z[1]^3).valuation()

[?7h[?12l[?25h[?2004l[?7h-150
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lmagical_element(threshold=20)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lgical_element(threshold=20)[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element(threshold=20)

[?7h[?12l[?25h[?2004l[?7h[x^8 + x^4*z0*z1 + z0^2*z1^2]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element(threshold=20)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.magical_element(threshold=20)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.magical_element(threshold=20)[?7h[?12l[?25h[?25l[?7lexponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lonent_of_different_prim()[?7h[?12l[?25h[?25l[?7lsage: AS.exponent_of_different_prim()

[?7h[?12l[?25h[?2004l[?7h52
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[0]^(p-1)*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0]^(p-1)*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()).valuation()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]^(p-1)*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[]()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l[]*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(().valuation()[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l().valuation()[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]*AS.z[1]).valuation()

[?7h[?12l[?25h[?2004l[?7h-36
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(AS.z[0]*AS.z[1]).valuation()[?7h[?12l[?25h[?25l[?7lAS.exponent_of_differen_prim()[?7h[?12l[?25h[?25l[?7lmagical_element(threshold=20)[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element(threshold=20)

[?7h[?12l[?25h[?2004l[?7h[x^6*z0 + x^5*z1 + z0^2*z1^2]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

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

[?7h[?12l[?25h[?2004l[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element(threshold=20)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_differentias_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[(1) * dx,
 (x^3*z0 + z1) * dx,
 (z0) * dx,
 (x) * dx,
 (x*z0) * dx,
 (x^2) * dx,
 (x^2*z0) * dx,
 (x^3) * dx,
 (x^4) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^3
z1^2 - z1 = x^9

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lus()[?7h[?12l[?25h[?25l[?7lsage: AS.genus()

[?7h[?12l[?25h[?2004l[?7h3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[(1) * dx, ((a + 1)*z0 + z1) * dx, (x) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis()

[?7h[?12l[?25h[?2004l/ext/sage/9.7/src/sage/rings/polynomial/polynomial_singular_interface.py:372:
********************************************************************************
Denominators of fraction field elements are sometimes dropped without warning.
This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696.
********************************************************************************
[?7h[( (1) * dx, 0 ),
 ( ((a + 1)*z0 + z1) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( (0) * dx, z1/x ),
 ( (a*x*z0 + x*z1) * dx, z0*z1/x ),
 ( (a*z0 + z1) * dx, z0*z1/x^2 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1/(a+1)[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l(+1)[?7h[?12l[?25h[?25l[?7lsage: 1/(a+1)

[?7h[?12l[?25h[?2004l[?7ha
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1/(a+1)[?7h[?12l[?25h[?25l[?7lsage: 1/(a+1)

[?7h[?12l[?25h[?2004l[?7ha
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1/(a+1)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lno  3 -th root; divide by a^2 + a + 1
---------------------------------------------------------------------------
ValueError                                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>: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: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>:14, in <module>

File <string>:44, in __init__(self, C, list_of_fcts, prec)

ValueError: not enough values to unpack (expected 4, got 2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis()

[?7h[?12l[?25h[?2004l/ext/sage/9.7/src/sage/rings/polynomial/polynomial_singular_interface.py:372:
********************************************************************************
Denominators of fraction field elements are sometimes dropped without warning.
This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696.
********************************************************************************
[?7h[( (1) * dx, 0 ),
 ( ((a^2 + a)*z0 + z1) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( (0) * dx, z1/x ),
 ( (a*x*z0 + x*z1) * dx, z0*z1/x ),
 ( (a*z0 + z1) * dx, z0*z1/x^2 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1/(a+1)[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l^3 + a^12 + a^11 + a^9 + a^8 + a^4 + a^3 + a)[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: 1/(a^2+a)

[?7h[?12l[?25h[?2004l[?7ha + 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l^3[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: a^2

[?7h[?12l[?25h[?2004l[?7ha^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la^2[?7h[?12l[?25h[?25l[?7l1/(a^2+a)[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: 1/(a^2+a)^2

[?7h[?12l[?25h[?2004l[?7ha^2 + 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1/(a^2+a)^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(a^2+a)^2[?7h[?12l[?25h[?25l[?7l(a^2+a)^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (a^2+a)^2

[?7h[?12l[?25h[?2004l[?7ha
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: AS.dx

[?7h[?12l[?25h[?2004l[?7h(1) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.dx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lty[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.dx.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h(a + 1)*t^4 + a*t^16 + t^22 + a^2*t^52 + t^64 + (a^2 + 1)*t^70 + (a^2 + a + 1)*t^76 + (a + 1)*t^88 + a^2*t^94 + (a^2 + 1)*t^196 + (a^2 + a)*t^208 + (a + 1)*t^214 + (a^2 + a + 1)*t^244 + (a + 1)*t^256 + a^2*t^262 + a*t^268 + (a^2 + 1)*t^280 + (a^2 + a + 1)*t^286 + (a^2 + a)*t^292 + O(t^295)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.dx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 2^3 with the equations:
z0^2 - z0 = x^3
z1^2 - z1 = a*x^3

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.dx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7l.dx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: AS.x.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ha*t^-4 + t^2 + (a + 1)*t^5 + (a^2 + 1)*t^8 + a*t^17 + (a^2 + a)*t^20 + t^23 + t^44 + (a^2 + 1)*t^50 + a^2*t^53 + (a^2 + a + 1)*t^56 + t^65 + (a^2 + 1)*t^71 + a^2*t^74 + (a^2 + a + 1)*t^77 + a*t^80 + (a + 1)*t^89 + (a^2 + 1)*t^92 + a^2*t^95 + (a^2 + a)*t^188 + (a + 1)*t^194 + (a^2 + 1)*t^197 + a^2*t^200 + (a^2 + a)*t^209 + t^212 + (a + 1)*t^215 + (a + 1)*t^236 + a^2*t^242 + (a^2 + a + 1)*t^245 + a*t^248 + (a + 1)*t^257 + a^2*t^263 + (a^2 + a + 1)*t^266 + a*t^269 + (a^2 + a)*t^272 + (a^2 + 1)*t^281 + (a^2 + a + 1)*t^287 + a*t^290 + (a^2 + a)*t^293 + O(t^296)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.x.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexponet_fdifferent_prim()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lonent_of_different_prim()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.exponent_of_differen()

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

AttributeError: 'as_cover' object has no attribute 'exponent_of_differen'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_differen()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lt()[?7h[?12l[?25h[?25l[?7lsage: AS.exponent_of_different()

[?7h[?12l[?25h[?2004l[?7h12
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lS.exponent_of_different()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[0]^(p-1)*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.z[0].valuation()

[?7h[?12l[?25h[?2004l[?7h-6
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[0].valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l].valuation()[?7h[?12l[?25h[?25l[?7l1].valuation()[?7h[?12l[?25h[?25l[?7lsage: AS.z[1].valuation()

[?7h[?12l[?25h[?2004l[?7h-6
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[?7h[?12l[?25h[?2004l[?7hz1/x
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[?7h[?12l[?25h[?2004l[?7h((a*x^3 + z1)/x^2) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[1]/AS.x[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 2^3 with the equations:
z0^2 - z0 = x^3
z1^2 - z1 = a*x^3

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[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[1]/AS.x).diffn().valuation()[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7l(AS.z[1]/AS.x).diffn().valuation()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l]/AS.x).difn([?7h[?12l[?25h[?25l[?7l0]/AS.x).difn([?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[]*/AS.x).difn([?7h[?12l[?25h[?25l[?7lA/AS.x).difn([?7h[?12l[?25h[?25l[?7lS/AS.x).difn([?7h[?12l[?25h[?25l[?7l./AS.x).difn([?7h[?12l[?25h[?25l[?7lz/AS.x).difn([?7h[?12l[?25h[?25l[?7l[/AS.x).difn([?7h[?12l[?25h[?25l[?7l1/AS.x).difn([?7h[?12l[?25h[?25l[?7l[]/AS.x).difn([?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)([?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]*AS.z[1]/AS.x).diffn()

[?7h[?12l[?25h[?2004l[?7h((a*x^3*z0 + x^3*z1 + z0*z1)/x^2) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]*AS.z[1]/AS.x).diffn()[?7h[?12l[?25h[?25l[?7l1/x).diffn(valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7l(AS.z[1]/AS.x).diffn().valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l0*z[1]/AS.xdiffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.x).difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()^.difn()[?7h[?12l[?25h[?25l[?7l2.difn()[?7h[?12l[?25h[?25l[?7l(2).difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]*AS.z[1]/(AS.x)^2).diffn()

[?7h[?12l[?25h[?2004l[?7h(a*z0 + z1) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7l, B = group_action_matrices_dR(AS); magmathis(A, B)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l = group_action_matrices_dR(AS); magmathis(A, B)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l(); magmathis(A, B)[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_dR(AS)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lsage: A

[?7h[?12l[?25h[?2004l[?7h[      1 a^2 + a       0       0       0       a]
[      0       1       0       0       0       0]
[      0       0       1       0       a       0]
[      0       0       0       1       1       0]
[      0       0       0       0       1       0]
[      0       0       0       0       0       1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lenumerate(lll)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7las[?7h[?12l[?25h[?25l[?7las_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lAx)[?7h[?12l[?25h[?25l[?7lSx)[?7h[?12l[?25h[?25l[?7l.x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[1]/AS.x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: e1 = as_cech(AS, 0*AS.dx, (AS.z[1]/AS.x)^2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le1 = as_cech(AS, 0*AS.dx, (AS.z[1]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: e1

[?7h[?12l[?25h[?2004l[?7h( (0) * dx, z1^2/x^2 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: e1.coordinates()

[?7h[?12l[?25h[?2004l[?7h(a, 0, 0, 0, 0, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le1.coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = as_cech(AS, 0*AS.dx, (AS.z[1]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l0]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]*/AS.x)^2)[?7h[?12l[?25h[?25l[?7lA/AS.x)^2)[?7h[?12l[?25h[?25l[?7lS/AS.x)^2)[?7h[?12l[?25h[?25l[?7l./AS.x)^2)[?7h[?12l[?25h[?25l[?7lz/AS.x)^2)[?7h[?12l[?25h[?25l[?7lp/AS.x)^2)[?7h[?12l[?25h[?25l[?7l[/AS.x)^2)[?7h[?12l[?25h[?25l[?7l/AS.x)^2)[?7h[?12l[?25h[?25l[?7l/AS.x)^2)[?7h[?12l[?25h[?25l[?7l[/AS.x)^2)[?7h[?12l[?25h[?25l[?7l1/AS.x)^2)[?7h[?12l[?25h[?25l[?7l[]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: e1 = as_cech(AS, 0*AS.dx, (AS.z[0]*AS.z[1]/AS.x)^2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le1 = as_cech(AS, 0*AS.dx, (AS.z[0]*AS.z[1]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = as_cech(AS, 0*AS.dx, (AS.z[1]/AS.x)^2)[?7h[?12l[?25h[?25l[?7lsage: e1 = as_cech(AS, 0*AS.dx, (AS.z[1]/AS.x)^2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le1 = as_cech(AS, 0*AS.dx, (AS.z[1]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l0*z[1]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = as_cech(AS, 0*AS.dx, (AS.z[0]*AS.z[1]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l2 = as_cech(AS, 0*AS.dx, (AS.z[0]*AS.z[1]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: e2 = as_cech(AS, 0*AS.dx, (AS.z[0]*AS.z[1]/AS.x)^2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le2 = as_cech(AS, 0*AS.dx, (AS.z[0]*AS.z[1]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ldinates[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: e2.coordinates()

[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, 0, 0, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le2.coordinates()[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7las[?7h[?12l[?25h[?25l[?7las_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7las[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le2.coordinates()[?7h[?12l[?25h[?25l[?7l = as_cech(AS, 0*AS.dx, (AS.z[0]*AS.z[1]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l^)^2)[?7h[?12l[?25h[?25l[?7l2)^2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = as_cech(AS, 0*AS.dx, (AS.z[0]*AS.z[1]/AS.x^2)^2)[?7h[?12l[?25h[?25l[?7l3 = as_cech(AS, 0*AS.dx, (AS.z[0]*AS.z[1]/AS.x^2)^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: e3 = as_cech(AS, 0*AS.dx, (AS.z[0]*AS.z[1]/AS.x^2)^2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le3 = as_cech(AS, 0*AS.dx, (AS.z[0]*AS.z[1]/AS.x^2)^2)[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: e3.coordinates()

[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, a^2 + a + 1, 0, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la^2 + a + 1[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a^2 + a + 1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: (a^2 + a + 1)^2

[?7h[?12l[?25h[?2004l[?7ha + 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a^2 + a + 1)^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1(a^2 + a + 1)^2[?7h[?12l[?25h[?25l[?7l/(a^2 + a + 1)^2[?7h[?12l[?25h[?25l[?7lsage: 1/(a^2 + a + 1)^2

[?7h[?12l[?25h[?2004l[?7ha^2 + a
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1/(a^2 + a + 1)^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(a^2 + a + 1)^2[?7h[?12l[?25h[?25l[?7l(a^2 + a + 1)^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.z[1]/AS.x[?7h[?12l[?25h[?25l[?7ldx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7le_rham_basis()[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( ((a^2 + a)*z0 + z1) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( (0) * dx, z1/x ),
 ( (a*x*z0 + x*z1) * dx, z0*z1/x ),
 ( (a*z0 + z1) * dx, z0*z1/x^2 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmatrix(v0).transpose()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lgmathis(A, B, text=True)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lathis(A, B, text=True)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lTru)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l")[?7h[?12l[?25h[?25l[?7l")[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lG")[?7h[?12l[?25h[?25l[?7lF")[?7h[?12l[?25h[?25l[?7l")[?7h[?12l[?25h[?25l[?7l")[?7h[?12l[?25h[?25l[?7lF")[?7h[?12l[?25h[?25l[?7l,")[?7h[?12l[?25h[?25l[?7la")[?7h[?12l[?25h[?25l[?7l.")[?7h[?12l[?25h[?25l[?7l")[?7h[?12l[?25h[?25l[?7l")[?7h[?12l[?25h[?25l[?7l")[?7h[?12l[?25h[?25l[?7l<")[?7h[?12l[?25h[?25l[?7la")[?7h[?12l[?25h[?25l[?7l>?")[?7h[?12l[?25h[?25l[?7l")[?7h[?12l[?25h[?25l[?7l ")[?7h[?12l[?25h[?25l[?7l:")[?7h[?12l[?25h[?25l[?7l=")[?7h[?12l[?25h[?25l[?7l ")[?7h[?12l[?25h[?25l[?7lG")[?7h[?12l[?25h[?25l[?7lF")[?7h[?12l[?25h[?25l[?7l(")[?7h[?12l[?25h[?25l[?7l4")[?7h[?12l[?25h[?25l[?7l()")[?7h[?12l[?25h[?25l[?7l();")[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B, prefix="F<a> := GF(4);")

[?7h[?12l[?25h[?2004l[?7h>> F<a> := GF(4);A := MatrixAlgebra<GF(8),6|[1, a^2 + a, 0, 0, 0, a, 0, 1, 0,
                                   ^
Runtime error in MatrixAlgebra< ... >: Rhs argument 1 is invalid for this constructor
>> RModule(RSpace(GF(8),6), A);IndecomposableSummands(M);
                            ^
User error: Identifier 'A' has not been declared or assigned
>> RModule(RSpace(GF(8),6), A);IndecomposableSummands(M);
                                                      ^
User error: Identifier 'M' has not been declared or assigned
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 2^3 with the equations:
z0^2 - z0 = x^3
z1^2 - z1 = a*x^3

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lmagmathis(A, B, prefix="F<a> := GF(4);")[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lmagmathis(A, B, prefix="F<a> := GF(4);")[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l);")[?7h[?12l[?25h[?25l[?7l8);")[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B, prefix="F<a> := GF(8);")

[?7h[?12l[?25h[?2004l[?7h[
RModule of dimension 3 over GF(2^3),
RModule of dimension 3 over GF(2^3)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lsage: A

[?7h[?12l[?25h[?2004l[?7h[      1 a^2 + a       0       0       0       a]
[      0       1       0       0       0       0]
[      0       0       1       0       a       0]
[      0       0       0       1       1       0]
[      0       0       0       0       1       0]
[      0       0       0       0       0       1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lsage: B

[?7h[?12l[?25h[?2004l[?7h[    1     1     0     0     0     1]
[    0     1     0     0     0     0]
[    0     0     1     0     1     0]
[    0     0     0     1 a + 1     0]
[    0     0     0     0     1     0]
[    0     0     0     0     0     1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lmagmathis(A, B, prefix="F<a> := GF(8);")[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7lt=)[?7h[?12l[?25h[?25l[?7lT)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7lTrue)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B, prefix="F<a> := GF(8);", text=True)

[?7h[?12l[?25h[?2004l[?7h'F<a> := GF(8);A := MatrixAlgebra<GF(8),6|[1, a^2 + a, 0, 0, 0, a, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, a, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1],[1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, a + 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),6), A);IndecomposableSummands(M);'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l1 = matrix(ZZ, [[1, 3], [3, 4]])[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l, B = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1, B = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1 = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7lh(AS)[?7h[?12l[?25h[?25l[?7lo(AS)[?7h[?12l[?25h[?25l[?7ll(AS)[?7h[?12l[?25h[?25l[?7lo(AS)[?7h[?12l[?25h[?25l[?7lsage: A1, B1 = group_action_matrices_holo(AS)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lmagmathis(A, B, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B, prefix="F<a> := GF(8);", text=True)

[?7h[?12l[?25h[?2004l[?7h'F<a> := GF(8);A := MatrixAlgebra<GF(8),6|[1, a^2 + a, 0, 0, 0, a, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, a, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1],[1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, a + 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),6), A);IndecomposableSummands(M);'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lTru)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B, prefix="F<a> := GF(8);")

[?7h[?12l[?25h[?2004l[?7h[
RModule of dimension 3 over GF(2^3),
RModule of dimension 3 over GF(2^3)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B, prefix="F<a> := GF(8);")[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1, B, prefix="F<a> := GF(8);")[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1, prefix="F<a> := GF(8);")[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: magmathis(A1, B1, prefix="F<a> := GF(8);")

[?7h[?12l[?25h[?2004l[?7h[
RModule of dimension 1 over GF(2^3),
RModule of dimension 2 over GF(2^3)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);")[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lxt)[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7lT)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7lTrue)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A1, B1, prefix="F<a> := GF(8);", text=True)

[?7h[?12l[?25h[?2004l[?7h'F<a> := GF(8);A := MatrixAlgebra<GF(8),3|[1, a^2 + a, 0, 0, 1, 0, 0, 0, 1],[1, 1, 0, 0, 1, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),3), A);IndecomposableSummands(M);'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l, B, prefix="F<a> := GF(8);")[?7h[?12l[?25h[?25l[?7l, text=True)[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lsage: A1, B1 = group_action_matrices_holo(AS)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A1, B1, prefix="F<a> := GF(8);", text=True)

[?7h[?12l[?25h[?2004l[?7h'F<a> := GF(8);A := MatrixAlgebra<GF(8),3|[1, a^2 + a + 1, 0, 0, 1, 0, 0, 0, 1],[1, 1, 0, 0, 1, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),3), A);IndecomposableSummands(M);'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7ld(AS)[?7h[?12l[?25h[?25l[?7lR(AS)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A1, B1 = group_action_matrices_dR(AS)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A1, B1, prefix="F<a> := GF(8);", text=True)

[?7h[?12l[?25h[?2004l[?7h'F<a> := GF(8);A := MatrixAlgebra<GF(8),6|[1, a^2 + a + 1, 0, 0, 0, a + 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, a + 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1],[1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, a^2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),6), A);IndecomposableSummands(M);'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lsage: A1, B1 = group_action_matrices_dR(AS)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A1, B1, prefix="F<a> := GF(8);", text=True)

[?7h[?12l[?25h[?2004l[?7h'F<a> := GF(8);A := MatrixAlgebra<GF(8),6|[1, a^2 + a, 0, 0, 0, a, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, a, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1],[1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, a + 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),6), A);IndecomposableSummands(M);'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7lh(AS)[?7h[?12l[?25h[?25l[?7lo(AS)[?7h[?12l[?25h[?25l[?7ll(AS)[?7h[?12l[?25h[?25l[?7lo(AS)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A1, B1 = group_action_matrices_holo(AS)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A1, B1, prefix="F<a> := GF(8);", text=True)

[?7h[?12l[?25h[?2004l[?7h'F<a> := GF(8);A := MatrixAlgebra<GF(8),3|[1, a^2 + a, 0, 0, 1, 0, 0, 0, 1],[1, 1, 0, 0, 1, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),3), A);IndecomposableSummands(M);'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lsage: A1, B1 = group_action_matrices_holo(AS)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A1, B1, prefix="F<a> := GF(8);", text=True)

[?7h[?12l[?25h[?2004l[?7h'F<a> := GF(8);A := MatrixAlgebra<GF(8),3|[1, a^2 + a + 1, 0, 0, 1, 0, 0, 0, 1],[1, 1, 0, 0, 1, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),3), A);IndecomposableSummands(M);'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
 ( ((a^2 + a)*z0 + z1) * dx, 0 ),
 ( (x) * dx, 0 ),
 ( (0) * dx, z1/x ),
 ( (a*x*z0 + x*z1) * dx, z0*z1/x ),
 ( (a*z0 + z1) * dx, z0*z1/x^2 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le3.coordinates()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lrham_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: eta6 = AS.de_rham_basis()[5]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta6 = AS.de_rham_basis()[5][?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: eta6.group_action([1, 0]).coordinates()

[?7h[?12l[?25h[?2004l[?7h(a, 0, 0, 0, 0, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta6.group_action([1, 0]).coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 0]).cordinates()[?7h[?12l[?25h[?25l[?7l0, 0]).cordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]).cordinates()[?7h[?12l[?25h[?25l[?7l1]).cordinates()[?7h[?12l[?25h[?25l[?7lsage: eta6.group_action([0, 1]).coordinates()

[?7h[?12l[?25h[?2004l[?7h(1, 0, 0, 0, 0, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[
RModule M of dimension 2 over GF(2^2)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lF<a> := GF(4);A := MatrixAlgebra<GF(4),2|[1, 1, 0, 1],[1, a, 0, 1]>;M := RModule(RSpace(GF(4),2), A);IndecomposableSummands(M);
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lF<a> := GF(4);A := MatrixAlgebra<GF(4),2|[1, 0, 1, 1],[1, 0, a, 1]>;M := RModule(RSpace(GF(4),2), A);IndecomposableSummands(M);
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l/ext/sage/9.7/src/sage/rings/polynomial/polynomial_singular_interface.py:372:
********************************************************************************
Denominators of fraction field elements are sometimes dropped without warning.
This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696.
********************************************************************************
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7l, B = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l(); magmathis(A, B)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lagmathis(A, B)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l")[?7h[?12l[?25h[?25l[?7l")[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lF")[?7h[?12l[?25h[?25l[?7l<")[?7h[?12l[?25h[?25l[?7l>")[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la>")[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l:")[?7h[?12l[?25h[?25l[?7l=")[?7h[?12l[?25h[?25l[?7lG")[?7h[?12l[?25h[?25l[?7lF")[?7h[?12l[?25h[?25l[?7l(")[?7h[?12l[?25h[?25l[?7l4")[?7h[?12l[?25h[?25l[?7l()")[?7h[?12l[?25h[?25l[?7l();")[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l);")[?7h[?12l[?25h[?25l[?7l8);")[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7let6.group_action([0, 1]).coordinates()[?7h[?12l[?25h[?25l[?7llod('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lF<a> := GF(8);A := MatrixAlgebra<GF(8),3|[1, a^2 + a, 0, 0, 1, 0, 0, 0, 1],[1, 1, 0, 0, 1, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),3), A);IndecomposableSummands(M);
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la^2[?7h[?12l[?25h[?25l[?7lsage: a

[?7h[?12l[?25h[?2004l[?7ha
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a.square_root()

[?7h[?12l[?25h[?2004l[?7ha^2 + a
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a^2 + a + 1)^2[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+a)^2[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l)^2[?7h[?12l[?25h[?25l[?7lsage: (a^2+a)^2

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

[?7h[?12l[?25h[?2004lF<a> := GF(8);A := MatrixAlgebra<GF(8),3|[1, a^2 + a, 0, 0, 1, 0, 0, 0, 1],[1, 1, 0, 0, 1, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),3), A);IndecomposableSummands(M);
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lF<a> := GF(8);A := MatrixAlgebra<GF(8),3|[1, a^2 + a, 0, 0, 1, 0, 0, 0, 1],[1, 1, 0, 0, 1, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),3), A);IndecomposableSummands(M);
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lF<a> := GF(8);A := MatrixAlgebra<GF(8),3|[1, a^2 + a, 0, 0, 1, 0, 0, 0, 1],[1, 1, 0, 0, 1, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),3), A);IndecomposableSummands(M);
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lF<a> := GF(4);A := MatrixAlgebra<GF(8),2|[1, 1, 0, 1],[1, a, 0, 1]>;M := RModule(RSpace(GF(8),2), A);IndecomposableSummands(M);
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lF<a> := GF(4);A := MatrixAlgebra<GF(8),2|[1, 0, 1, 1],[1, 0, a^2 + 1, 1]>;M := RModule(RSpace(GF(8),2), A);IndecomposableSummands(M);
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lF<a> := GF(8);A := MatrixAlgebra<GF(8),2|[1, 1, 0, 1],[1, a^2 + 1, 0, 1]>;M := RModule(RSpace(GF(8),2), A);IndecomposableSummands(M);
F<a> := GF(8);A := MatrixAlgebra<GF(8),2|[1, 0, 1, 1],[1, 0, a^2 + 1, 1]>;M := RModule(RSpace(GF(8),2), A);IndecomposableSummands(M);
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lF<a> := GF(8);A := MatrixAlgebra<GF(8),2|[1, 1, 0, 1],[1, a, 0, 1]>;M := RModule(RSpace(GF(8),2), A);IndecomposableSummands(M);
F<a> := GF(8);A := MatrixAlgebra<GF(8),2|[1, 0, 1, 1],[1, 0, a, 1]>;M := RModule(RSpace(GF(8),2), A);IndecomposableSummands(M);
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l/ext/sage/9.7/src/sage/rings/polynomial/polynomial_singular_interface.py:372:
********************************************************************************
Denominators of fraction field elements are sometimes dropped without warning.
This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696.
********************************************************************************
F<a> := GF(8);A := MatrixAlgebra<GF(8),3|[1, a^2 + a, 0, 0, 1, 0, 0, 0, 1],[1, 1, 0, 0, 1, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),3), A);IndecomposableSummands(M);
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l{
[  1]
}
{
[  1 a^4]
[  0   1],
[  1   1]
[  0   1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l/ext/sage/9.7/src/sage/rings/polynomial/polynomial_singular_interface.py:372:
********************************************************************************
Denominators of fraction field elements are sometimes dropped without warning.
This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696.
********************************************************************************
{
[  1]
}
{
[  1 a^4]
[  0   1],
[  1   1]
[  0   1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l{
[1]
}
{
[1 0 1 0]
[0 1 0 0]
[0 0 1 0]
[0 1 0 1],
[1 1 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[
RModule of dimension 1 over GF(2),
RModule of dimension 4 over GF(2)
]
{
[1]
}
{
[1 0 1 0]
[0 1 0 0]
[0 0 1 0]
[0 1 0 1],
[1 1 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 1 1]
[0 1 0]
[0 0 1]
}
{
[1 0 1]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lno  7 -th root; divide by a
---------------------------------------------------------------------------
ValueError                                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>: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: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>:15, in <module>

File <string>:44, in __init__(self, C, list_of_fcts, prec)

ValueError: not enough values to unpack (expected 4, got 2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lno  7 -th root; divide by a + 1
---------------------------------------------------------------------------
ValueError                                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>: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: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>:15, in <module>

File <string>:44, in __init__(self, C, list_of_fcts, prec)

ValueError: not enough values to unpack (expected 4, got 2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lno  7 -th root; divide by a + 1
---------------------------------------------------------------------------
ValueError                                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>: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: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>:15, in <module>

File <string>:44, in __init__(self, C, list_of_fcts, prec)

ValueError: not enough values to unpack (expected 4, got 2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lno  7 -th root; divide by a + 1
---------------------------------------------------------------------------
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>: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: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>:15, in <module>

File <string>:44, in __init__(self, C, list_of_fcts, prec)

ValueError: not enough values to unpack (expected 4, got 2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lno  7 -th root; divide by a^2
---------------------------------------------------------------------------
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>: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: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>:15, in <module>

File <string>:44, in __init__(self, C, list_of_fcts, prec)

ValueError: not enough values to unpack (expected 4, got 2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lno  7 -th root; divide by a^2 + a
---------------------------------------------------------------------------
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>: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: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>:15, in <module>

File <string>:44, in __init__(self, C, list_of_fcts, prec)

ValueError: not enough values to unpack (expected 4, got 2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[
RModule of dimension 2 over GF(2^3),
RModule of dimension 2 over GF(2^3),
RModule of dimension 2 over GF(2^3),
RModule of dimension 2 over GF(2^3),
RModule of dimension 3 over GF(2^3),
RModule of dimension 3 over GF(2^3)
]
{
[  1   0]
[a^2   1],
[  1   0]
[  0   1]
}
{
[  1   0]
[a^6   1],
[  1   0]
[  0   1]
}
{
[  1   0]
[a^2   1],
[  1   0]
[  0   1]
}
{
[  1   0]
[a^6   1],
[  1   0]
[  0   1]
}
{
[  1 a^2   1]
[  0   1   0]
[  0   0   1],
[  1   1   0]
[  0   1   0]
[  0   0   1]
}
{
[  1   0 a^5]
[  0   1 a^6]
[  0   0   1],
[  1   0 a^4]
[  0   1 a^4]
[  0   0   1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.square_root()[?7h[?12l[?25h[?25l[?7lsage: a

[?7h[?12l[?25h[?2004l[?7ha
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lmin[?7h[?12l[?25h[?25l[?7lmini[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: minimal_polynomial(a)

[?7h[?12l[?25h[?2004l[?7hx^3 + x + 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lminimal_polynomial(a)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(a^2+a)^2[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[
RModule of dimension 2 over GF(2^4),
RModule of dimension 2 over GF(2^4),
RModule of dimension 2 over GF(2^4),
RModule of dimension 2 over GF(2^4),
RModule of dimension 3 over GF(2^4),
RModule of dimension 3 over GF(2^4)
]
{
[   1    0]
[   0    1],
[   1    0]
[   a    1]
}
{
[   1    0]
[   0    1],
[   1    0]
[   1    1]
}
{
[   1  a^2]
[   0    1],
[   1    0]
[   0    1]
}
{
[   1    0]
[a^14    1],
[   1    0]
[   0    1]
}
{
[   1    1    0]
[   0    1    0]
[   0    0    1],
[   1  a^5    1]
[   0    1    0]
[   0    0    1]
}
{
[   1    0 a^12]
[   0    1    0]
[   0    0    1],
[   1    0    a]
[   0    1 a^14]
[   0    0    1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ljumps[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lsage: AS.jumps

[?7h[?12l[?25h[?2004l[?7h[[3, 11]]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.jumps[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lraification_jumps()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lmification_jumps()[?7h[?12l[?25h[?25l[?7lsage: AS.ramification_jumps()

[?7h[?12l[?25h[?2004l[?7h[3, 11]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l>> F<a> := GF(16);A := MatrixAlgebra<GF(8),12|[1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0
                                    ^
Runtime error in MatrixAlgebra< ... >: Rhs argument 1 is invalid for this constructor
>> ;M := RModule(RSpace(GF(8),12), A);L := IndecomposableSummands(M); L;for i
                                   ^
User error: Identifier 'A' has not been declared or assigned
>> ;M := RModule(RSpace(GF(8),12), A);L := IndecomposableSummands(M); L;for i
                                                                  ^
User error: Identifier 'M' has not been declared or assigned
>> ;M := RModule(RSpace(GF(8),12), A);L := IndecomposableSummands(M); L;for i
                                                                      ^
User error: Identifier 'L' has not been declared or assigned
>> ummands(M); L;for i in [1 .. #L] do print(Generators(Action(L[i]))); end fo
                                 ^
User error: Identifier 'L' has not been declared or assigned
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[
RModule of dimension 3 over GF(2^3),
RModule of dimension 3 over GF(2^3),
RModule of dimension 3 over GF(2^3),
RModule of dimension 3 over GF(2^3)
]
{
[  1   0 a^5]
[  0   1 a^4]
[  0   0   1],
[  1   0 a^3]
[  0   1 a^5]
[  0   0   1]
}
{
[  1   0 a^3]
[  0   1 a^2]
[  0   0   1],
[  1   0   1]
[  0   1   a]
[  0   0   1]
}
{
[  1   0   1]
[  0   1   0]
[  0   0   1],
[  1   1   0]
[  0   1   0]
[  0   0   1]
}
{
[  1   0   1]
[  0   1   0]
[  0   0   1],
[  1   1   0]
[  0   1   0]
[  0   0   1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.ramification_jumps()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 2^3 with the equations:
z0^2 - z0 = x^5
z1^2 - z1 = a*x^5 + x^3

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.ramification_jumps()[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lus()[?7h[?12l[?25h[?25l[?7lsage: AS.genus()

[?7h[?12l[?25h[?2004l[?7h6
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7l, B = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l_(AS)[?7h[?12l[?25h[?25l[?7lh(AS)[?7h[?12l[?25h[?25l[?7lo(AS)[?7h[?12l[?25h[?25l[?7ll(AS)[?7h[?12l[?25h[?25l[?7lo(AS)[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_holo(AS)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lminimal_polynomial(a)[?7h[?12l[?25h[?25l[?7lagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lTru)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, B)[?7h[?12l[?25h[?25l[?7l, B)[?7h[?12l[?25h[?25l[?7lA, B)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B)

[?7h[?12l[?25h[?2004l[?7h>> 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, a^2 + a, 0, 0, 0, 0, 0, 1, 0, 0, 0,
                                          ^
User error: Identifier 'a' has not been declared or assigned
>>  0, 0, 1, 0, 0, 0, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),6), A);L := Indec
                                                                 ^
User error: Identifier 'A' has not been declared or assigned
>> 8),6), A);L := IndecomposableSummands(M); L;for i in [1 .. #L] do print(Gen
                                         ^
User error: Identifier 'M' has not been declared or assigned
>> 8),6), A);L := IndecomposableSummands(M); L;for i in [1 .. #L] do print(Gen
                                             ^
User error: Identifier 'L' has not been declared or assigned
>> 8),6), A);L := IndecomposableSummands(M); L;for i in [1 .. #L] do print(Gen
                                                               ^
User error: Identifier 'L' has not been declared or assigned
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A

[?7h[?12l[?25h[?2004l[?7h[      1       0       1       0       0       0]
[      0       1       0       0       0       0]
[      0       0       1       0       0       0]
[      0       0       0       1 a^2 + a       0]
[      0       0       0       0       1       0]
[      0       0       0       0       0       1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(A).base_ring().order()[?7h[?12l[?25h[?25l[?7lsage: parent(A).base_ring().order()

[?7h[?12l[?25h[?2004l[?7h8
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zz_pex.pyx:280, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.__call__()
    279 try:
--> 280     if a.parent() is not K:
    281         a = K.coerce(a)

AttributeError: 'tuple' object has no attribute 'parent'

During handling of the above exception, another exception occurred:

KeyboardInterrupt                         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>: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: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>:15, in <module>

File <string>:44, in __init__(self, C, list_of_fcts, prec)

File <string>:134, in artin_schreier_transform(power_series, prec)

File <string>:12, in new_reverse(power_series, prec)

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1831, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
   1829 if x:
   1830     raise ValueError("must not specify %s keyword and positional argument" % name)
-> 1831 a = self(kwds[name])
   1832 del kwds[name]
   1833 try:

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1852, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
   1850         x = x[0]
   1851 
-> 1852     return self.__u(*x)*(x[0]**self.__n)
   1853 
   1854 def __pari__(self):

File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:365, in sage.rings.power_series_poly.PowerSeries_poly.__call__()
    363         x[0] = a
    364         x = tuple(x)
--> 365     return self.__f(x)
    366 
    367 def _unsafe_mutate(self, i, value):

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zz_pex.pyx:283, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.__call__()
    281         a = K.coerce(a)
    282 except (TypeError, AttributeError, NotImplementedError):
--> 283     return Polynomial.__call__(self, a)
    284 
    285 _a = self._parent._modulus.ZZ_pE(list(a.polynomial()))

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:898, in sage.rings.polynomial.polynomial_element.Polynomial.__call__()
    896             return result
    897         pol._compiled = CompiledPolynomialFunction(pol.list())
--> 898     return pol._compiled.eval(a)
    899 
    900 def compose_trunc(self, Polynomial other, long n):

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:125, in sage.rings.polynomial.polynomial_compiled.CompiledPolynomialFunction.eval()
    123 cdef object temp
    124 try:
--> 125     pd_eval(self._dag, x, self._coeffs)  #see further down
    126     temp = self._dag.value               #for an explanation
    127     pd_clean(self._dag)                  #of these 3 lines

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
    352     if pd.value is None:
--> 353         pd.eval(vars, coeffs)
    354     pd.hits += 1
    355 

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
    505 
    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507         pd_eval(self.left, vars, coeffs)
    508         pd_eval(self.right, vars, coeffs)
    509         self.value = self.left.value * self.right.value + coeffs[self.index]

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
    352     if pd.value is None:
--> 353         pd.eval(vars, coeffs)
    354     pd.hits += 1
    355 

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
    505 
    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507         pd_eval(self.left, vars, coeffs)
    508         pd_eval(self.right, vars, coeffs)
    509         self.value = self.left.value * self.right.value + coeffs[self.index]

    [... skipping similar frames: sage.rings.polynomial.polynomial_compiled.pd_eval at line 353 (47 times), sage.rings.polynomial.polynomial_compiled.abc_pd.eval at line 507 (46 times)]

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
    505 
    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507         pd_eval(self.left, vars, coeffs)
    508         pd_eval(self.right, vars, coeffs)
    509         self.value = self.left.value * self.right.value + coeffs[self.index]

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
    352     if pd.value is None:
--> 353         pd.eval(vars, coeffs)
    354     pd.hits += 1
    355 

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:509, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
    507 pd_eval(self.left, vars, coeffs)
    508 pd_eval(self.right, vars, coeffs)
--> 509 self.value = self.left.value * self.right.value + coeffs[self.index]
    510 pd_clean(self.left)
    511 pd_clean(self.right)

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

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lparent(A).base_ring().order()[?7h[?12l[?25h[?25l[?7lmgmahis(A, B)[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lS.genus()[?7h[?12l[?25h[?25l[?7l, B = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_holo(AS)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lparent(A).base_ring().order()[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lmagmathis(A, B)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B)

[?7h[?12l[?25h[?2004l[?7h[
RModule of dimension 1 over GF(2^3),
RModule of dimension 2 over GF(2^3),
RModule of dimension 3 over GF(2^3)
]
{
[  1]
}
{
[  1 a^4]
[  0   1],
[  1   1]
[  0   1]
}
{
[  1   0   1]
[  0   1   0]
[  0   0   1],
[  1   1   0]
[  0   1   0]
[  0   0   1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l12.factor()[1][0][?7h[?12l[?25h[?25l[?7l/(a^2 + a + 1)^2[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: 1/a

[?7h[?12l[?25h[?2004l[?7ha^2 + 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l^2[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: a^8

[?7h[?12l[?25h[?2004l[?7ha
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ losage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x-x^3)^2 - x^2[?7h[?12l[?25h[?25l[?7l(x-x^3) + (-x^3)^3)^2-x^2[?7h[?12l[?25h[?25l[?7lR.<x> = PolynomialRing(QQ)[?7h[?12l[?25h[?25l[?7l((x-x^3) + (x-x^3)^3)^2-x^2[?7h[?12l[?25h[?25l[?7lx-x^3)^2 - ^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.derivative()[?7h[?12l[?25h[?25l[?7lpatil_fraction_decomposition()[?7h[?12l[?25h[?25l[?7l = (x^2 + 1)/(x^2*(x^3 - x))[?7h[?12l[?25h[?25l[?7lsage: F.<x> = PolynomialRing(GF(3))

....: FF = FractionField(F)[?7h[?12l[?25h[?25l[?7lf = (x^2 + 1)/(x^2*(x^3 - x)

 [?7h[?12l[?25h[?25l[?7l.partial_fraction_decomposition()[?7h[?12l[?25h[?25l[?7ldeivtive()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.derivative()[?7h[?12l[?25h[?25l[?7l = (x^2 + 1)/(x^2*(x^3 - x))[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: f = C.y

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [2], in <cell line: 1>()
----> 1 f = C.y

NameError: name 'C' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lsage: C_super

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: C_super.x

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [4], in <cell line: 1>()
----> 1 C_super.x

AttributeError: 'superelliptic' object has no attribute 'x'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super.x[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: C_super.x

[?7h[?12l[?25h[?2004l[?7hx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y, z0, z1 = Rxyz.gens()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxC_super.x[?7h[?12l[?25h[?25l[?7lxC_super.x[?7h[?12l[?25h[?25l[?7l,C_super.x[?7h[?12l[?25h[?25l[?7l C_super.x[?7h[?12l[?25h[?25l[?7lyC_super.x[?7h[?12l[?25h[?25l[?7lyC_super.x[?7h[?12l[?25h[?25l[?7l C_super.x[?7h[?12l[?25h[?25l[?7l=C_super.x[?7h[?12l[?25h[?25l[?7l C_super.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, C.super.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = C_super.x, C.super.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, y = C_super.x, C.super.y[?7h[?12l[?25h[?25l[?7lsage: x, y = C_super.x, C.super.y

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [7], in <cell line: 1>()
----> 1 x, y = C_super.x, C.super.y

NameError: name 'C' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y = C_super.x, C.super.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuper.y[?7h[?12l[?25h[?25l[?7l_super.y[?7h[?12l[?25h[?25l[?7lsage: x, y = C_super.x, C_super.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = C.y[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = C.y[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: f = y+y/x^2

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = y+y/x^2[?7h[?12l[?25h[?25l[?7l.derivative()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7liscrimnant()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lerivative()[?7h[?12l[?25h[?25l[?7lrivative()[?7h[?12l[?25h[?25l[?7lsage: f.derivative()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [10], in <cell line: 1>()
----> 1 f.derivative()

AttributeError: 'superelliptic_function' object has no attribute 'derivative'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld = f.degree()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: diffn(f)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [11], in <cell line: 1>()
----> 1 diffn(f)

NameError: name 'diffn' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldiffn(f)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.derivative()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7liscrimnant()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f.diffn()

[?7h[?12l[?25h[?2004l[?7h((-1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7ldiffn(f)[?7h[?12l[?25h[?25l[?7lf.derivative()[?7h[?12l[?25h[?25l[?7l = y+y/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly/x^2[?7h[?12l[?25h[?25l[?7l-y/x^2[?7h[?12l[?25h[?25l[?7lsage: f = y-y/x^2

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = y-y/x^2[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7lsage: f.diffn()

[?7h[?12l[?25h[?2004l[?7h0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.diffn()[?7h[?12l[?25h[?25l[?7l = y-y/x^2[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f = y*(x^3 + 2*x+2/x^3+1/x^5)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [15], in <cell line: 1>()
----> 1 f = y*(x**Integer(3) + Integer(2)*x+Integer(2)/x**Integer(3)+Integer(1)/x**Integer(5))

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: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 *: 'Integer Ring' and '<class '__main__.superelliptic_function'>'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = y*(x^3 + 2*x+2/x^3+1/x^5)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: f = y*(x^3 + 2*x+2/x^3+1/x^5)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [16], in <cell line: 1>()
----> 1 f = y*(x**Integer(3) + Integer(2)*x+Integer(2)/x**Integer(3)+Integer(1)/x**Integer(5))

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: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 *: 'Integer Ring' and '<class '__main__.superelliptic_function'>'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lf = y*(x^3 + 2*x+2/x^3+1/x^5)[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7l = y-y/x^2[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ldiffn(f)[?7h[?12l[?25h[?25l[?7lf.derivative()[?7h[?12l[?25h[?25l[?7l = y+y/x^2[?7h[?12l[?25h[?25l[?7lx, y = C_super.x, C_super.y[?7h[?12l[?25h[?25l[?7lsage: x, y = C_super.x, C_super.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y = C_super.x, C_super.y[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lf = y*(x^3 + 2*x+2/x^3+1/x^5)[?7h[?12l[?25h[?25l[?7lsage: f = y*(x^3 + 2*x+2/x^3+1/x^5)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [19], in <cell line: 1>()
----> 1 f = y*(x**Integer(3) + Integer(2)*x+Integer(2)/x**Integer(3)+Integer(1)/x**Integer(5))

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, constant)

File <string>:6, in __init__(self, C, g)

AttributeError: 'superelliptic' object has no attribute 'height'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = y*(x^3 + 2*x+2/x^3+1/x^5)[?7h[?12l[?25h[?25l[?7lx, y = C_super., C_super.y[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lf = y*(x^3 + 2*x+2/x^3+1/x^5)[?7h[?12l[?25h[?25l[?7lx, y = C_super., C_super.y[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lf = y*(x^3 + 2*x+2/x^3+1/x^5)[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7l = y-y/x^2[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ldiffn(f)[?7h[?12l[?25h[?25l[?7lf.derivative()[?7h[?12l[?25h[?25l[?7l = y+y/x^2[?7h[?12l[?25h[?25l[?7lx, y = C_super.x, C_super.y[?7h[?12l[?25h[?25l[?7lsage: x, y = C_super.x, C_super.y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lf = y*(x^3 + 2*x+2/x^3+1/x^5)[?7h[?12l[?25h[?25l[?7lsage: f = y*(x^3 + 2*x+2/x^3+1/x^5)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [22], in <cell line: 1>()
----> 1 f = y*(x**Integer(3) + Integer(2)*x+Integer(2)/x**Integer(3)+Integer(1)/x**Integer(5))

File /ext/sage/9.7/src/sage/rings/integer.pyx:2037, in sage.rings.integer.Integer.__truediv__()
   2035         return y
   2036 
-> 2037     return coercion_model.bin_op(left, right, operator.truediv)
   2038 
   2039 cpdef _div_(self, right):

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 /: 'Integer Ring' and '<class '__main__.superelliptic_function'>'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = y*(x^3 + 2*x+2/x^3+1/x^5)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = y*(x^3 + 2*x+2/x^3+1/x^5)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuperelliptic_function(C, g)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_, g)[?7h[?12l[?25h[?25l[?7ls, g)[?7h[?12l[?25h[?25l[?7lu, g)[?7h[?12l[?25h[?25l[?7lp, g)[?7h[?12l[?25h[?25l[?7le, g)[?7h[?12l[?25h[?25l[?7lr, g)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7lsage: f1 = superelliptic_function(C_super, 1)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = superelliptic_function(C_super, 1)[?7h[?12l[?25h[?25l[?7l = y*(x^3 + 2*x+2/x^3+1/x^5)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1/x^5)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf2/x^3+f1/x^5)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx^3+f1/x^5)[?7h[?12l[?25h[?25l[?7lx^3+f1/x^5)[?7h[?12l[?25h[?25l[?7l1x^3+f1/x^5)[?7h[?12l[?25h[?25l[?7l/x^3+f1/x^5)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2f1/x^3+f1/x^5)[?7h[?12l[?25h[?25l[?7l*f1/x^3+f1/x^5)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: f = y*(x^3 + 2*x+2*f1/x^3+f1/x^5)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = y*(x^3 + 2*x+2*f1/x^3+f1/x^5)[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f.diffn()

[?7h[?12l[?25h[?2004l[?7h0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l = y*(x^3 + 2*x+2*f1/x^3+f1/x^5)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: f = y*(x^3 + 2*x)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = y*(x^3 + 2*x)[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f.diffn()

[?7h[?12l[?25h[?2004l[?7h0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super.x[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lrham_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C_super.de_rham_basis()

[?7h[?12l[?25h[?2004lsage/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 [28], in <cell line: 1>()
----> 1 C_super.de_rham_basis()

File <string>:94, in de_rham_basis(self)

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

File <string>:150, in cut(f, i)

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>:150, in <genexpr>(.0)

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: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:176, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_template.__init__()
    174     self.__class__.__init__(self, parent, x, check=check, is_gen=is_gen, construct=construct)
    175 else:
--> 176     x = parent.base_ring()(x)
    177     self.__class__.__init__(self, parent, x, check=check, is_gen=is_gen, construct=construct)
    178 

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:391, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
    389             z = value % self.__modulus.sageInteger
    390         else:
--> 391             raise
    392 self.set_from_mpz(z.value)
    393 

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: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/integer.pyx:717, in sage.rings.integer.Integer.__init__()
    715                 return
    716 
--> 717             raise TypeError("unable to coerce %s to an integer" % type(x))
    718 
    719 def __reduce__(self):

TypeError: unable to coerce <class '__main__.superelliptic_function'> to an integer
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

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

[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.discriminant()%8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llista += [[e, f, g]][?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
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>: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: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>:10, in <module>

AttributeError: 'superelliptic' object has no attribute 'holo_basis'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super.de_rham_basis()[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C_super.

  C_super.a_number                               C_super.cartier_matrix                         C_super.degrees_de_rham1                        

  C_super.base_ring                              C_super.characteristic                         C_super.degrees_holomorphic_differentials       

  C_super.basis_de_rham_degrees                  C_super.de_rham_basis                          C_super.exponent                               >

  C_super.basis_holomorphic_differentials_degree C_super.degrees_de_rham0                       C_super.final_type                              

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

 C_super.a_number                              







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

 C_super.a_number                               C_super.cartier_matrix                        [?7h[?12l[?25h[?25l[?7ldegresde_ham1

 C_super.cartier_matrix                         C_super.degrees_de_rham1                      [?7h[?12l[?25h[?25l[?7lfrobnius_matrix

 cartier_matrixdegresde_ham1frobnius_matrix

 characteristicdegees_holomorphic_differentialsgnus                            

<de_rham_basis        exponent     holmorphic_differentials_basis

 degrees_de_rham0                      final_typ      is_smooth [?7h[?12l[?25h[?25l[?7lpolynomial

degresde_ham1frobnius_matrixpolynomial       

degees_holomorphic_differentialsgnus                            vrschiebung_matrix 

exponent     holmorphic_differentials_basisx                               

final_typ      is_smooth y         [?7h[?12l[?25h[?25l[?7lfrobenius_matrix

 C_super.frobenius_matrix                       C_super.polynomial                            [?7h[?12l[?25h[?25l[?7linal_type

 C_super.frobenius_matrix                      





 C_super.final_type                            [?7h[?12l[?25h[?25l[?7lrobenius_matrix

 C_super.frobenius_matrix                      





 C_super.final_type                            [?7h[?12l[?25h[?25l[?7lgenus

 C_super.frobenius_matrix                      

 C_super.genus                                 [?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis



 C_super.genus                                 

 C_super.holomorphic_differentials_basis       [?7h[?12l[?25h[?25l[?7l









[?7h[?12l[?25h[?25l[?7lsage: C_super.holomorphic_differentials_basis

[?7h[?12l[?25h[?2004l[?7h<bound method superelliptic.holomorphic_differentials_basis of Superelliptic curve with the equation y^2 = x^15 + x^13 + x^11 + 2*x^9 + 2*x^7 + 2*x^5 + 1 over Finite Field of size 3>
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 



 [?7h[?12l[?25h[?25l[?7lC_super.holomorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C_super.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[(1/y) dx,
 (x/y) dx,
 (x^2/y) dx,
 (x^3/y) dx,
 (x^4/y) dx,
 (x^5/y) dx,
 (x^6/y) dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAC_super.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7l C_super.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7l=C_super.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7l C_super.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7lsage: A = C_super.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = C_super.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l[:, 2] = vector([1, 1, 1])[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: A[0]

[?7h[?12l[?25h[?2004l[?7h(1/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lrun.term-0.term[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lrun.term-0.term[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom, f = AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = AS.holomophic_differentials_basis()[5]; om.serre_duality_pairing(A)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: om = A[0]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = A[0][?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.serre_duality_pairing(A)[?7h[?12l[?25h[?25l[?7lsage: om.serre_duality_pairing(A)

 om.cartier              om.expansion_at_infty   om.is_regular_on_Uinfty

 om.coordinates          om.form                 om.jth_component       

 om.curve                om.is_regular_on_U0                            



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

 om.cartier             





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

 om.cartier              om.expansion_at_infty  [?7h[?12l[?25h[?25l[?7lis_regular_on_Uinfty

 om.expansion_at_infty   om.is_regular_on_Uinfty[?7h[?12l[?25h[?25l[?7ljth_component

 om.is_regular_on_Uinfty

 om.jth_component       [?7h[?12l[?25h[?25l[?7lform



 om.form                 om.jth_component       [?7h[?12l[?25h[?25l[?7lis_regular_on_U0



 om.form                

 om.is_regular_on_U0    [?7h[?12l[?25h[?25l[?7lform



 om.form                

 om.is_regular_on_U0    [?7h[?12l[?25h[?25l[?7lexpansion_at_infty

 om.expansion_at_infty  

 om.form                [?7h[?12l[?25h[?25l[?7lcartier

 om.cartier              om.expansion_at_infty  [?7h[?12l[?25h[?25l[?7lexpansion_at_infty

 om.cartier              om.expansion_at_infty  [?7h[?12l[?25h[?25l[?7lform

 om.expansion_at_infty  

 om.form                [?7h[?12l[?25h[?25l[?7l







[?7h[?12l[?25h[?25l[?7lsage: om.form

[?7h[?12l[?25h[?2004l[?7h1/y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





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

[?7h[?12l[?25h[?2004lTraceback (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 [8] 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>:15
    return superelliptic_form(C1, f(x=x+_sage_const_1 , y))
                                                         ^
SyntaxError: positional argument follows keyword argument

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

[?7h[?12l[?25h[?2004l[(1/y) dx, (x/y) dx, (x^2/y) dx, (x^3/y) dx, (x^4/y) dx, (x^5/y) dx, (x^6/y) dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la_lead = f.coefficients(sparse=False)[d][?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.form[?7h[?12l[?25h[?25l[?7l = A[0][?7h[?12l[?25h[?25l[?7lA[0][?7h[?12l[?25h[?25l[?7l = C_super.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: A = C_super.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = C_super.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = C_super.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.form[?7h[?12l[?25h[?25l[?7l = A[0][?7h[?12l[?25h[?25l[?7lA[0][?7h[?12l[?25h[?25l[?7lom = A[0][?7h[?12l[?25h[?25l[?7lsage: om = A[0]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la_lead = f.coefficients(sparse=False)[d][?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(om)

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

File <string>:15, in autom(omega)

NameError: name 'y' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(om)[?7h[?12l[?25h[?25l[?7lom = A[0][?7h[?12l[?25h[?25l[?7lA = C_super.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTraceback (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 [13] 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>:21
    print [autom(omm) for omm in A]
    ^
SyntaxError: Missing parentheses in call to 'print'. Did you mean print(...)?

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

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 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>: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: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>:21, in <listcomp>(.0)

File <string>:16, in autom(omega)

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

[?7h[?12l[?25h[?2004l[(1/y) dx, ((x + 1)/y) dx, ((x^2 - x + 1)/y) dx, ((x^3 + 1)/y) dx, ((x^4 + x^3 + x + 1)/y) dx, ((x^5 - x^4 + x^3 + x^2 - x + 1)/y) dx, ((x^6 - x^3 + 1)/y) dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[(1/y) dx, ((x + 1)/y) dx, ((x^2 - x + 1)/y) dx, ((x^3 + 1)/y) dx, ((x^4 + x^3 + x + 1)/y) dx, ((x^5 - x^4 + x^3 + x^2 - x + 1)/y) dx, ((x^6 - x^3 + 1)/y) dx]
[(1, 0, 0, 0, 0, 0, 0), (1, 1, 0, 0, 0, 0, 0), (1, 2, 1, 0, 0, 0, 0), (1, 0, 0, 1, 0, 0, 0), (1, 1, 0, 1, 1, 0, 0), (1, 2, 1, 1, 2, 1, 0), (1, 0, 0, 2, 0, 0, 1)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[(1/y) dx, ((x + 1)/y) dx, ((x^2 - x + 1)/y) dx, ((x^3 + 1)/y) dx, ((x^4 + x^3 + x + 1)/y) dx, ((x^5 - x^4 + x^3 + x^2 - x + 1)/y) dx, ((x^6 - x^3 + 1)/y) dx]
[(1, 0, 0, 0, 0, 0, 0), (1, 1, 0, 0, 0, 0, 0), (1, 2, 1, 0, 0, 0, 0), (1, 0, 0, 1, 0, 0, 0), (1, 1, 0, 1, 1, 0, 0), (1, 2, 1, 1, 2, 1, 0), (1, 0, 0, 2, 0, 0, 1)]
[1 1 1 1 1 1 1]
[0 1 2 0 1 2 0]
[0 0 1 0 0 1 0]
[0 0 0 1 1 1 2]
[0 0 0 0 1 2 0]
[0 0 0 0 0 1 0]
[0 0 0 0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7lsage: M

[?7h[?12l[?25h[?2004l[?7h[1 1 1 1 1 1 1]
[0 1 2 0 1 2 0]
[0 0 1 0 0 1 0]
[0 0 0 1 1 1 2]
[0 0 0 0 1 2 0]
[0 0 0 0 0 1 0]
[0 0 0 0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l.determinant()[?7h[?12l[?25h[?25l[?7lj[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: M.jordan_form()

[?7h[?12l[?25h[?2004l[?7h[1 1 0|0 0 0|0]
[0 1 1|0 0 0|0]
[0 0 1|0 0 0|0]
[-----+-----+-]
[0 0 0|1 1 0|0]
[0 0 0|0 1 1|0]
[0 0 0|0 0 1|0]
[-----+-----+-]
[0 0 0|0 0 0|1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^15 + x^13 + x^11 + 2*x^9 + 2*x^7 + 2*x^5 + 1 over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[(1/y) dx, ((x + 1)/y) dx, ((x^2 - x + 1)/y) dx, ((x^3 + 1)/y) dx, ((x^4 + x^3 + x + 1)/y) dx, ((x^5 - x^4 + x^3 + x^2 - x + 1)/y) dx, ((x^6 - x^3 + 1)/y) dx]
[(1, 0, 0, 0, 0, 0, 0), (1, 1, 0, 0, 0, 0, 0), (1, 2, 1, 0, 0, 0, 0), (1, 0, 0, 1, 0, 0, 0), (1, 1, 0, 1, 1, 0, 0), (1, 2, 1, 1, 2, 1, 0), (1, 0, 0, 2, 0, 0, 1)]
[1 1 1 1 1 1 1]
[0 1 2 0 1 2 0]
[0 0 1 0 0 1 0]
[0 0 0 1 1 1 2]
[0 0 0 0 1 2 0]
[0 0 0 0 0 1 0]
[0 0 0 0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: Cf

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^5 + 1 over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: Cf.genus()

[?7h[?12l[?25h[?2004l[?7h2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCf.genus()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: Cf.is_smooth()

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCf.is_smooth()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lschiebung_matrix[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.verschiebung_matrix()

[?7h[?12l[?25h[?2004l[?7h[0 2 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0 0 0 0 0]
[1 0 0 2 0 1 0 0 0 0 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 2 0 1 0 0 0 0 0 0 0 0]
[0 1 0 0 2 0 1 0 0 0 0 0 0 0]
[0 0 0 2 0 1 0 0 0 0 0 0 0 0]
[0 1 0 2 0 0 0 0 0 0 0 0 0 0]
[2 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[1 0 2 0 0 0 0 0 0 0 0 0 0 0]
[0 1 2 0 1 0 0 0 0 0 0 0 0 0]
[0 1 0 2 0 0 0 0 0 0 0 0 0 0]
[0 2 1 0 2 0 0 0 0 0 0 0 0 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.verschiebung_matrix()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ltier_matrix[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.cartier_matrix()

[?7h[?12l[?25h[?2004l[?7h[0 2 0 1 0 0 0]
[0 0 2 0 1 0 0]
[1 0 0 2 0 1 0]
[0 0 2 0 1 0 0]
[0 0 0 2 0 1 0]
[0 1 0 0 2 0 1]
[0 0 0 2 0 1 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm = 7[?7h[?12l[?25h[?25l[?7lagmathis(A, B)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lmathis(A, B)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[(1/y) dx, ((x + 1)/y) dx, ((x^2 - x + 1)/y) dx, ((x^3 + 1)/y) dx, ((x^4 + x^3 + x + 1)/y) dx, ((x^5 - x^4 + x^3 + x^2 - x + 1)/y) dx, ((x^6 - x^3 + 1)/y) dx]
[(1, 0, 0, 0, 0, 0, 0), (1, 1, 0, 0, 0, 0, 0), (1, 2, 1, 0, 0, 0, 0), (1, 0, 0, 1, 0, 0, 0), (1, 1, 0, 1, 1, 0, 0), (1, 2, 1, 1, 2, 1, 0), (1, 0, 0, 2, 0, 0, 1)]
[1 1 1 1 1 1 1]
[0 1 2 0 1 2 0]
[0 0 1 0 0 1 0]
[0 0 0 1 1 1 2]
[0 0 0 0 1 2 0]
[0 0 0 0 0 1 0]
[0 0 0 0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 1 1 1 1 1 1]
[0 1 2 0 1 2 0]
[0 0 1 0 0 1 0]
[0 0 0 1 1 1 2]
[0 0 0 0 1 2 0]
[0 0 0 0 0 1 0]
[0 0 0 0 0 0 1]
[
RModule M of dimension 7 over GF(3)
]
{
[1 1 1 1 1 1 1]
[0 1 2 0 1 2 0]
[0 0 1 0 0 1 0]
[0 0 0 1 1 1 2]
[0 0 0 0 1 2 0]
[0 0 0 0 0 1 0]
[0 0 0 0 0 0 1],
[0 2 0 1 0 0 0]
[0 0 2 0 1 0 0]
[1 0 0 2 0 1 0]
[0 0 2 0 1 0 0]
[0 0 0 2 0 1 0]
[0 1 0 0 2 0 1]
[0 0 0 2 0 1 0]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = C_super.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l[0][?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A[0].cartier()

[?7h[?12l[?25h[?2004l[?7h((x^3 - x)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[0].cartier()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A[0].cartier().coordinates()

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

[?7h[?12l[?25h[?2004l[1 1 1 1 1 1 1]
[0 1 2 0 1 2 0]
[0 0 1 0 0 1 0]
[0 0 0 1 1 1 2]
[0 0 0 0 1 2 0]
[0 0 0 0 0 1 0]
[0 0 0 0 0 0 1]
[
RModule M of dimension 7 over GF(3)
]
{
[1 1 1 1 1 1 1]
[0 1 2 0 1 2 0]
[0 0 1 0 0 1 0]
[0 0 0 1 1 1 2]
[0 0 0 0 1 2 0]
[0 0 0 0 0 1 0]
[0 0 0 0 0 0 1],
[0 0 1 0 0 0 0]
[2 0 0 0 0 1 0]
[0 2 0 2 0 0 0]
[1 0 2 0 2 0 2]
[0 1 0 1 0 2 0]
[0 0 1 0 1 0 1]
[0 0 0 0 0 1 0]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cartier_matrix()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[((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),
 (((x^13 - x^11 - x^7 + x^5)/y) dx, 2/x*y, ((-1)/(x^2*y)) dx),
 (((-x^12 + x^8 + x^6 - x^2)/y) dx, 2/x^2*y, (1/(x^3*y)) dx),
 (((x^9 - x^7 - x^3 + x)/y) dx, 2/x^3*y, 0 dx),
 (((x^10 - x^8 - x^4 + x^2)/y) dx, 2/x^4*y, ((-1)/(x^5*y)) dx),
 (((-x^9 + x^5 + x^3)/y) dx, 2/x^5*y, ((x^5 + 1)/(x^6*y)) dx),
 (((x^6 - x^4 - 1)/y) dx, 2/x^6*y, ((-1)/(x^2*y)) dx),
 (((x^7 - x^5 - x)/y) dx, 2/x^7*y, ((-x^7 - 1)/(x^8*y)) dx)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [33], 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: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>:29, in <module>

File <string>:17, in autom(omega)

AttributeError: 'superelliptic_cech' object has no attribute 'form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[0].cartier().coordinates()[?7h[?12l[?25h[?25l[?7lsage: A

[?7h[?12l[?25h[?2004l[?7h[((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),
 (((x^13 - x^11 - x^7 + x^5)/y) dx, 2/x*y, ((-1)/(x^2*y)) dx),
 (((-x^12 + x^8 + x^6 - x^2)/y) dx, 2/x^2*y, (1/(x^3*y)) dx),
 (((x^9 - x^7 - x^3 + x)/y) dx, 2/x^3*y, 0 dx),
 (((x^10 - x^8 - x^4 + x^2)/y) dx, 2/x^4*y, ((-1)/(x^5*y)) dx),
 (((-x^9 + x^5 + x^3)/y) dx, 2/x^5*y, ((x^5 + 1)/(x^6*y)) dx),
 (((x^6 - x^4 - 1)/y) dx, 2/x^6*y, ((-1)/(x^2*y)) dx),
 (((x^7 - x^5 - x)/y) dx, 2/x^7*y, ((-x^7 - 1)/(x^8*y)) dx)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[0].cartier().coordinates()[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: A[0]

[?7h[?12l[?25h[?2004l[?7h((1/y) dx, 0, (1/y) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm = 7[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: mm = A[0]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmm = A[0][?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lsage: mm.

 mm.coordinates  mm.frobenius    mm.omega8      

 mm.curve        mm.is_cocycle   mm.verschiebung

 mm.f            mm.omega0                      



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





[?7h[?12l[?25h[?25l[?7lsage: mm.f

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lA[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: A[-1]

[?7h[?12l[?25h[?2004l[?7h(((x^7 - x^5 - x)/y) dx, 2/x^7*y, ((-x^7 - 1)/(x^8*y)) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7lA[-1][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: A[-1].f

[?7h[?12l[?25h[?2004l[?7h2/x^7*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[-1].f[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lsage: A[-1].f.fct

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [40], in <cell line: 1>()
----> 1 A[-Integer(1)].f.fct

AttributeError: 'superelliptic_function' object has no attribute 'fct'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[-1].f.fct[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7luct[?7h[?12l[?25h[?25l[?7lnct[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsage: A[-1].f.function

[?7h[?12l[?25h[?2004l[?7h2/x^7*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lset(*lista2)[?7h[?12l[?25h[?25l[?7lubset_um_quadratic_form(A0, q)[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l?[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lsage: ?superelliptic_cech

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
OSError                                   Traceback (most recent call last)
Input In [42], in <cell line: 1>()
----> 1 get_ipython().run_line_magic('pinfo', 'superelliptic_cech')

File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:2305, in InteractiveShell.run_line_magic(self, magic_name, line, _stack_depth)
   2303     kwargs['local_ns'] = self.get_local_scope(stack_depth)
   2304 with self.builtin_trap:
-> 2305     result = fn(*args, **kwargs)
   2306 return result

File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/magics/namespace.py:58, in NamespaceMagics.pinfo(self, parameter_s, namespaces)
     56     self.psearch(oname)
     57 else:
---> 58     self.shell._inspect('pinfo', oname, detail_level=detail_level,
     59                         namespaces=namespaces)

File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:1685, in InteractiveShell._inspect(self, meth, oname, namespaces, **kw)
   1683     pmethod(info.obj, oname, formatter)
   1684 elif meth == 'pinfo':
-> 1685     pmethod(
   1686         info.obj,
   1687         oname,
   1688         formatter,
   1689         info,
   1690         enable_html_pager=self.enable_html_pager,
   1691         **kw,
   1692     )
   1693 else:
   1694     pmethod(info.obj, oname)

File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/oinspect.py:698, in Inspector.pinfo(self, obj, oname, formatter, info, detail_level, enable_html_pager, omit_sections)
    665 def pinfo(
    666     self,
    667     obj,
   (...)
    673     omit_sections=(),
    674 ):
    675     """Show detailed information about an object.
    676 
    677     Optional arguments:
   (...)
    696     - omit_sections: set of section keys and titles to omit
    697     """
--> 698     info = self._get_info(
    699         obj, oname, formatter, info, detail_level, omit_sections=omit_sections
    700     )
    701     if not enable_html_pager:
    702         del info['text/html']

File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/oinspect.py:591, in Inspector._get_info(self, obj, oname, formatter, info, detail_level, omit_sections)
    571 def _get_info(
    572     self, obj, oname="", formatter=None, info=None, detail_level=0, omit_sections=()
    573 ):
    574     """Retrieve an info dict and format it.
    575 
    576     Parameters
   (...)
    588         Titles or keys to omit from output (can be set, tuple, etc., anything supporting `in`)
    589     """
--> 591     info = self.info(obj, oname=oname, info=info, detail_level=detail_level)
    593     _mime = {
    594         'text/plain': [],
    595         'text/html': '',
    596     }
    598     def append_field(bundle, title:str, key:str, formatter=None):

File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/oinspect.py:762, in Inspector.info(self, obj, oname, info, detail_level)
    760             ds += "\nDocstring:\n" + obj.__doc__
    761 else:
--> 762     ds = getdoc(obj)
    763     if ds is None:
    764         ds = '<no docstring>'

File /ext/sage/9.7/src/sage/misc/lazy_import.pyx:391, in sage.misc.lazy_import.LazyImport.__call__()
    389         True
    390     """
--> 391     return self.get_object()(*args, **kwds)
    392 
    393 def __repr__(self):

File /ext/sage/9.7/src/sage/misc/sageinspect.py:2107, in sage_getdoc(obj, obj_name, embedded)
   2105 r = sage_getdoc_original(obj)
   2106 s = sage.misc.sagedoc.format(r, embedded=embedded)
-> 2107 f = sage_getfile(obj)
   2108 if f and os.path.exists(f):
   2109     from sage.doctest.control import skipfile

File /ext/sage/9.7/src/sage/misc/sageinspect.py:1414, in sage_getfile(obj)
   1412 # No go? fall back to inspect.
   1413 try:
-> 1414     sourcefile = inspect.getabsfile(obj)
   1415 except TypeError: # this happens for Python builtins
   1416     return ''

File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/inspect.py:844, in getabsfile(object, _filename)
    839 """Return an absolute path to the source or compiled file for an object.
    840 
    841 The idea is for each object to have a unique origin, so this routine
    842 normalizes the result as much as possible."""
    843 if _filename is None:
--> 844     _filename = getsourcefile(object) or getfile(object)
    845 return os.path.normcase(os.path.abspath(_filename))

File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/inspect.py:817, in getsourcefile(object)
    813 def getsourcefile(object):
    814     """Return the filename that can be used to locate an object's source.
    815     Return None if no way can be identified to get the source.
    816     """
--> 817     filename = getfile(object)
    818     all_bytecode_suffixes = importlib.machinery.DEBUG_BYTECODE_SUFFIXES[:]
    819     all_bytecode_suffixes += importlib.machinery.OPTIMIZED_BYTECODE_SUFFIXES[:]

File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/inspect.py:785, in getfile(object)
    783             return module.__file__
    784         if object.__module__ == '__main__':
--> 785             raise OSError('source code not available')
    786     raise TypeError('{!r} is a built-in class'.format(object))
    787 if ismethod(object):

OSError: source code not available
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l?superelliptic_cech[?7h[?12l[?25h[?25l[?7lA[-1].f.function[?7h[?12l[?25h[?25l[?7l?superelliptic_cech[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
UnboundLocalError                         Traceback (most recent call last)
Input In [43], 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: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>:44, in <module>

File <string>:33, in automdR(omega)

UnboundLocalError: local variable 'om8' referenced before assignment
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1 1 1 1 1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 1 2 0 0 0 0 0 0 0 0]
[0 0 1 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 1 1 1 2 0 0 0 0 0 0 0]
[0 0 0 0 1 2 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[
RModule of dimension 1 over GF(3),
RModule of dimension 1 over GF(3),
RModule of dimension 1 over GF(3),
RModule of dimension 1 over GF(3),
RModule of dimension 10 over GF(3)
]
{
[0]
}
{
[0]
}
{
[0]
}
{
[0]
}
{
[1 1 1 1 1 1 1 0 0 0]
[0 1 2 0 1 2 0 0 0 0]
[0 0 1 0 0 1 0 0 0 0]
[0 0 0 1 1 1 2 0 0 0]
[0 0 0 0 1 2 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0],
[0 0 1 0 0 0 0 0 2 0]
[2 0 0 0 0 1 0 1 0 1]
[0 2 0 2 0 0 0 0 1 2]
[1 0 2 0 2 0 2 2 0 0]
[0 1 0 1 0 2 0 0 0 1]
[0 0 1 0 1 0 1 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 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>: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: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>:43, in <module>

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

File <string>:113, in degree_of_rational_fctn(f, F)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:554, in 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):
--> 554     raise TypeError("base_ring {!r} must be a ring".format(base_ring))
    556 n = -1  # Unknown number of variables
    557 names = None  # Unknown variable names

TypeError: base_ring 3 must be a ring
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y = C_super.x, C_super.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y = C_super.x, C_super.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: C.x

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

NameError: name 'C' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x[?7h[?12l[?25h[?25l[?7l_super.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: C_super.x

[?7h[?12l[?25h[?2004l[?7hx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltC_super.x[?7h[?12l[?25h[?25l[?7lyC_super.x[?7h[?12l[?25h[?25l[?7lpC_super.x[?7h[?12l[?25h[?25l[?7leC_super.x[?7h[?12l[?25h[?25l[?7ltype(C_super.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: type(C_super.x)

[?7h[?12l[?25h[?2004l[?7h<class '__main__.superelliptic_function'>
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(C_super.x)[?7h[?12l[?25h[?25l[?7lC_super.x[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C_super.x.diffn()

[?7h[?12l[?25h[?2004l[?7h1 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
---------------------------------------------------------------------------
AttributeError                            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>: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: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>:46, in __mul__(self, other)

AttributeError: 'superelliptic_form' object has no attribute 'function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super.x.diffn()[?7h[?12l[?25h[?25l[?7l_super.x.diffn()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7liC_super.x[?7h[?12l[?25h[?25l[?7lsC_super.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_C_super.x[?7h[?12l[?25h[?25l[?7liC_super.x[?7h[?12l[?25h[?25l[?7lsC_super.x[?7h[?12l[?25h[?25l[?7lC_super.x[?7h[?12l[?25h[?25l[?7lnC_super.x[?7h[?12l[?25h[?25l[?7lsC_super.x[?7h[?12l[?25h[?25l[?7ltC_super.x[?7h[?12l[?25h[?25l[?7laC_super.x[?7h[?12l[?25h[?25l[?7lnC_super.x[?7h[?12l[?25h[?25l[?7lcC_super.x[?7h[?12l[?25h[?25l[?7leC_super.x[?7h[?12l[?25h[?25l[?7l(C_super.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lsuper)[?7h[?12l[?25h[?25l[?7lsupere)[?7h[?12l[?25h[?25l[?7ll)[?7h[?12l[?25h[?25l[?7ll)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l_)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7lsage: is_instance(C_super.x, superelliptic_function)

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

NameError: name 'is_instance' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_instance(C_super.x, superelliptic_function)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lisinstance(C_super.x, supereliptic_function)[?7h[?12l[?25h[?25l[?7lsage: isinstance(C_super.x, superelliptic_function)

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lisinstance(C_super.x, superelliptic_function)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: isinstance(C_super.x, superelliptic_function)

[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super.x.diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(C_super.x)[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7ltype[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l(C_super.x)[?7h[?12l[?25h[?25l[?7lsage: type(C_super.x)

[?7h[?12l[?25h[?2004l[?7h<class '__main__.superelliptic_function'>
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(C_super.x)[?7h[?12l[?25h[?25l[?7lisinstance(C_super.x, superelliptic_function)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsuper)[?7h[?12l[?25h[?25l[?7lsupe)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsuperelliptic_function)[?7h[?12l[?25h[?25l[?7lsage: isinstance(C_super.x, superelliptic_function)

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

[?7h[?12l[?25h[?2004l[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
!
!
---------------------------------------------------------------------------
AttributeError                            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>: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: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>:47, in __mul__(self, other)

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

[?7h[?12l[?25h[?2004l[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [13], 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: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 /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.fraction_field_element.FractionFieldElement' object has no attribute 'diffn'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super.x.diffn()[?7h[?12l[?25h[?25l[?7l.x[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: C.dx

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

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

[?7h[?12l[?25h[?2004l[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [15], 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: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 /ext/sage/9.7/src/sage/rings/integer.pyx:2037, in sage.rings.integer.Integer.__truediv__()
   2035         return y
   2036 
-> 2037     return coercion_model.bin_op(left, right, operator.truediv)
   2038 
   2039 cpdef _div_(self, right):

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 /: 'Integer Ring' and '<class '__main__.superelliptic_function'>'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTraceback (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 [16] 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>:1 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>:21
    self.gen(1) = superelliptic_function(self, Rxy(_sage_const_1 ))
    ^
SyntaxError: cannot assign to function call here. Maybe you meant '==' instead of '='?

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
((x^11 - x^9 + x^7 - x^3 + y)/(x^5*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l((x^12 - x^10 + x^8 - x^4 - x^2 + 1)/(x^6*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

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





 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lIfactors = I.factor()[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()([?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: Integers(9)(5/2)

[?7h[?12l[?25h[?2004l[?7h7
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7lIntegers(9)(5/2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l/2)[?7h[?12l[?25h[?25l[?7l-/2)[?7h[?12l[?25h[?25l[?7l7/2)[?7h[?12l[?25h[?25l[?7lsage: Integers(9)(-7/2)

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^2-1)^4[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (x^2/y^3).expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^5 + O(t^15)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^2/y^3).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l/y^3).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l4/y^3).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: (x^4/y^3).expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht + 2*t^5 + 2*t^9 + O(t^11)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^4/y^3).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^4/y^3).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (x^2+x^4)*y^2*y.diffn()

[?7h[?12l[?25h[?2004l[?7h((x^7 - x^3)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = A[0][?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^2+x^4)*y^2*y.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp(x^2+x^4)*y^2*y.difn()[?7h[?12l[?25h[?25l[?7l(x^2+x^4)*y^2*y.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo(x^2+x^4)*y^2*y.difn()[?7h[?12l[?25h[?25l[?7lm(x^2+x^4)*y^2*y.difn()[?7h[?12l[?25h[?25l[?7l (x^2+x^4)*y^2*y.difn()[?7h[?12l[?25h[?25l[?7l=(x^2+x^4)*y^2*y.difn()[?7h[?12l[?25h[?25l[?7l (x^2+x^4)*y^2*y.difn()[?7h[?12l[?25h[?25l[?7lsage: om = (x^2+x^4)*y^2*y.diffn()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = (x^2+x^4)*y^2*y.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.form[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsion_at_infty[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-14 + O(t^-4)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

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

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lP[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: P1

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^1 = x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7h(Z/p)-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equation:
 z^3 - z = x^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.dx[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le_rham_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lgical_element[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.

  C.at_most_poles                       C.cohomology_of_structure_sheaf_basis C.exponent_of_different               C.genus                               
 

  C.at_most_poles_forms                 C.de_rham_basis                       C.exponent_of_different_prim          C.group                               
 

  C.base_ring                           C.dx                                  C.fct_field                           C.height                              
>

  C.characteristic                      C.dx_series                           C.functions                           C.holomorphic_differentials_basis     
 

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

 C.at_most_poles                      







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

 C.at_most_poles                       C.cohomology_of_structure_sheaf_basis[?7h[?12l[?25h[?25l[?7lexpnent_of_different

 C.cohomology_of_structure_sheaf_basis C.exponent_of_different              [?7h[?12l[?25h[?25l[?7lgenus

 C.exponent_of_different               C.genus                              [?7h[?12l[?25h[?25l[?7lith_ramification_gp

 cohomology_of_structure_sheaf_basisexpnent_of_different              genus                ith_ramification_gp

 derhambasi      exponent_of_different_primgroup                     jumps

<dx       fct_fieldheight   lift_o_de_rham

 dx_seris     functionholomorphic_differentials_basismagical_element                [?7h[?12l[?25h[?25l[?7lnb_of_pts_at_nfty

expnent_of_different              genus                ith_ramification_gpnb_of_pts_at_nfty 

exponent_of_different_primgroup                     jumpsprec 

fct_fieldheight   lift_o_de_rhampseudo_magical_element

functionholomorphic_differentials_basismagical_element                quotient       [?7h[?12l[?25h[?25l[?7lramiicationjumps

genus                ith_ramification_gpnb_of_pts_at_nfty ramiicationjumps

group                     jumpsprec uniformizer

height   lift_o_de_rhampseudo_magical_elementx                     

holomorphic_differentials_basismagical_element                quotient       x_series[?7h[?12l[?25h[?25l[?7ly

ith_ramification_gpnb_of_pts_at_nfty ramiicationjumpsy                  

jumpsprec uniformizery_series    

lift_o_de_rhampseudo_magical_elementx                     z 

magical_element                quotient       x_seriesz 
[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_series

 C.y                                  

 C.y_series                           [?7h[?12l[?25h[?25l[?7lz



 C.y_series                           

 C.z                                  [?7h[?12l[?25h[?25l[?7l_series





 C.z                                  

 C.z_series                           [?7h[?12l[?25h[?25l[?7l

 a_most_poles      cohmology_of_structure_sheaf_basisexponent_of_differentgenus 

 at_most_poles_formsde_rham_basisexponent_of_different_primgroup    

 basering      dx                    fct_fieldheight>

 characteristic dx_seriesfunctons C.holomorphic_differentials_basis     

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







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

  C                                  CFiniteSequence                    CPRFanoToricVariety                CRT_vectors                         

  CBF                                CFiniteSequences                   CRT                                C_super                             

  CC                                 CIF                                CRT_basis                          CachedFunction                     >

  CDF                                CLF                                CRT_list                           CallableSymbolicExpressionRing      [?7h[?12l[?25h[?25l[?7l

 C                                 







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

 C                                  CFiniteSequence                   [?7h[?12l[?25h[?25l[?7lPRFanoToricVariety.

 CFiniteSequence                    CPRFanoToricVariety               [?7h[?12l[?25h[?25l[?7l.









[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.dx[?7h[?12l[?25h[?25l[?7l

  C.at_most_poles                       C.cohomology_of_structure_sheaf_basis C.exponent_of_different               C.genus                               
 

  C.at_most_poles_forms                 C.de_rham_basis                       C.exponent_of_different_prim          C.group                               
 

  C.base_ring                           C.dx                                  C.fct_field                           C.height                              
>

  C.characteristic                      C.dx_series                           C.functions                           C.holomorphic_differentials_basis     
 
[?7h[?12l[?25h[?25l[?7lat_most_poles

 C.at_most_poles                      







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

 C.at_most_poles                      

 C.at_most_poles_forms                [?7h[?12l[?25h[?25l[?7lbase_ring



 C.at_most_poles_forms                

 C.base_ring                          [?7h[?12l[?25h[?25l[?7lcharacteristic





 C.base_ring                          

 C.characteristic                     [?7h[?12l[?25h[?25l[?7lohomology_of_structure_sheaf_basis

 C.cohomology_of_structure_sheaf_basis





 C.characteristic                     [?7h[?12l[?25h[?25l[?7lde_rham_basis

 C.cohomology_of_structure_sheaf_basis

 C.de_rham_basis                      [?7h[?12l[?25h[?25l[?7lx



 C.de_rham_basis                      

 C.dx                                 [?7h[?12l[?25h[?25l[?7l_series





 C.dx                                 

 C.dx_series                          [?7h[?12l[?25h[?25l[?7leponent_of_different

 C.exponent_of_different              





 C.dx_series                          [?7h[?12l[?25h[?25l[?7l_prim

 C.exponent_of_different              

 C.exponent_of_different_prim         [?7h[?12l[?25h[?25l[?7lfct_field



 C.exponent_of_different_prim         

 C.fct_field                          [?7h[?12l[?25h[?25l[?7lunctons





 C.fct_field                          

 C.functions                          [?7h[?12l[?25h[?25l[?7lgeus

 C.genus                              





 C.functions                          [?7h[?12l[?25h[?25l[?7lrop

 C.genus                              

 C.group                              [?7h[?12l[?25h[?25l[?7lheight



 C.group                              

 C.height                             [?7h[?12l[?25h[?25l[?7lolomorphic_differentials_basis





 C.height                             

 C.holomorphic_differentials_basis    [?7h[?12l[?25h[?25l[?7lith_ramifaton_gp

 cohomology_of_structure_sheaf_basisexpnent_of_different              genus                 C.ith_ramification_gp                

 derhambasi      exponent_of_different_primgroup                     jumps

<dx       fct_fieldheight   lift_o_de_rham

 dx_seris     functionholomorphic_differentials_basis C.magical_element                    [?7h[?12l[?25h[?25l[?7ljumps

 C.ith_ramification_gp                

 C.jumps                              [?7h[?12l[?25h[?25l[?7llift_to_de_rham



 C.jumps                              

 C.lift_to_de_rham                    [?7h[?12l[?25h[?25l[?7lmagicalelement





 C.lift_to_de_rham                    

 C.magical_element                    [?7h[?12l[?25h[?25l[?7lnb_of_pts_at_infty

expnent_of_different              genus                ith_ramification_gp C.nb_of_pts_at_infty                 

exponent_of_different_primgroup                     jumpsprec 

fct_fieldheight   lift_o_de_rhampseudo_magical_element

functionholomorphic_differentials_basismagical_element                 C.quotient                           [?7h[?12l[?25h[?25l[?7lprec

 C.nb_of_pts_at_infty                 

 C.prec                               [?7h[?12l[?25h[?25l[?7lsudo_magical_element



 C.prec                               

 C.pseudo_magical_element             [?7h[?12l[?25h[?25l[?7lquotient





 C.pseudo_magical_element             

 C.quotient                           [?7h[?12l[?25h[?25l[?7lramification_jumps

genus                ith_ramification_gpnb_of_pts_at_nfty  C.ramification_jumps                 

group                     jumpsprec uniformizer

height   lift_o_de_rhampseudo_magical_elementx                     

holomorphic_differentials_basismagical_element                quotient        C.x_series                           [?7h[?12l[?25h[?25l[?7luniformizer

 C.ramification_jumps                 

 C.uniformizer                        [?7h[?12l[?25h[?25l[?7lx



 C.uniformizer                        

 C.x                                  [?7h[?12l[?25h[?25l[?7l_series





 C.x                                  

 C.x_series                           [?7h[?12l[?25h[?25l[?7ly

ith_ramification_gpnb_of_pts_at_nfty ramiicationjumps C.y                                   

jumpsprec uniformizery_series    

lift_o_de_rhampseudo_magical_elementx                     z 

magical_element                quotient       x_series C.z_series                            
[?7h[?12l[?25h[?25l[?7l_series

 C.y                                  

 C.y_series                           [?7h[?12l[?25h[?25l[?7lz



 C.y_series                           

 C.z                                  [?7h[?12l[?25h[?25l[?7l_series





 C.z                                  

 C.z_series                           [?7h[?12l[?25h[?25l[?7l

 a_most_poles      cohmology_of_structure_sheaf_basisexponent_of_differentgenus 

 at_most_poles_formsde_rham_basisexponent_of_different_primgroup    

 basering      dx                    fct_fieldheight>

 characteristic dx_seriesfunctons C.holomorphic_differentials_basis     

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

 C.at_most_poles                      







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

 C.at_most_poles                       C.cohomology_of_structure_sheaf_basis[?7h[?12l[?25h[?25l[?7lexpnent_of_different

 C.cohomology_of_structure_sheaf_basis C.exponent_of_different              [?7h[?12l[?25h[?25l[?7lgenus

 C.exponent_of_different               C.genus                              [?7h[?12l[?25h[?25l[?7lith_ramification_gp

 cohomology_of_structure_sheaf_basisexpnent_of_different              genus                ith_ramification_gp

 derhambasi      exponent_of_different_primgroup                     jumps

<dx       fct_fieldheight   lift_o_de_rham

 dx_seris     functionholomorphic_differentials_basismagical_element                [?7h[?12l[?25h[?25l[?7lnb_of_pts_at_nfty

expnent_of_different              genus                ith_ramification_gpnb_of_pts_at_nfty 

exponent_of_different_primgroup                     jumpsprec 

fct_fieldheight   lift_o_de_rhampseudo_magical_element

functionholomorphic_differentials_basismagical_element                quotient       [?7h[?12l[?25h[?25l[?7lramiicationjumps

genus                ith_ramification_gpnb_of_pts_at_nfty ramiicationjumps

group                     jumpsprec uniformizer

height   lift_o_de_rhampseudo_magical_elementx                     

holomorphic_differentials_basismagical_element                quotient       x_series[?7h[?12l[?25h[?25l[?7ly

ith_ramification_gpnb_of_pts_at_nfty ramiicationjumpsy                  

jumpsprec uniformizery_series    

lift_o_de_rhampseudo_magical_elementx                     z 

magical_element                quotient       x_seriesz 
[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lramification_jumps

 C.ramification_jumps                  C.y                                  [?7h[?12l[?25h[?25l[?7luniformizer

 C.ramification_jumps                 

 C.uniformizer                        [?7h[?12l[?25h[?25l[?7lx



 C.uniformizer                        

 C.x                                  [?7h[?12l[?25h[?25l[?7lpseudo_magical_element





 C.pseudo_magical_element              C.x                                  [?7h[?12l[?25h[?25l[?7lquotient





 C.pseudo_magical_element             

 C.quotient                           [?7h[?12l[?25h[?25l[?7lpseudo_magical_element





 C.pseudo_magical_element             

 C.quotient                           [?7h[?12l[?25h[?25l[?7lrc



 C.prec                               

 C.pseudo_magical_element             [?7h[?12l[?25h[?25l[?7lnb_of_pts_at_infty

 C.nb_of_pts_at_infty                 

 C.prec                               [?7h[?12l[?25h[?25l[?7lith_ramificaton_gp

 C.ith_ramification_gp                 C.nb_of_pts_at_infty                 [?7h[?12l[?25h[?25l[?7ljumps

 C.ith_ramification_gp                

 C.jumps                              [?7h[?12l[?25h[?25l[?7llift_to_de_rham



 C.jumps                              

 C.lift_to_de_rham                    [?7h[?12l[?25h[?25l[?7lmagicalelement





 C.lift_to_de_rham                    

 C.magical_element                    [?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis

genus              ith_ramificaton_gpnb_o_pts_atinftyramification_jumps 

groupjumpsprec       uniformizer 

heigh         lift_to_de_rham       pseudo_magical_elementx>

holomorphic_differentials_basismagical_elementquotientx 
[?7h[?12l[?25h[?25l[?7leight





 C.height                             

 C.holomorphic_differentials_basis    [?7h[?12l[?25h[?25l[?7lgroup



 C.group                              

 C.height                             [?7h[?12l[?25h[?25l[?7lens

 C.genus                              

 C.group                              [?7h[?12l[?25h[?25l[?7lexponent_of_different

exponent_of_differentgenus              ith_ramificaton_gpnb_o_pts_atinfty

exponent_of_different_primgroupjumpsprec       

fct_fieldheigh         lift_to_de_rham       pseudo_magical_element

functions                      holomorphic_differentials_basismagical_elementquotient[?7h[?12l[?25h[?25l[?7l_prim

 C.exponent_of_different              

 C.exponent_of_different_prim         [?7h[?12l[?25h[?25l[?7lfct_field



 C.exponent_of_different_prim         

 C.fct_field                          [?7h[?12l[?25h[?25l[?7lunctons





 C.fct_field                          

 C.functions                          [?7h[?12l[?25h[?25l[?7ldx_serie

cohmology_of_structure_sheaf_basisexponent_of_differentgenus              ith_ramificaton_gp

de_rham_basis             exponent_of_different_primgroupjumps

dx       fct_fieldheigh         lift_to_de_rham       

dx_seriefunctions                      holomorphic_differentials_basismagical_element[?7h[?12l[?25h[?25l[?7lcharactristic

 at_most_poles                      cohmology_of_structure_sheaf_basisexponent_of_differentgenus              

 atmostpole_formsde_rham_basis             exponent_of_different_primgroup

 base_ringdx       fct_fieldheigh         

 charactristicdx_seriefunctions                      holomorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l









[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[[1 2]
[0 1]]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 



 [?7h[?12l[?25h[?25l[?7lIntegers(9)(-7/2)[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l9)(-7/2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l/2)[?7h[?12l[?25h[?25l[?7l/2)[?7h[?12l[?25h[?25l[?7l5/2)[?7h[?12l[?25h[?25l[?7lsage: Integers(9)(5/2)

[?7h[?12l[?25h[?2004l[?7h7
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l%[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: 7%3

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sa
bash: sa: command not found
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ gesage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llista2 = [][?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[[1 2]
[0 1]]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7h(Z/p)-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equation:
 z^3 - z = x^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.dx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: C.x

[?7h[?12l[?25h[?2004l[?7hx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion_at_infty[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-3 + t + t^5 + O(t^7)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty()[-3]

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty()[-3][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l2][?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty()[-2]

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty()[-2][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l1][?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty()[-1]

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty()[-1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l1][?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty()[1]

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

[?7h[?12l[?25h[?2004lTraceback (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 [9] 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>:32
    basis += [superelliptic_cohomology(C, Fxy(m*y**(m-j)/x**i)))]
                                                               ^
SyntaxError: closing parenthesis ')' does not match opening parenthesis '['

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

[?7h[?12l[?25h[?2004l[[1 2]
[0 1]]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: basis

 basis              

 basis_of_cohomology





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

 basis              



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

 basis              

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





[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: basis_of_cohomology(C)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [11], in <cell line: 1>()
----> 1 basis_of_cohomology(C)

File <string>:18, in basis_of_cohomology(C)

AttributeError: 'as_cover' object has no attribute 'exponent'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty()[1][?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7h(Z/p)-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equation:
 z^3 - z = x^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lbasis_of_cohomology(C)[?7h[?12l[?25h[?25l[?7lsage: basis_of_cohomology(C)

[?7h[?12l[?25h[?2004l[?7h[<__main__.superelliptic_cohomology object at 0x7f4110fc8a60>]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbasis_of_cohomology(C)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lbasis_of_cohomology(C)[?7h[?12l[?25h[?25l[?7lsage: basis_of_cohomology(C)

[?7h[?12l[?25h[?2004l[?7h[[(-y)/x]]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.x.expansion_at_infty()[1][?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: C.bas

 C.base_ring                             

 C.basis_de_rham_degrees                 

 C.basis_holomorphic_differentials_degree



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





[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[(1/y) dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lbasis_of_cohomology(C)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTraceback (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 [18] 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>:22 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>:10
    print f.prod(omega)
    ^
SyntaxError: Missing parentheses in call to 'print'. Did you mean print(...)?

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

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [19], 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>:22, 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>:9, in <module>

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

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [20], 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>:22, 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>:10, in <module>

File <string>:13, in prod(self, form)

TypeError: unsupported operand type(s) for *: 'superelliptic_form' and 'superelliptic_cohomology'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
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>:22, 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>:10, in <module>

File <string>:14, in prod(self, form)

File <string>:59, in __rmul__(self, constant)

TypeError: unsupported operand type(s) for *: 'superelliptic_form' and 'PolynomialRing_field_with_category.element_class'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 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>:22, 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>:10, in <module>

File <string>:14, in prod(self, form)

TypeError: superelliptic_form.expansion_at_infty() got an unexpected keyword argument 'place'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Input In [24], 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>:22, 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>:10, in <module>

File <string>:14, in prod(self, form)

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

[?7h[?12l[?25h[?2004l2*t^-11 + O(t^-1)
---------------------------------------------------------------------------
IndexError                                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>:22, 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>:10, in <module>

File <string>:15, in prod(self, form)

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

[?7h[?12l[?25h[?2004l2*t^-11 + 2*t^5 + O(t^9)
0
2*t^-7 + 2*t^9 + O(t^13)
0
2*t^-3 + 2*t^13 + O(t^17)
0
2*t^-6 + t^10 + O(t^14)
0
2*t^-2 + t^14 + O(t^18)
0
2*t^-1 + O(t^19)
2
2*t^-6 + t^10 + O(t^14)
0
2*t^-2 + t^14 + O(t^18)
0
2*t^2 + t^18 + O(t^22)
0
2*t^-1 + O(t^19)
2
2*t^3 + O(t^23)
0
2*t^4 + t^20 + O(t^24)
0
2*t^-10 + t^6 + O(t^10)
0
2*t^-6 + t^10 + O(t^14)
0
2*t^-2 + t^14 + O(t^18)
0
2*t^-5 + O(t^15)
0
2*t^-1 + O(t^19)
2
2 + t^16 + O(t^20)
0
2*t^-1 + O(t^19)
2
2*t^3 + O(t^23)
0
2*t^7 + O(t^27)
0
2*t^4 + t^20 + O(t^24)
0
2*t^8 + t^24 + O(t^28)
0
2*t^9 + O(t^29)
0
2*t^-5 + O(t^15)
0
2*t^-1 + O(t^19)
2
2*t^3 + O(t^23)
0
2 + t^16 + O(t^20)
0
2*t^4 + t^20 + O(t^24)
0
2*t^5 + O(t^25)
0
2*t^-9 + O(t^11)
0
2*t^-5 + O(t^15)
0
2*t^-1 + O(t^19)
2
2*t^-4 + t^12 + O(t^16)
0
2 + t^16 + O(t^20)
0
2*t + O(t^21)
0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^4 = x^5 + x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[(1/y) dx, (1/y^2) dx, (x/y^2) dx, (1/y^3) dx, (x/y^3) dx, (x^2/y^3) dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l_of_pts_at_infty[?7h[?12l[?25h[?25l[?7lsage: C.nb_of_pts_at_infty

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.nb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_smooth[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.is_smooth()

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbasis_of_cohomology(C)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls_of_cohomology(C)[?7h[?12l[?25h[?25l[?7lsage: basis_of_cohomology(C)

[?7h[?12l[?25h[?2004l[?7h[[y^3/x], [y^3/x^2], [y^3/x^3], [y^2/x], [y^2/x^2], [y/x]]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbasis_of_cohomology(C)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7labasis_of_cohomology(C)[0][?7h[?12l[?25h[?25l[?7l basis_of_cohomology(C)[0][?7h[?12l[?25h[?25l[?7l=basis_of_cohomology(C)[0][?7h[?12l[?25h[?25l[?7l basis_of_cohomology(C)[0][?7h[?12l[?25h[?25l[?7lsage: a = basis_of_cohomology(C)[0]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = basis_of_cohomology(C)[0][?7h[?12l[?25h[?25l[?7l.squre_rot()[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: a.prod(C.holomorphic_differentials_basis()[0])

[?7h[?12l[?25h[?2004l2*t^-11 + 2*t^5 + O(t^9)
[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.prod(C.holomorphic_differentials_basis()[0])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l1])[?7h[?12l[?25h[?25l[?7lsage: a.prod(C.holomorphic_differentials_basis()[1])

[?7h[?12l[?25h[?2004l2*t^-6 + t^10 + O(t^14)
[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.prod(C.holomorphic_differentials_basis()[1])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l2])[?7h[?12l[?25h[?25l[?7lsage: a.prod(C.holomorphic_differentials_basis()[2])

[?7h[?12l[?25h[?2004l2*t^-10 + t^6 + O(t^10)
[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.prod(C.holomorphic_differentials_basis()[2])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l3])[?7h[?12l[?25h[?25l[?7lsage: a.prod(C.holomorphic_differentials_basis()[3])

[?7h[?12l[?25h[?2004l2*t^-1 + O(t^19)
[?7h2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.is_smooth()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.genus()

[?7h[?12l[?25h[?2004l[?7h6
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lista2 = [][?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7llist[?7h[?12l[?25h[?25l[?7llista[?7h[?12l[?25h[?25l[?7l = [][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: lista = ['a', 'b', 'c']

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in lista2:[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lirange(0, p):[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, f in enumerate(AS.cohomology_of_structure_sheaf_basis()):[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: for i, x in enum

 enum_affine_finite_field          enumerate_totallyreal_fields_all 

 enum_affine_rational_field        enumerate_totallyreal_fields_prim

 enumerate                         enumerate_totallyreal_fields_rel 



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





[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lenumerate[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7llist[?7h[?12l[?25h[?25l[?7llista[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7l

....: [?7h[?12l[?25h[?25l[?7lprint(a, lista.count(a))[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()

....: [?7h[?12l[?25h[?25l[?7lsage: for i, x in enumerate(lista):

....:     print(i, x)

....: 

[?7h[?12l[?25h[?2004l0 a
1 b
2 c
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llista = ['a', 'b', 'c'][?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[0, 0, 0, 1, 0, 0]
[0, 0, 0, 0, 1, 0]
[0, 0, 0, 0, 0, 1]
[0, 1, 0, 0, 0, 0]
[0, 0, 1, 0, 0, 0]
[1, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

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

[?7h[?12l[?25h[?2004l[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]
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [44], 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>:22, 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>:10, in <module>

File <string>:59, in frobenius_matrix(C)

File <string>:35, in frobenius(self)

AttributeError: 'superelliptic_cohomology' object has no attribute 'base_ring'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[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]
---------------------------------------------------------------------------
TypeError                                 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>:22, 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>:10, in <module>

File <string>:59, in frobenius_matrix(C)

File /ext/sage/9.7/src/sage/matrix/matrix0.pyx:1509, in sage.matrix.matrix0.Matrix.__setitem__()
   1507     raise IndexError("value does not have the right number of rows")
   1508 for value_row in value_list:
-> 1509     if col_list_len != len(value_row):
   1510         raise IndexError("value does not have the right number of columns")
   1511 

TypeError: object of type 'sage.rings.finite_rings.integer_mod.IntegerMod_int' has no len()
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[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]
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Input In [46], 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>:22, 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>:10, in <module>

File <string>:59, in frobenius_matrix(C)

File <string>:29, in coordinates(self, basis, basis_holo)

File <string>:14, in prod(self, form, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[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]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM.jordan_form()[?7h[?12l[?25h[?25l[?7lsage: M

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [48], in <cell line: 1>()
----> 1 M

NameError: name 'M' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i, x in enumerate(lista):[?7h[?12l[?25h[?25l[?7lrom itertools import product[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: frobenius_matrix(C)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Input In [49], in <cell line: 1>()
----> 1 frobenius_matrix(C)

File <string>:59, in frobenius_matrix(C, prec)

File <string>:29, in coordinates(self, basis, basis_holo, prec)

File <string>:14, in prod(self, form, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(C)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l5)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7lsage: frobenius_matrix(C, prec=50)

[?7h[?12l[?25h[?2004l[?7h[0 0 0 1 0 0]
[0 0 1 0 0 0]
[0 1 0 0 0 0]
[0 0 0 0 0 0]
[0 0 0 0 0 0]
[1 0 0 0 0 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(C, prec=50)[?7h[?12l[?25h[?25l[?7l(),[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic_curve(2, x^3 - x)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [51], in <cell line: 1>()
----> 1 C = superelliptic_curve(Integer(2), x**Integer(3) - x)

NameError: name 'superelliptic_curve' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic_curve(2, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(2, x^3 - x)[?7h[?12l[?25h[?25l[?7l(2, x^3 - x)[?7h[?12l[?25h[?25l[?7l(2, x^3 - x)[?7h[?12l[?25h[?25l[?7l(2, x^3 - x)[?7h[?12l[?25h[?25l[?7l(2, x^3 - x)[?7h[?12l[?25h[?25l[?7l(2, x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(2, x^3 - x)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2441, in sage.rings.polynomial.polynomial_element.Polynomial.__pow__()
   2440 try:
-> 2441     right = Integer(right)
   2442 except TypeError:

File /ext/sage/9.7/src/sage/rings/integer.pyx:658, in sage.rings.integer.Integer.__init__()
    657 if otmp is not None:
--> 658     set_from_Integer(self, otmp(the_integer_ring))
    659     return

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:1390, 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))

TypeError: cannot convert nonconstant polynomial

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
Input In [52], in <cell line: 1>()
----> 1 C = superelliptic(Integer(2), x**Integer(3) - x)

File <string>:19, in __init__(self, f, m)

File <string>:13, in __init__(self, C, g)

File <string>:188, in reduction(C, g)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2443, in sage.rings.polynomial.polynomial_element.Polynomial.__pow__()
   2441         right = Integer(right)
   2442     except TypeError:
-> 2443         raise TypeError("non-integral exponents not supported")
   2444 
   2445 d = self.degree()

TypeError: non-integral exponents not supported
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(2, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx^3 - x)[?7h[?12l[?25h[?25l[?7lx^3 - x)[?7h[?12l[?25h[?25l[?7lx^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.gens()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(C, prec=50)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lus_matrix(C, prec=50)[?7h[?12l[?25h[?25l[?7lsage: frobenius_matrix(C, prec=50)

[?7h[?12l[?25h[?2004l[?7h[0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(C, prec=50)[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l+, 2)[?7h[?12l[?25h[?25l[?7l , 2)[?7h[?12l[?25h[?25l[?7l1, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 + 1, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(C, prec=50)[?7h[?12l[?25h[?25l[?7lsage: frobenius_matrix(C, prec=50)

[?7h[?12l[?25h[?2004l[?7h[0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(C, prec=50)[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7lx, 2)[?7h[?12l[?25h[?25l[?7l , 2)[?7h[?12l[?25h[?25l[?7l+, 2)[?7h[?12l[?25h[?25l[?7l , 2)[?7h[?12l[?25h[?25l[?7l1, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 + x + 1, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 + x + 1, 2)[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(C, prec=50)[?7h[?12l[?25h[?25l[?7lsage: frobenius_matrix(C, prec=50)

[?7h[?12l[?25h[?2004l[?7h[0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE.local_data(2)[?7h[?12l[?25h[?25l[?7l = ElipticCurve([0, 16])[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lEllipticCurve([0, 16])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lG[0, 16])[?7h[?12l[?25h[?25l[?7lF[0, 16])[?7h[?12l[?25h[?25l[?7l([0, 16])[?7h[?12l[?25h[?25l[?7l)[0, 16])[?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l3)[0, 16])[?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l,[0, 16])[?7h[?12l[?25h[?25l[?7l [0, 16])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l1])[?7h[?12l[?25h[?25l[?7l,])[?7h[?12l[?25h[?25l[?7l ])[?7h[?12l[?25h[?25l[?7l1])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: E = EllipticCurve(GF(3), [1, 1])

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE = EllipticCurve(GF(3), [1, 1])[?7h[?12l[?25h[?25l[?7l.loca_data(2)[?7h[?12l[?25h[?25l[?7lis_goo(3)[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lsingular(2)[?7h[?12l[?25h[?25l[?7lupersingular(2)[?7h[?12l[?25h[?25l[?7lpersingular(2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: E.is_supersingular()

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE.is_supersingular()[?7h[?12l[?25h[?25l[?7l = EllipticCurve(GF(3), [1, 1])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l2])[?7h[?12l[?25h[?25l[?7lsage: E = EllipticCurve(GF(3), [1, 2])

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE = EllipticCurve(GF(3), [1, 2])[?7h[?12l[?25h[?25l[?7l.is_supersingular()[?7h[?12l[?25h[?25l[?7lsage: E.is_supersingular()

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE.is_supersingular()[?7h[?12l[?25h[?25l[?7l = EllipticCurve(GF(3), [1, 2])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l0])[?7h[?12l[?25h[?25l[?7lsage: E = EllipticCurve(GF(3), [1, 0])

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE = EllipticCurve(GF(3), [1, 0])[?7h[?12l[?25h[?25l[?7l.is_supersingular()[?7h[?12l[?25h[?25l[?7lsage: E.is_supersingular()

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE.is_supersingular()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l = EllipticCurve(GF(3), [1, 0])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 0])[?7h[?12l[?25h[?25l[?7l2, 0])[?7h[?12l[?25h[?25l[?7lsage: E = EllipticCurve(GF(3), [2, 0])

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE = EllipticCurve(GF(3), [2, 0])[?7h[?12l[?25h[?25l[?7l.is_supersingular()[?7h[?12l[?25h[?25l[?7lsage: E.is_supersingular()

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE.is_supersingular()[?7h[?12l[?25h[?25l[?7l = EllipticCurve(GF(3), [2, 0])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l2])[?7h[?12l[?25h[?25l[?7lsage: E = EllipticCurve(GF(3), [2, 2])

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE = EllipticCurve(GF(3), [2, 2])[?7h[?12l[?25h[?25l[?7l.is_supersingular()[?7h[?12l[?25h[?25l[?7lsage: E.is_supersingular()

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

[?7h[?12l[?25h[?2004l[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]
[0 0 0 1 0 0]
[0 0 1 0 0 0]
[0 1 0 0 0 0]
[0 0 0 0 0 0]
[0 0 0 0 0 0]
[1 0 0 0 0 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[5]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[5]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lkronecker_symbol(7, 8)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lel[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(C, prec=50)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: frobenius_

 frobenius_kernel

 frobenius_matrix





 [?7h[?12l[?25h[?25l[?7lmatrix(C, prec=50)[?7h[?12l[?25h[?25l[?7lkernel

 frobenius_kernel



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





[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [73], in <cell line: 1>()
----> 1 frobenius_kernel(C, prec=Integer(50))

File <string>:89, in frobenius_kernel(C, 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

TypeError: unsupported operand type(s) for +: 'int' and 'superelliptic_function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[5]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)

[?7h[?12l[?25h[?2004l[?7h[1/x*y^3, 1/x^2*y^3]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)[0].frobenius().coordinates()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [76], in <cell line: 1>()
----> 1 frobenius_kernel(C, prec=Integer(50))[Integer(0)].frobenius().coordinates()

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

[?7h[?12l[?25h[?2004l[5]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[0].frobenius().coordinates()[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)[0].frobenius().coordinates()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Input In [78], in <cell line: 1>()
----> 1 frobenius_kernel(C, prec=Integer(50))[Integer(0)].frobenius().coordinates()

File <string>:48, in coordinates(self, basis, basis_holo, prec)

File <string>:14, in prod(self, form, 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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[0].frobenius().coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l5)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)[0].frobenius().coordinates(prec=50)

[?7h[?12l[?25h[?2004l[?7h[1, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[0].frobenius().coordinates(prec=50)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)[0].frobenius()

[?7h[?12l[?25h[?2004l[?7h[1/x^3*y^9]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7lsage: M

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [81], in <cell line: 1>()
----> 1 M

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

[?7h[?12l[?25h[?2004l[5]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[0].frobenius()[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)[0].frobenius()

[?7h[?12l[?25h[?2004l[?7h[1/x^6*y^9]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[0].frobenius()[?7h[?12l[?25h[?25l[?7l().coordinates(prec=50)[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ltes(prec=50)[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)[0].frobenius().coordinates(prec=50)

[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq = 5[?7h[?12l[?25h[?25l[?7luadratic_form(parity_quadratic_form(v0, q))[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[5]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[0].frobenius().coordinates(prec=50)[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)[0].frobenius().coordinates(prec=50)

[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[0].frobenius().coordinates(prec=50)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)[0]

[?7h[?12l[?25h[?2004l[?7h[1/x^2*y^3]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 + x + 1, 2)[?7h[?12l[?25h[?25l[?7l.gens()[?7h[?12l[?25h[?25l[?7ldx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: C.dx

[?7h[?12l[?25h[?2004l[?7h1 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.dx.cartier()

[?7h[?12l[?25h[?2004l[?7h0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^2+x^4)*y^2*y.diffn()[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.cartier()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty()[1][?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lD[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.x*C.dx).cartier()

[?7h[?12l[?25h[?2004l[?7h0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.dx).cartier()[?7h[?12l[?25h[?25l[?7l.dx).cartier()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lC.dx).cartier()[?7h[?12l[?25h[?25l[?7l.C.dx).cartier()[?7h[?12l[?25h[?25l[?7loC.dx).cartier()[?7h[?12l[?25h[?25l[?7lnC.dx).cartier()[?7h[?12l[?25h[?25l[?7leC.dx).cartier()[?7h[?12l[?25h[?25l[?7l.C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.dx).cartier()[?7h[?12l[?25h[?25l[?7l.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.dx).cartier()[?7h[?12l[?25h[?25l[?7leC.dx).cartier()[?7h[?12l[?25h[?25l[?7l/C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.dx).cartier()[?7h[?12l[?25h[?25l[?7l.C.dx).cartier()[?7h[?12l[?25h[?25l[?7lxC.dx).cartier()[?7h[?12l[?25h[?25l[?7l*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lsage: (C.one/C.x*C.dx).cartier()

[?7h[?12l[?25h[?2004l[?7h0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.one/C.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lrun.term-0.term[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[0][?7h[?12l[?25h[?25l[?7lor i, x in eumerate(lista:[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l i, x in enumerate(lista):[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lsage: for om in C.basis_

 C.basis_de_rham_degrees                 

 C.basis_holomorphic_differentials_degree





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



[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7l

....: [?7h[?12l[?25h[?25l[?7lprint(i, x)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lom.serre_duality_pairing(f))[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()

....: [?7h[?12l[?25h[?25l[?7lsage: for om in C.holomorphic_differentials_basis():

....:     print(om.cartier())

....: 

[?7h[?12l[?25h[?2004l(1/y^3) dx
(x/y^2) dx
(1/y^2) dx
0 dx
0 dx
(1/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for om in C.holomorphic_differentials_basis():

....:     print(om.cartier())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(C.one/C.x*C.dx).carter()

 [?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.one/C.x*C.dx)

[?7h[?12l[?25h[?2004l[?7h(1/x) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.one/C.x*C.dx)[?7h[?12l[?25h[?25l[?7l().cartier()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrtier()[?7h[?12l[?25h[?25l[?7lsage: (C.one/C.x*C.dx).cartier()

[?7h[?12l[?25h[?2004l[?7h0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.cartier()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^4 = x^5 + x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.dx.cartier()[?7h[?12l[?25h[?25l[?7lis_smooth()[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_smooth()[?7h[?12l[?25h[?25l[?7lsage: C.is_smooth()

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.is_smooth()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.one/C.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l(C.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l()^*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l2*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lsage: ((C.x)^2*C.dx).cartier()

[?7h[?12l[?25h[?2004l[?7h0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x)^2*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l()*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l()*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l.*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lx*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lsage: ((C.x)*C.x*C.dx).cartier()

[?7h[?12l[?25h[?2004l[?7h0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq = 5[?7h[?12l[?25h[?25l[?7luadratic_form(parity_quadratic_form(v0, q))[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd
]0;~~$ cd Research/2021\ De\ Rham/DEReRhamComputation/
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add draft/supsage/drafty/superelliptic_cohomology_class.sage 
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ gid add -u
bash: gid: command not found
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ gid add -u[1@t
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git commit -m ""C"o"h"o"m"o"l"o"g"y" "o"f" "s"t"r"u"c"t"u"r"e" "s"h"e"a"f" "o"f" "s"u"p"e"r"e"l"l"i"p"t"i"c"
[master be66e7b] Cohomology of structure sheaf of superelliptic
 11 files changed, 7056 insertions(+), 82 deletions(-)
 delete mode 100644 sage/as_covers/as_cover/uniformizer.sage
 rewrite sage/drafty/draft3.sage (90%)
 create mode 100644 sage/drafty/superelliptic_cohomology_class.sage
]0;~/Research/2021 De Rham/DeRhamComputation~/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: 37, done.
Counting objects:   2% (1/37)
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Counting objects: 100% (37/37)
Counting objects: 100% (37/37), done.
Delta compression using up to 4 threads
Compressing objects:   4% (1/23)
Compressing objects:   8% (2/23)
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Compressing objects: 100% (23/23)
Compressing objects: 100% (23/23), done.
Writing objects:   4% (1/23)
Writing objects:   8% (2/23)
Writing objects:  13% (3/23)
Writing objects:  17% (4/23)
Writing objects:  26% (6/23)
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Writing objects:  47% (11/23)
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Writing objects:  56% (13/23)
Writing objects:  60% (14/23)
Writing objects:  65% (15/23)
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Writing objects:  95% (22/23)
Writing objects: 100% (23/23)
Writing objects: 100% (23/23), 73.16 KiB | 337.00 KiB/s, done.
Total 23 (delta 15), reused 0 (delta 0)
remote: . Processing 1 references
remote: Processed 1 references in total
To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git
   d77adde..be66e7b  master -> master
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[5]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.is_smooth()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^4 = x^5 + x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.is_smooth()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lbenius_matrix[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [3], in <cell line: 1>()
----> 1 C.frobenius_matrix()

File <string>:163, in frobenius_matrix(self, prec)

TypeError: unsupported operand type(s) for ** or pow(): 'superelliptic_cohomology' and 'method'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lbenius_matrix()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l5)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l5)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l5)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix(prec=50)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [5], in <cell line: 1>()
----> 1 C.frobenius_matrix(prec=Integer(50))

File <string>:163, in frobenius_matrix(self, prec)

TypeError: unsupported operand type(s) for ** or pow(): 'superelliptic_cohomology' and 'method'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix(prec=50)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2441, in sage.rings.polynomial.polynomial_element.Polynomial.__pow__()
   2440 try:
-> 2441     right = Integer(right)
   2442 except TypeError:

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 'method'> to an integer

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
Input In [7], in <cell line: 1>()
----> 1 C.frobenius_matrix(prec=Integer(50))

File <string>:163, in frobenius_matrix(self, prec)

File <string>:71, in __pow__(self, exp)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2443, in sage.rings.polynomial.polynomial_element.Polynomial.__pow__()
   2441         right = Integer(right)
   2442     except TypeError:
-> 2443         raise TypeError("non-integral exponents not supported")
   2444 
   2445 d = self.degree()

TypeError: non-integral exponents not supported
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x)*C.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.one/[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lsage: (C.x)^p

[?7h[?12l[?25h[?2004l[?7hx^7
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^4 = x^5 + x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprint(len(lista))[?7h[?12l[?25h[?25l[?7lsage: p

[?7h[?12l[?25h[?2004l[?7h7
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.frobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix(prec=50)

[?7h[?12l[?25h[?2004l[?7h[0 0 0 0 0 1]
[0 0 1 0 0 0]
[0 1 0 0 0 0]
[1 0 0 0 0 0]
[0 0 0 0 0 0]
[0 0 0 0 0 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldx.cartier()[?7h[?12l[?25h[?25l[?7le_rham_basis()[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: C.basis_

 C.basis_de_rham_degrees                 

 C.basis_holomorphic_differentials_degree

 C.basis_of_cohomology                   



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

 C.basis_de_rham_degrees                 





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

 C.basis_de_rham_degrees                 

 C.basis_holomorphic_differentials_degree[?7h[?12l[?25h[?25l[?7lof_cohomology



 C.basis_holomorphic_differentials_degree

 C.basis_of_cohomology                   [?7h[?12l[?25h[?25l[?7l







[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.basis_of_cohomology()

[?7h[?12l[?25h[?2004l[?7h[1/x*y, 1/x*y^2, 1/x^2*y^2, 1/x*y^3, 1/x^2*y^3, 1/x^3*y^3]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lC.basis_of_cohomology()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]^[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.basis_of_cohomology()[0]^p)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.basis_of_cohomology()[0]^p).coordinates()

[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 1, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

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

[?7h[?12l[?25h[?2004l[?7h7
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.basis_of_cohomology()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^4 = x^5 + x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l = 5[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: p = 3

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp = 3[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l(C.basis_of_cohomology()[0]^p).coordinates()[?7h[?12l[?25h[?25l[?7lsage: (C.basis_of_cohomology()[0]^p).coordinates()

[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq = 5[?7h[?12l[?25h[?25l[?7luadratic_form(parity_quadratic_form(v0, q))[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd ..
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ cd ..sagegit pushcommit -m "Cohomology of structure sheaf of superelliptic"
add -u
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -ucd ..sagegit pushsagecd ..git add -ugit add -ucd ..sagegit pushcommit -m "Cohomology of structure sheaf of superelliptic"
add -ucommit -m "Cohomology of structure sheaf of superelliptic"""""""""""""""""""""""""""""""""""""""""""""""c"o"h"o"m"o"l"o"g"y" "o"f" "s"t"r" "s"h"e"a"f" "d"o"d"a"n"y";" "z"m"i"""a"c"z"y"n"a"m"y" "z"m"i"e"n"i"a"c" "w"s"p"o"l"r"z"e"d"n"e" "w" "s"u"p"e"r"e"l"l"i"p"t"i"c" "h"o"l"o"
[master f683017] cohomology of str sheaf dodany; zaczynamy zmieniac wspolrzedne w superelliptic holo
 5 files changed, 194 insertions(+), 4 deletions(-)
]0;~/Research/2021 De Rham/DeRhamComputation~/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: 16, done.
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Counting objects: 100% (16/16), done.
Delta compression using up to 8 threads
Compressing objects:  11% (1/9)
Compressing objects:  22% (2/9)
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Compressing objects:  88% (8/9)
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Compressing objects: 100% (9/9), done.
Writing objects:  11% (1/9)
Writing objects:  22% (2/9)
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Writing objects:  44% (4/9)
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Writing objects: 100% (9/9), 4.68 KiB | 4.68 MiB/s, done.
Total 9 (delta 7), reused 0 (delta 0)
remote: . Processing 1 references
remote: Processed 1 references in total
To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git
   be66e7b..f683017  master -> master
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ cd sage
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd drafty/sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.basis_of_cohomology()[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7llomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[(1/y) dx, (1/y^2) dx, (x/y^2) dx, (1/y^3) dx, (x/y^3) dx, (x^2/y^3) dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbC.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7lbC.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7lbC.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7l C.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7l C.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7lC.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7l=C.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7l C.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: bbb = C.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3b[1][?7h[?12l[?25h[?25l[?7l*b[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la3*b[1][?7h[?12l[?25h[?25l[?7l 3*b[1][?7h[?12l[?25h[?25l[?7l=3*b[1][?7h[?12l[?25h[?25l[?7l 3*b[1][?7h[?12l[?25h[?25l[?7l3*b[1][?7h[?12l[?25h[?25l[?7l3*b[1][?7h[?12l[?25h[?25l[?7l3*b[1][?7h[?12l[?25h[?25l[?7la3*b[1][?7h[?12l[?25h[?25l[?7la3*b[1][?7h[?12l[?25h[?25l[?7la3*b[1][?7h[?12l[?25h[?25l[?7l 3*b[1][?7h[?12l[?25h[?25l[?7l=3*b[1][?7h[?12l[?25h[?25l[?7l 3*b[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = 3*b[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l ][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*b[1] -[?7h[?12l[?25h[?25l[?7l2*b[1] -[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: aaa = 2*bbb[1] + 2*bbb[2] + bbb[5]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa = 2*bbb[1] + 2*bbb[2] + bbb[5][?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aaa.coordinates()

[?7h[?12l[?25h[?2004l[?7h(0, 2, 2, 0, 0, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa.coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l2()[?7h[?12l[?25h[?25l[?7lsage: aaa.coordinates2()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [6], in <cell line: 1>()
----> 1 aaa.coordinates2()

File <string>:101, in coordinates2(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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa.coordinates2()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l = 2*bbb[1] + 2*bbb[2] + bbb[5][?7h[?12l[?25h[?25l[?7lbbbC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa.coordinates2()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcoordinates2()[?7h[?12l[?25h[?25l[?7lsage: aaa.coordinates2()

[?7h[?12l[?25h[?2004lbasis [((x^5 + x)/y^2) dx, ((x^5 + x)/y^3) dx, ((x^6 + x^2)/y^3) dx, 1 dx, x dx, (x^2) dx]
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [8], in <cell line: 1>()
----> 1 aaa.coordinates2()

File <string>:102, in coordinates2(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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7laa.coordinates2()[?7h[?12l[?25h[?25l[?7lsage: aaa.coordinates2()

[?7h[?12l[?25h[?2004lbasis [((x^5 + x)/y^2) dx, ((x^5 + x)/y^3) dx, ((x^6 + x^2)/y^3) dx, 1 dx, x dx, (x^2) dx]
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [10], in <cell line: 1>()
----> 1 aaa.coordinates2()

File <string>:102, in coordinates2(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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lsage: bbb

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

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lbbb[?7h[?12l[?25h[?25l[?7laaa.coordinates2()[?7h[?12l[?25h[?25l[?7lsage: aaa.coordinates2()

[?7h[?12l[?25h[?2004l[(1/y) dx, (1/y^2) dx, (x/y^2) dx, (1/y^3) dx, (x/y^3) dx, (x^2/y^3) dx] [y, y^2, y^2, y^3, y^3, y^3]
basis [((x^5 + x)/y^2) dx, ((x^5 + x)/y^3) dx, ((x^6 + x^2)/y^3) dx, 1 dx, x dx, (x^2) dx]
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [13], in <cell line: 1>()
----> 1 aaa.coordinates2()

File <string>:103, in coordinates2(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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(0, 2, 2, 0, 0, 1)
[(1/y) dx, (1/y^2) dx, (x/y^2) dx, (1/y^3) dx, (x/y^3) dx, (x^2/y^3) dx] [y, y^2, y^2, y^3, y^3, y^3] y^3
basis [((x^5 + x)/y^2) dx, ((x^5 + x)/y^3) dx, ((x^6 + x^2)/y^3) dx, 1 dx, x dx, (x^2) dx]
---------------------------------------------------------------------------
TypeError                                 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>:22, 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>:103, in coordinates2(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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lsage: bbb

[?7h[?12l[?25h[?2004l[?7h[(1/y) dx, (1/y^2) dx, (x/y^2) dx, (1/y^3) dx, (x/y^3) dx, (x^2/y^3) dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(0, 2, 2, 0, 0, 1)
[(1/y) dx, (1/y^2) dx, (x/y^2) dx, (1/y^3) dx, (x/y^3) dx, (x^2/y^3) dx] [y, y^2, y^2, y^3, y^3, y^3] y^3
basis [y^2, y, x*y, 1, x, x^2]
---------------------------------------------------------------------------
TypeError                                 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>:22, 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>:103, in coordinates2(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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(0, 2, 2, 0, 0, 1)
[(1/y) dx, (1/y^2) dx, (x/y^2) dx, (1/y^3) dx, (x/y^3) dx, (x^2/y^3) dx] [y, y^2, y^2, y^3, y^3, y^3] y^3
basis [y^2, y, x*y, 1, x, x^2]
[0, 2, 2, 0, 0, 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(0, 2, 2, 0, 0, 1)
[(1/y) dx, (1/y^2) dx, (x/y^2) dx, (1/y^3) dx, (x/y^3) dx, (x^2/y^3) dx] [y, y^2, y^2, y^3, y^3, y^3] y^3
basis [y^2, y, x*y, 1, x, x^2]
[0, 2, 2, 0, 0, 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7lt.sage')[?7h[?12l[?25h[?25l[?7le.sage')[?7h[?12l[?25h[?25l[?7ls.sage')[?7h[?12l[?25h[?25l[?7lt.sage')[?7h[?12l[?25h[?25l[?7ls.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

[?7h[?12l[?25h[?2004lsuperelliptic form coordinates test:
[(1/y) dx, (1/y^2) dx, (x/y^2) dx, (1/y^3) dx, (x/y^3) dx, (x^2/y^3) dx] [y, y^2, y^2, y^3, y^3, y^3] y^3
basis [y^2, y, x*y, 1, x, x^2]
False
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

[?7h[?12l[?25h[?2004lsuperelliptic form coordinates test:
[(1/y) dx, (1/y^2) dx, (x/y^2) dx, (1/y^3) dx, (x/y^3) dx, (x^2/y^3) dx] [y, y^2, y^2, y^3, y^3, y^3] y^3
basis [y^2, y, x*y, 1, x, x^2]
False
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

[?7h[?12l[?25h[?2004lsuperelliptic form coordinates test:
[(1/y) dx, (1/y^2) dx, (x/y^2) dx, (1/y^3) dx, (x/y^3) dx, (x^2/y^3) dx] [y, y^2, y^2, y^3, y^3, y^3] y^3
basis [y^2, y, x*y, 1, x, x^2]
True
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('tests.sage')[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7li.sage')[?7h[?12l[?25h[?25l[?7ln.sage')[?7h[?12l[?25h[?25l[?7li.sage')[?7h[?12l[?25h[?25l[?7lt.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[0, 2, 2, 0, 0, 1]
---------------------------------------------------------------------------
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>:22, 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>

AttributeError: 'superelliptic_form' object has no attribute 'coordinates2'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7lt.sage')[?7h[?12l[?25h[?25l[?7le.sage')[?7h[?12l[?25h[?25l[?7ls.sage')[?7h[?12l[?25h[?25l[?7lt.sage')[?7h[?12l[?25h[?25l[?7ls.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

[?7h[?12l[?25h[?2004lsuperelliptic form coordinates test:
True
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^4 = x^5 + x over Finite Field of size 7
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7ldx.cartier()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxC.dx[?7h[?12l[?25h[?25l[?7l^C.dx[?7h[?12l[?25h[?25l[?7l(C.dx[?7h[?12l[?25h[?25l[?7l()C.dx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)C.dx[?7h[?12l[?25h[?25l[?7l-)C.dx[?7h[?12l[?25h[?25l[?7l1)C.dx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()*C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^(p-1)*C.dx[?7h[?12l[?25h[?25l[?7l.x^(p-1)*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfC.x^(p-1)*C.dx[?7h[?12l[?25h[?25l[?7lfC.x^(p-1)*C.dx[?7h[?12l[?25h[?25l[?7lfC.x^(p-1)*C.dx[?7h[?12l[?25h[?25l[?7lfC.x^(p-1)*C.dx[?7h[?12l[?25h[?25l[?7l C.x^(p-1)*C.dx[?7h[?12l[?25h[?25l[?7l=C.x^(p-1)*C.dx[?7h[?12l[?25h[?25l[?7l C.x^(p-1)*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ffff = C.x^(p-1)*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lffff = C.x^(p-1)*C.dx[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: ffff

[?7h[?12l[?25h[?2004l[?7h(x^6) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lffff[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ffff.cartier()

[?7h[?12l[?25h[?2004l[?7h0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lffff.cartier()[?7h[?12l[?25h[?25l[?7lor om in C.holomorphic_differentials_basis():[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li,x in enumerate(lista):[?7h[?12l[?25h[?25l[?7l inrange(0, p):[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7linr[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l range(0, p):[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lrange[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: for i in range(0, p^2):

....: [?7h[?12l[?25h[?25l[?7lfor B in range(-10, 30):[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l....:     ffff = (C.x)^i*C.dx

....: [?7h[?12l[?25h[?25l[?7lprint(om.cartier())[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:     print(ffff.cartier())

....: [?7h[?12l[?25h[?25l[?7lsage: for i in range(0, p^2):

....:     ffff = (C.x)^i*C.dx

....:     print(ffff.cartier())

....: 

[?7h[?12l[?25h[?2004l0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7li.sage')[?7h[?12l[?25h[?25l[?7ln.sage')[?7h[?12l[?25h[?25l[?7li.sage')[?7h[?12l[?25h[?25l[?7lt.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTraceback (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 [29] 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>:22 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>:9
    a = C.x**(p-_sage_const_1 )C.dx
                               ^
SyntaxError: invalid syntax

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

[?7h[?12l[?25h[?2004l0 0
0 0
0 0
0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lx^2 1
0 0
0 0
0 0
1 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa.coordinates2()[?7h[?12l[?25h[?25l[?7l.prod(C.holomorphic_differentials_basis()[3])[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a.cartier()

[?7h[?12l[?25h[?2004lx^2 1
0 0
0 0
0 0
[?7h1 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.cartier()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l1 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la.cartier()[?7h[?12l[?25h[?25l[?7lsage: a.cartier()

[?7h[?12l[?25h[?2004l[?7h1 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.cartier()[?7h[?12l[?25h[?25l[?7l = basis_of_cohomology(C)[0][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.cartier()[?7h[?12l[?25h[?25l[?7l = basis_of_cohomology(C)[0][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: a = C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = C.dx[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: a/C.x

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [36], in <cell line: 1>()
----> 1 a/C.x

TypeError: unsupported operand type(s) for /: 'superelliptic_form' and 'superelliptic_function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la/C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in range(0, p^2):[?7h[?12l[?25h[?25l[?7l =d/(e*g)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l1.[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f = superelliptic_function(C, 1/x)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = superelliptic_function(C, 1/x)[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: f*C.dx

[?7h[?12l[?25h[?2004l[?7h(1/x) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf*C.dx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(f*C.dx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (f*C.dx).cartier()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [39], in <cell line: 1>()
----> 1 (f*C.dx).cartier()

File <string>:52, in cartier(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
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l1 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(f*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lf*C.dx[?7h[?12l[?25h[?25l[?7l = superelliptic_function(C, 1/x)[?7h[?12l[?25h[?25l[?7la/C.x[?7h[?12l[?25h[?25l[?7lf = superelliptic_function(C, 1/x)[?7h[?12l[?25h[?25l[?7lsage: f = superelliptic_function(C, 1/x)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = superelliptic_function(C, 1/x)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(f*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lsage: (f*C.dx).cartier()

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

[?7h[?12l[?25h[?2004l0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l0 dx
1 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(1/x) dx
1 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llist_of_m = [m for m in list_of_m if m%p != 0][?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(1/x) dx
1 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^4 = x^5 + x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix(prec=50)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [3], in <cell line: 1>()
----> 1 C.frobenius_matrix(prec=Integer(50))

File <string>:164, in frobenius_matrix(self, prec)

File <string>:90, in coordinates(self, basis, basis_holo, prec)

NameError: name 'basis_of_cohomology' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lbasis_of_cohomology()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lis_of_cohomology()[?7h[?12l[?25h[?25l[?7lsage: C.basis_of_cohomology()

[?7h[?12l[?25h[?2004l[?7h[1/x*y, 1/x*y^2, 1/x^2*y^2, 1/x*y^3, 1/x^2*y^3, 1/x^3*y^3]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(1/x) dx
1 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.basis_of_cohomology()[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix(prec=50)

[?7h[?12l[?25h[?2004l[?7h[0 0 0 1 0 0]
[0 0 1 0 0 0]
[0 1 0 0 0 0]
[0 0 0 0 0 0]
[0 0 0 0 0 0]
[1 0 0 0 0 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lj[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lkronecker_symbol(7, 8)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = superelliptic_function(C, 1/x)[?7h[?12l[?25h[?25l[?7lrobenius_kernel(C, prec=50)[0][?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lenius_kernel(C, prec=50)[0][?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)[0]

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [7], in <cell line: 1>()
----> 1 frobenius_kernel(C, prec=Integer(50))[Integer(0)]

File <string>:3, in frobenius_kernel(C, prec)

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

[?7h[?12l[?25h[?2004l(1/x) dx
1 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[0][?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)[0]

[?7h[?12l[?25h[?2004l[?7h1/x*y^3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)

[?7h[?12l[?25h[?2004l[?7h[1/x*y^3, 1/x^2*y^3]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: bbb = C.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: bbb[0].cartier()

[?7h[?12l[?25h[?2004l[?7h(1/y^3) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcartier_matrix()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrtier_matrix()[?7h[?12l[?25h[?25l[?7lsage: C.cartier_matrix()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Input In [13], in <cell line: 1>()
----> 1 C.cartier_matrix()

File <string>:155, in cartier_matrix(self)

File /ext/sage/9.7/src/sage/matrix/matrix0.pyx:1507, in sage.matrix.matrix0.Matrix.__setitem__()
   1505 else:
   1506     if row_list_len != len(value_list):
-> 1507         raise IndexError("value does not have the right number of rows")
   1508     for value_row in value_list:
   1509         if col_list_len != len(value_row):

IndexError: value does not have the right number of rows
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cartier_matrix()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(1/x) dx
1 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cartier_matrix()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrtier_matrix()[?7h[?12l[?25h[?25l[?7lsage: C.cartier_matrix()

[?7h[?12l[?25h[?2004l[?7h[0 0 0 1 0 0]
[0 0 1 0 0 0]
[0 1 0 0 0 0]
[0 0 0 0 0 0]
[0 0 0 0 0 0]
[1 0 0 0 0 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[0].cartier()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: bbb = C.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[0].cartier()[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l].cartier()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l(*)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: bbb[0].cartier().coordinates()

[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 1, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(1/x) dx
1 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cartier_matrix()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcartier_matrix()[?7h[?12l[?25h[?25l[?7lsage: C.cartier_matrix()

[?7h[?12l[?25h[?2004l[?7h[0 0 0 0 0 1]
[0 0 1 0 0 0]
[0 1 0 0 0 0]
[1 0 0 0 0 0]
[0 0 0 0 0 0]
[0 0 0 0 0 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cartier_matrix()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lbbb[0].cartier().coordinates()[?7h[?12l[?25h[?25l[?7l = C.holomorphic_differntials_basis()[?7h[?12l[?25h[?25l[?7lsage: bbb = C.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lC.cartier_matrix()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lbbb[0].cartier().coordinates()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: bbb[0].cartier().coordinates()

[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 1, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[0].cartier().coordinates()[?7h[?12l[?25h[?25l[?7l = C.holomorphic_differntials_basis()[?7h[?12l[?25h[?25l[?7l[0].cartier().coordinats()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l].cartier().cordinates()[?7h[?12l[?25h[?25l[?7l1].cartier().cordinates()[?7h[?12l[?25h[?25l[?7lsage: bbb[1].cartier().coordinates()

[?7h[?12l[?25h[?2004l[?7h[0, 0, 1, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[1].cartier().coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l].cartier().cordinates()[?7h[?12l[?25h[?25l[?7l5].cartier().cordinates()[?7h[?12l[?25h[?25l[?7lsage: bbb[5].cartier().coordinates()

[?7h[?12l[?25h[?2004l[?7h[1, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [24], 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>:23, 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>:10, in <module>

File <string>:137, in pth_root(self)

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

[?7h[?12l[?25h[?2004l2*x^2*y^3 + x^5*y^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l2*x^2*y^3 + x^5*y^2 2*x^2*y^3 + x^5*y^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cartier_matrix()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)^p[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.x).pth_root()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [27], in <cell line: 1>()
----> 1 (C.x).pth_root()

File <string>:132, in pth_root(self)

ValueError: Function is not a p-th power.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lFalse
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [28], 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>:23, 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>:134, in pth_root(self)

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

[?7h[?12l[?25h[?2004lTrue
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [29], 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>:23, 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>:139, in pth_root(self)

ValueError: Function is not a p-th power.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ltess.sage')[?7h[?12l[?25h[?25l[?7l(ests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

[?7h[?12l[?25h[?2004lp-th root test:
True
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [30], 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>:4, 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>:139, in pth_root(self)

ValueError: Function is not a p-th power.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cartier_matrix()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^4 = x^5 + x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.cartier_matrix()[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lkronecker_symbol(7, 8)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lnel[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lobenius_kernel(C, prec=50)[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)

[?7h[?12l[?25h[?2004l[?7h[1/x*y^3, 1/x^2*y^3]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[?7h[?12l[?25h[?25l[?7l()[0][?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)[0]

[?7h[?12l[?25h[?2004l[?7h1/x*y^3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la/C.x[?7h[?12l[?25h[?25l[?7laacoordinates2()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = 2*bbb[1] + 2*bbb[2] + bbb[5][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lnius_kernel[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: aaa = frobenius_kernel(C)[0]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa = frobenius_kernel(C)[0][?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lsage: aaa^p

[?7h[?12l[?25h[?2004l[?7h((x^8 + 2*x^4 + 1)/x)*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[5].cartier().coordinates()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l = C.holomorphic_differntials_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l%[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lsage: bbb = aaa^p

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb = aaa^p[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsage: bbb.function

[?7h[?12l[?25h[?2004l[?7h((x^8 + 2*x^4 + 1)/x)*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb.function[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcb.function[?7h[?12l[?25h[?25l[?7lcb.function[?7h[?12l[?25h[?25l[?7lcb.function[?7h[?12l[?25h[?25l[?7l b.function[?7h[?12l[?25h[?25l[?7l-b.function[?7h[?12l[?25h[?25l[?7l b.function[?7h[?12l[?25h[?25l[?7lsage: ccc - bbb.function

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [38], in <cell line: 1>()
----> 1 ccc - bbb.function

NameError: name 'ccc' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lccc - bbb.function[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l b.function[?7h[?12l[?25h[?25l[?7l= b.function[?7h[?12l[?25h[?25l[?7lsage: ccc = bbb.function

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lccc = bbb.function[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lnc[?7h[?12l[?25h[?25l[?7luc[?7h[?12l[?25h[?25l[?7lmc[?7h[?12l[?25h[?25l[?7lec[?7h[?12l[?25h[?25l[?7lrc[?7h[?12l[?25h[?25l[?7lac[?7h[?12l[?25h[?25l[?7ltc[?7h[?12l[?25h[?25l[?7loc[?7h[?12l[?25h[?25l[?7lrc[?7h[?12l[?25h[?25l[?7l(c[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: numerator(ccc)

[?7h[?12l[?25h[?2004l[?7h(x^8 + 2*x^4 + 1)*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmm.f[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: monomials(ccc)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [41], in <cell line: 1>()
----> 1 monomials(ccc)

TypeError: monomials() missing 1 required positional argument: 'n'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmonomials(ccc)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcmonomials()[?7h[?12l[?25h[?25l[?7lcmonomials()[?7h[?12l[?25h[?25l[?7lcmonomials()[?7h[?12l[?25h[?25l[?7l.monomials()[?7h[?12l[?25h[?25l[?7lsage: ccc.monomials()

[?7h[?12l[?25h[?2004l[?7h[y]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lccc.monomials()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpc[?7h[?12l[?25h[?25l[?7lac[?7h[?12l[?25h[?25l[?7lrc[?7h[?12l[?25h[?25l[?7lec[?7h[?12l[?25h[?25l[?7lnc[?7h[?12l[?25h[?25l[?7ltc[?7h[?12l[?25h[?25l[?7l(c[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: parent(ccc)

[?7h[?12l[?25h[?2004l[?7hUnivariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFF = FractionField(F)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: Fxy

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [44], in <cell line: 1>()
----> 1 Fxy

NameError: name 'Fxy' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y = self.fct_field[?7h[?12l[?25h[?25l[?7lsage: Fxy, Rxy, x, y = self.fct_field

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [45], in <cell line: 1>()
----> 1 Fxy, Rxy, x, y = self.fct_field

NameError: name 'self' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y = self.fct_field[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsel.fct_field[?7h[?12l[?25h[?25l[?7l.fct_field[?7h[?12l[?25h[?25l[?7l.fct_field[?7h[?12l[?25h[?25l[?7l.fct_field[?7h[?12l[?25h[?25l[?7lC.fct_field[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: Fxy, Rxy, x, y = C.fct_field

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y = C.fct_field[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: Fxy

[?7h[?12l[?25h[?2004l[?7hFraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7lini.sage')[?7h[?12l[?25h[?25l[?7l(nit.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            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>:23, 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>:30, in <module>

File <string>:13, in decomposition_g0_g8(fct)

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

[?7h[?12l[?25h[?2004l[((x^8 + 2*x^4 + 1)/x)*y, ((x^8 + 2*x^4 + 1)/x^4)*y]
---------------------------------------------------------------------------
AttributeError                            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>:23, 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>:31, in <module>

File <string>:14, in decomposition_g0_g8(fct)

AttributeError: 'list' object has no attribute 'curve'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lkronecker_symbol(7, 8)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lsage: ker

[?7h[?12l[?25h[?2004l[?7h[1/x*y^3, 1/x^2*y^3]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa^p[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: aaa

[?7h[?12l[?25h[?2004l[?7h[((x^8 + 2*x^4 + 1)/x)*y, ((x^8 + 2*x^4 + 1)/x^4)*y]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: aaa

[?7h[?12l[?25h[?2004l[?7h[((x^8 + 2*x^4 + 1)/x)*y, ((x^8 + 2*x^4 + 1)/x^4)*y]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lker[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]^[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lsage: ker[0]^p

[?7h[?12l[?25h[?2004l[?7h((x^8 + 2*x^4 + 1)/x)*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l((x^8 + 2*x^4 + 1)/x)*y
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [54], 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>:23, 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>:31, in <module>

File <string>:15, in decomposition_g0_g8(fct)

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

[?7h[?12l[?25h[?2004l((x^8 + 2*x^4 + 1)/x)*y
---------------------------------------------------------------------------
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()

AttributeError: 'function' object has no attribute 'numerator'

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
Input In [55], 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>:23, 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>:31, in <module>

File <string>:19, in decomposition_g0_g8(fct)

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

File <string>:209, 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: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 <function denominator at 0x7f0bd4ee8820>/1 to an element of Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l! (x^8*y - x^4*y + y)/x
---------------------------------------------------------------------------
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()

AttributeError: 'function' object has no attribute 'numerator'

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
Input In [56], 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>:23, 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>:31, in <module>

File <string>:19, in decomposition_g0_g8(fct)

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

File <string>:209, 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: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 <function denominator at 0x7f0bd4ee8820>/1 to an element of Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: aaa

[?7h[?12l[?25h[?2004l[?7h[((x^8 + 2*x^4 + 1)/x)*y, ((x^8 + 2*x^4 + 1)/x^4)*y]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsage: aaa[0].function

[?7h[?12l[?25h[?2004l[?7h((x^8 + 2*x^4 + 1)/x)*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[0].function[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lna[0].function[?7h[?12l[?25h[?25l[?7lua[0].function[?7h[?12l[?25h[?25l[?7lma[0].function[?7h[?12l[?25h[?25l[?7lea[0].function[?7h[?12l[?25h[?25l[?7lra[0].function[?7h[?12l[?25h[?25l[?7la[0].function[?7h[?12l[?25h[?25l[?7lta[0].function[?7h[?12l[?25h[?25l[?7loa[0].function[?7h[?12l[?25h[?25l[?7lra[0].function[?7h[?12l[?25h[?25l[?7l(a[0].function[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: numerator(aaa[0].function)

[?7h[?12l[?25h[?2004l[?7h(x^8 + 2*x^4 + 1)*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[0].function[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpa[0][?7h[?12l[?25h[?25l[?7la[0][?7h[?12l[?25h[?25l[?7lra[0][?7h[?12l[?25h[?25l[?7lea[0][?7h[?12l[?25h[?25l[?7lna[0][?7h[?12l[?25h[?25l[?7lta[0][?7h[?12l[?25h[?25l[?7l(a[0][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: parent(aaa[0])

[?7h[?12l[?25h[?2004l[?7h<class '__main__.superelliptic_function'>
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(aaa[0])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7lsage: parent(aaa[0].function)

[?7h[?12l[?25h[?2004l[?7hUnivariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[0].function[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0].function[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lna[0][?7h[?12l[?25h[?25l[?7lua[0][?7h[?12l[?25h[?25l[?7lma[0][?7h[?12l[?25h[?25l[?7lea[0][?7h[?12l[?25h[?25l[?7lra[0][?7h[?12l[?25h[?25l[?7la[0][?7h[?12l[?25h[?25l[?7lta[0][?7h[?12l[?25h[?25l[?7loa[0][?7h[?12l[?25h[?25l[?7lra[0][?7h[?12l[?25h[?25l[?7l(a[0][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a[0][?7h[?12l[?25h[?25l[?7l(a[0][?7h[?12l[?25h[?25l[?7l(a[0][?7h[?12l[?25h[?25l[?7l(a[0][?7h[?12l[?25h[?25l[?7l(a[0][?7h[?12l[?25h[?25l[?7l(a[0][?7h[?12l[?25h[?25l[?7l(a[0][?7h[?12l[?25h[?25l[?7l(a[0][?7h[?12l[?25h[?25l[?7l(a[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lF(a[0][?7h[?12l[?25h[?25l[?7lx(a[0][?7h[?12l[?25h[?25l[?7ly(a[0][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: Fxy(aaa[0])

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
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()

AttributeError: 'superelliptic_function' object has no attribute 'numerator'

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
Input In [62], in <cell line: 1>()
----> 1 Fxy(aaa[Integer(0)])

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 ((x^8 + 2*x^4 + 1)/x)*y/1 to an element of Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy(aaa[0])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7lsage: Fxy(aaa[0].function)

[?7h[?12l[?25h[?2004l[?7h(x^8*y - x^4*y + y)/x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy(aaa[0].function)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: Fxy(aaa[0].function).denominator()

[?7h[?12l[?25h[?2004l[?7hx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy(aaa[0].function).denominator()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l! (x^8*y - x^4*y + y)/x
---------------------------------------------------------------------------
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()

AttributeError: 'function' object has no attribute 'numerator'

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
Input In [65], 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>:23, 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>:31, in <module>

File <string>:19, in decomposition_g0_g8(fct)

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

File <string>:209, 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: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 <function denominator at 0x7f0bd4ee8820>/1 to an element of Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l! (x^8*y - x^4*y + y)/x
x^8*y - x^4*y + y x
---------------------------------------------------------------------------
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()

AttributeError: 'function' object has no attribute 'numerator'

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
Input In [66], 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>:23, 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>:32, in <module>

File <string>:20, in decomposition_g0_g8(fct)

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

File <string>:209, 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: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 <function denominator at 0x7f0bd4ee8820>/1 to an element of Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l! (x^8*y - x^4*y + y)/x
x^8*y - x^4*y + y x
---------------------------------------------------------------------------
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/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    160     print(type(C._element_constructor), C._element_constructor)
--> 161 raise
    162 

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/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x)
   1184 try:
-> 1185     return integer_mod.IntegerMod(self, x)
   1186 except (NotImplementedError, PariError):

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

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:391, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
    390         else:
--> 391             raise
    392 self.set_from_mpz(z.value)

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:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    160     print(type(C._element_constructor), C._element_constructor)
--> 161 raise
    162 

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/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 'function'> to an integer

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
Input In [67], 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>:23, 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>:32, in <module>

File <string>:20, in decomposition_g0_g8(fct)

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

[?7h[?12l[?25h[?2004l! (x^8*y - x^4*y + y)/x
x^8*y - x^4*y + y x
---------------------------------------------------------------------------
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/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    160     print(type(C._element_constructor), C._element_constructor)
--> 161 raise
    162 

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/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x)
   1184 try:
-> 1185     return integer_mod.IntegerMod(self, x)
   1186 except (NotImplementedError, PariError):

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

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:391, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
    390         else:
--> 391             raise
    392 self.set_from_mpz(z.value)

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:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    160     print(type(C._element_constructor), C._element_constructor)
--> 161 raise
    162 

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/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 'function'> to an integer

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
Input In [68], 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>:23, 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>:33, in <module>

File <string>:20, in decomposition_g0_g8(fct)

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

[?7h[?12l[?25h[?2004l! (x^8*y - x^4*y + y)/x
x^8*y - x^4*y + y x Multivariate Polynomial Ring in x, y over Finite Field of size 3 <class 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular'>
---------------------------------------------------------------------------
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/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    160     print(type(C._element_constructor), C._element_constructor)
--> 161 raise
    162 

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/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x)
   1184 try:
-> 1185     return integer_mod.IntegerMod(self, x)
   1186 except (NotImplementedError, PariError):

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

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:391, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
    390         else:
--> 391             raise
    392 self.set_from_mpz(z.value)

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:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    160     print(type(C._element_constructor), C._element_constructor)
--> 161 raise
    162 

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/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 'function'> to an integer

During handling of the above exception, another exception occurred:

TypeError                                 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>:23, 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>:33, in <module>

File <string>:20, in decomposition_g0_g8(fct)

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

[?7h[?12l[?25h[?2004l((x^8 + 2*x^4 + 1)*y, 0)
((x^8 + 2*x^4)*y, y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(((x^8 + 2*x^4 + 1)/x)*y, 0)
((x^4 + 2)*y, 1/x^4*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.cartier_matrix()[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lX[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.y/C.x).coordinates()

[?7h[?12l[?25h[?2004l[?7h[1, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[0].function[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: aaa

[?7h[?12l[?25h[?2004l[?7h[((x^8 + 2*x^4 + 1)/x)*y, ((x^8 + 2*x^4 + 1)/x^4)*y]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[0].function[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].function[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7linates()[?7h[?12l[?25h[?25l[?7lsage: aaa[0].coordinates()

[?7h[?12l[?25h[?2004l[?7h[1, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lker[0]^p[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lsage: ker

[?7h[?12l[?25h[?2004l[?7h[1/x*y^3, 1/x^2*y^3]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lker[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[0]^p[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]^[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^4 = x^5 + x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(aaa[0].function)[?7h[?12l[?25h[?25l[?7lsage: p

[?7h[?12l[?25h[?2004l[?7h3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lker[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[0]^p[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]^p[?7h[?12l[?25h[?25l[?7lsage: ker[0]^p

[?7h[?12l[?25h[?2004l[?7h((x^8 + 2*x^4 + 1)/x)*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lker[0]^p[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(ker[0]^p)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (ker[0]^p).coordinates()

[?7h[?12l[?25h[?2004l[?7h[1, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^4 = x^5 + x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.cartier_matrix()[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lbenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix(prec=50)

[?7h[?12l[?25h[?2004l[?7h[0 0 0 1 0 0]
[0 0 1 0 0 0]
[0 1 0 0 0 0]
[0 0 0 0 0 0]
[0 0 0 0 0 0]
[1 0 0 0 0 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[0].coordinates()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = frbenus_kernel(C)[0][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCbasis_of[?7h[?12l[?25h[?25l[?7l.basis_of[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_cohomology[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aaa = C.basis_of_cohomology()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa = C.basis_of_cohomology()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[0].coordinates()[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: aaa[0]

[?7h[?12l[?25h[?2004l[?7h1/x*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[0][?7h[?12l[?25h[?25l[?7l[].coordinates()[?7h[?12l[?25h[?25l[?7lfuncton[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aaa[0].frobenius()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [84], in <cell line: 1>()
----> 1 aaa[Integer(0)].frobenius()

AttributeError: 'superelliptic_function' object has no attribute 'frobenius'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[0].frobenius()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]^[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aaa[0]^p.coordinates()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [85], in <cell line: 1>()
----> 1 aaa[Integer(0)]**p.coordinates()

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 'coordinates'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[0]^p.coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a[0]^p.cordinates()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().cordinates()[?7h[?12l[?25h[?25l[?7lsage: (aaa[0]^p).coordinates()

[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[0]^p.coordinates()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: aaa[4]

[?7h[?12l[?25h[?2004l[?7h1/x^2*y^3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[4][?7h[?12l[?25h[?25l[?7l[]^[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aaa[4]^p.coordinates()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [88], in <cell line: 1>()
----> 1 aaa[Integer(4)]**p.coordinates()

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 'coordinates'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[4]^p.coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l).cordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a[4]^p).cordinates()[?7h[?12l[?25h[?25l[?7lsage: (aaa[4]^p).coordinates()

[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(aaa[4]^p).coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]^p).cordinates()[?7h[?12l[?25h[?25l[?7l5]^p).cordinates()[?7h[?12l[?25h[?25l[?7lsage: (aaa[5]^p).coordinates()

[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[4]^p.coordinates()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: aaa[4]

[?7h[?12l[?25h[?2004l[?7h1/x^2*y^3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[4][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l5][?7h[?12l[?25h[?25l[?7lsage: aaa[5]

[?7h[?12l[?25h[?2004l[?7h1/x^3*y^3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[0][?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lbenius_kernel(C, prec=50)[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)

[?7h[?12l[?25h[?2004l[?7h[1/x*y^3, 1/x^2*y^3]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[
(0, 0, 0, 1, 0, 0),
(0, 0, 0, 0, 1, 0)
]
(((x^8 + 2*x^4 + 1)/x)*y, 0)
((x^4 + 2)*y, 1/x^4*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lbenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix(prec=50).kernel().basis()

[?7h[?12l[?25h[?2004l[?7h[
(0, 0, 0, 1, 0, 0),
(0, 0, 0, 0, 1, 0)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50).kernel().basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.frobenius_matrix(prec=50).kernel().basis()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lrkernel().basis()[?7h[?12l[?25h[?25l[?7lkernel().basis()[?7h[?12l[?25h[?25l[?7ltkernel().basis()[?7h[?12l[?25h[?25l[?7lrkernel().basis()[?7h[?12l[?25h[?25l[?7lakernel().basis()[?7h[?12l[?25h[?25l[?7lnkernel().basis()[?7h[?12l[?25h[?25l[?7lskernel().basis()[?7h[?12l[?25h[?25l[?7lpkernel().basis()[?7h[?12l[?25h[?25l[?7lokernel().basis()[?7h[?12l[?25h[?25l[?7lskernel().basis()[?7h[?12l[?25h[?25l[?7lekernel().basis()[?7h[?12l[?25h[?25l[?7l(kernel().basis()[?7h[?12l[?25h[?25l[?7l()kernel().basis()[?7h[?12l[?25h[?25l[?7l().kernel().basis()[?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix(prec=50).transpose().kernel().basis()

[?7h[?12l[?25h[?2004l[?7h[
(0, 0, 0, 0, 1, 0),
(0, 0, 0, 0, 0, 1)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldimension_of_RHS = p*gY + (len(list_of_m) - 1)*(p-1) + sum(sum(i*alpha(i, m, p) for i in range(1, p)) for m in list_of_m)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[
(0, 0, 0, 0, 1, 0),
(0, 0, 0, 0, 0, 1)
]
((x^4 + 2)*y, 1/x^4*y)
(x*y, ((2*x^4 + 1)/x^7)*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[
(0, 0, 0, 0, 1, 0),
(0, 0, 0, 0, 0, 1)
]
((x^4 + 2)*y, 1/x^4*y)
(x*y, ((2*x^4 + 1)/x^7)*y)
((x/(x^4 + 1))*y^3, (1/(x^7 + x^3))*y^3)
(0, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[
(0, 0, 0, 0, 1, 0),
(0, 0, 0, 0, 0, 1)
]
((x^4 + 2)*y, 1/x^4*y)
(x*y, ((2*x^4 + 1)/x^7)*y)
!
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [99], 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>:23, 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>:52, in <module>

File <string>:47, in decomposition_omega0_omega8(omega, prec)

File <string>:38, in __add__(self, other)

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

[?7h[?12l[?25h[?2004l[
(0, 0, 0, 0, 1, 0),
(0, 0, 0, 0, 0, 1)
]
((x^4 + 2)*y, 1/x^4*y)
(x*y, ((2*x^4 + 1)/x^7)*y)
!
((x^2/y) dx, (1/(x^2*y)) dx)
(0 dx, 0 dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lker[0]^p[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lsage: ker

[?7h[?12l[?25h[?2004l[?7h[1/x^2*y^3, 1/x^3*y^3]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[
(0, 0, 0, 0, 1, 0),
(0, 0, 0, 0, 0, 1)
]
((x^4 + 2)*y, 1/x^4*y)
(x*y, ((2*x^4 + 1)/x^7)*y)
!
1
1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[
(0, 0, 0, 0, 1, 0),
(0, 0, 0, 0, 0, 1)
]
((x^4 + 2)*y, 1/x^4*y)
(x*y, ((2*x^4 + 1)/x^7)*y)
!
1
1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50).transpose().kernel().basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basi()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7llomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [104], 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>:23, 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>

NameError: name 'basis_W2Omega' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[<__main__.superelliptic_drw_form object at 0x7f0b7df25930>, <__main__.superelliptic_drw_form object at 0x7f0b7df26050>, <__main__.superelliptic_drw_form object at 0x7f0b7df256f0>, <__main__.superelliptic_drw_form object at 0x7f0b7df25330>, <__main__.superelliptic_drw_form object at 0x7f0b7df265f0>, <__main__.superelliptic_drw_form object at 0x7f0b7df263e0>]
!
1
1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[[0] d[x] + V((x^2/y^3) dx) + dV([0]), [0] d[x] + V((x/(x^4*y^2 + y^2)) dx) + dV([0]), [0] d[x] + V((x^4/(x^4*y^2 + y^2)) dx) + dV([0]), [0] d[x] + V((1/(x^8*y - x^4*y + y)) dx) + dV([0]), [0] d[x] + V((x^3/(x^8*y - x^4*y + y)) dx) + dV([0]), [0] d[x] + V((x^6/(x^8*y - x^4*y + y)) dx) + dV([0])]
!
1
1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: V = GF(p)^3

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV = GF(p)^3[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[],[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: V.subspace([1, 2, 2], [1, 1, 1])

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
File /ext/sage/9.7/src/sage/modules/free_module.py:6394, in FreeModule_submodule_with_basis_pid.__init__(self, ambient, basis, check, echelonize, echelonized_basis, already_echelonized)
   6393 try:
-> 6394     basis = [ambient(x) for x in basis]
   6395 except TypeError:
   6396     # That failed, try the ambient vector space instead

File /ext/sage/9.7/src/sage/modules/free_module.py:6394, in <listcomp>(.0)
   6393 try:
-> 6394     basis = [ambient(x) for x in basis]
   6395 except TypeError:
   6396     # That failed, try the ambient vector space instead

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:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    160     print(type(C._element_constructor), C._element_constructor)
--> 161 raise
    162 

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/modules/free_module.py:6281, in FreeModule_ambient_field._element_constructor_(self, e, *args, **kwds)
   6280     pass
-> 6281 return FreeModule_generic_field._element_constructor_(self, e, *args, **kwds)

File /ext/sage/9.7/src/sage/modules/free_module.py:2096, in FreeModule_generic._element_constructor_(self, x, coerce, copy, check)
   2095 if isinstance(self, FreeModule_ambient):
-> 2096     return self.element_class(self, x, coerce, copy)
   2097 try:

File /ext/sage/9.7/src/sage/modules/vector_modn_dense.pyx:188, in sage.modules.vector_modn_dense.Vector_modn_dense.__init__()
    187 if x != 0:
--> 188     raise TypeError("can't initialize vector from nonzero non-list")
    189 else:

TypeError: can't initialize vector from nonzero non-list

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
File /ext/sage/9.7/src/sage/modules/free_module.py:6400, in FreeModule_submodule_with_basis_pid.__init__(self, ambient, basis, check, echelonize, echelonized_basis, already_echelonized)
   6399 try:
-> 6400     basis = [V(x) for x in basis]
   6401 except TypeError:

File /ext/sage/9.7/src/sage/modules/free_module.py:6400, in <listcomp>(.0)
   6399 try:
-> 6400     basis = [V(x) for x in basis]
   6401 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:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    160     print(type(C._element_constructor), C._element_constructor)
--> 161 raise
    162 

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/modules/free_module.py:6281, in FreeModule_ambient_field._element_constructor_(self, e, *args, **kwds)
   6280     pass
-> 6281 return FreeModule_generic_field._element_constructor_(self, e, *args, **kwds)

File /ext/sage/9.7/src/sage/modules/free_module.py:2096, in FreeModule_generic._element_constructor_(self, x, coerce, copy, check)
   2095 if isinstance(self, FreeModule_ambient):
-> 2096     return self.element_class(self, x, coerce, copy)
   2097 try:

File /ext/sage/9.7/src/sage/modules/vector_modn_dense.pyx:188, in sage.modules.vector_modn_dense.Vector_modn_dense.__init__()
    187 if x != 0:
--> 188     raise TypeError("can't initialize vector from nonzero non-list")
    189 else:

TypeError: can't initialize vector from nonzero non-list

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
Input In [108], in <cell line: 1>()
----> 1 V.subspace([Integer(1), Integer(2), Integer(2)], [Integer(1), Integer(1), Integer(1)])

File /ext/sage/9.7/src/sage/modules/free_module.py:4598, in FreeModule_generic_field.subspace(self, gens, check, already_echelonized)
   4555 def subspace(self, gens, check=True, already_echelonized=False):
   4556     """
   4557     Return the subspace of ``self`` spanned by the elements of gens.
   4558 
   (...)
   4596         ArithmeticError: argument gens (= [[1, 1, 0]]) does not generate a submodule of self
   4597     """
-> 4598     return self.submodule(gens, check=check, already_echelonized=already_echelonized)

File /ext/sage/9.7/src/sage/modules/free_module.py:1744, in Module_free_ambient.submodule(self, gens, check, already_echelonized)
   1742 if isinstance(gens, Module_free_ambient):
   1743     gens = gens.gens()
-> 1744 V = self.span(gens, check=check, already_echelonized=already_echelonized)
   1745 if check:
   1746     if not V.is_submodule(self):

File /ext/sage/9.7/src/sage/modules/free_module.py:1659, in Module_free_ambient.span(self, gens, base_ring, check, already_echelonized)
   1657     gens = gens.gens()
   1658 if base_ring is None or base_ring is self.base_ring():
-> 1659     return self._submodule_class(self.ambient_module(), gens, check=check, already_echelonized=already_echelonized)
   1661 # The base ring has changed
   1662 try:

File /ext/sage/9.7/src/sage/modules/free_module.py:7690, in FreeModule_submodule_field.__init__(self, ambient, gens, check, already_echelonized)
   7688 if is_FreeModule(gens):
   7689     gens = gens.gens()
-> 7690 FreeModule_submodule_with_basis_field.__init__(self, ambient, basis=gens, check=check,
   7691     echelonize=not already_echelonized, already_echelonized=already_echelonized)

File /ext/sage/9.7/src/sage/modules/free_module.py:7491, in FreeModule_submodule_with_basis_field.__init__(self, ambient, basis, check, echelonize, echelonized_basis, already_echelonized)
   7476 def __init__(self, ambient, basis, check=True,
   7477     echelonize=False, echelonized_basis=None, already_echelonized=False):
   7478     """
   7479     Create a vector space with given basis.
   7480 
   (...)
   7489         [4 5 6]
   7490     """
-> 7491     FreeModule_submodule_with_basis_pid.__init__(
   7492         self, ambient, basis=basis, check=check, echelonize=echelonize,
   7493         echelonized_basis=echelonized_basis, already_echelonized=already_echelonized)

File /ext/sage/9.7/src/sage/modules/free_module.py:6402, in FreeModule_submodule_with_basis_pid.__init__(self, ambient, basis, check, echelonize, echelonized_basis, already_echelonized)
   6400         basis = [V(x) for x in basis]
   6401     except TypeError:
-> 6402         raise TypeError("each element of basis must be in "
   6403                         "the ambient vector space")
   6405 if echelonize and not already_echelonized:
   6406     basis = self._echelonized_basis(ambient, basis)

TypeError: each element of basis must be in the ambient vector space
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV.subspace([1, 2, 2], [1, 1, 1])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lv[1, 2, 2], [1, 1, 1])[?7h[?12l[?25h[?25l[?7le[1, 2, 2], [1, 1, 1])[?7h[?12l[?25h[?25l[?7lc[1, 2, 2], [1, 1, 1])[?7h[?12l[?25h[?25l[?7lt[1, 2, 2], [1, 1, 1])[?7h[?12l[?25h[?25l[?7lo[1, 2, 2], [1, 1, 1])[?7h[?12l[?25h[?25l[?7lr[1, 2, 2], [1, 1, 1])[?7h[?12l[?25h[?25l[?7l([1, 2, 2], [1, 1, 1])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l([]), [1, 1, 1])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lv[1, 1, 1])[?7h[?12l[?25h[?25l[?7le[1, 1, 1])[?7h[?12l[?25h[?25l[?7lc[1, 1, 1])[?7h[?12l[?25h[?25l[?7lt[1, 1, 1])[?7h[?12l[?25h[?25l[?7lo[1, 1, 1])[?7h[?12l[?25h[?25l[?7lr[1, 1, 1])[?7h[?12l[?25h[?25l[?7l([1, 1, 1])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: V.subspace(vector([1, 2, 2]), vector([1, 1, 1]))

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
File /ext/sage/9.7/src/sage/modules/free_module.py:6394, in FreeModule_submodule_with_basis_pid.__init__(self, ambient, basis, check, echelonize, echelonized_basis, already_echelonized)
   6393 try:
-> 6394     basis = [ambient(x) for x in basis]
   6395 except TypeError:
   6396     # That failed, try the ambient vector space instead

File /ext/sage/9.7/src/sage/modules/free_module.py:6394, in <listcomp>(.0)
   6393 try:
-> 6394     basis = [ambient(x) for x in basis]
   6395 except TypeError:
   6396     # That failed, try the ambient vector space instead

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:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    160     print(type(C._element_constructor), C._element_constructor)
--> 161 raise
    162 

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/modules/free_module.py:6281, in FreeModule_ambient_field._element_constructor_(self, e, *args, **kwds)
   6280     pass
-> 6281 return FreeModule_generic_field._element_constructor_(self, e, *args, **kwds)

File /ext/sage/9.7/src/sage/modules/free_module.py:2096, in FreeModule_generic._element_constructor_(self, x, coerce, copy, check)
   2095 if isinstance(self, FreeModule_ambient):
-> 2096     return self.element_class(self, x, coerce, copy)
   2097 try:

File /ext/sage/9.7/src/sage/modules/vector_modn_dense.pyx:188, in sage.modules.vector_modn_dense.Vector_modn_dense.__init__()
    187 if x != 0:
--> 188     raise TypeError("can't initialize vector from nonzero non-list")
    189 else:

TypeError: can't initialize vector from nonzero non-list

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
File /ext/sage/9.7/src/sage/modules/free_module.py:6400, in FreeModule_submodule_with_basis_pid.__init__(self, ambient, basis, check, echelonize, echelonized_basis, already_echelonized)
   6399 try:
-> 6400     basis = [V(x) for x in basis]
   6401 except TypeError:

File /ext/sage/9.7/src/sage/modules/free_module.py:6400, in <listcomp>(.0)
   6399 try:
-> 6400     basis = [V(x) for x in basis]
   6401 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:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    160     print(type(C._element_constructor), C._element_constructor)
--> 161 raise
    162 

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/modules/free_module.py:6281, in FreeModule_ambient_field._element_constructor_(self, e, *args, **kwds)
   6280     pass
-> 6281 return FreeModule_generic_field._element_constructor_(self, e, *args, **kwds)

File /ext/sage/9.7/src/sage/modules/free_module.py:2096, in FreeModule_generic._element_constructor_(self, x, coerce, copy, check)
   2095 if isinstance(self, FreeModule_ambient):
-> 2096     return self.element_class(self, x, coerce, copy)
   2097 try:

File /ext/sage/9.7/src/sage/modules/vector_modn_dense.pyx:188, in sage.modules.vector_modn_dense.Vector_modn_dense.__init__()
    187 if x != 0:
--> 188     raise TypeError("can't initialize vector from nonzero non-list")
    189 else:

TypeError: can't initialize vector from nonzero non-list

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
Input In [109], in <cell line: 1>()
----> 1 V.subspace(vector([Integer(1), Integer(2), Integer(2)]), vector([Integer(1), Integer(1), Integer(1)]))

File /ext/sage/9.7/src/sage/modules/free_module.py:4598, in FreeModule_generic_field.subspace(self, gens, check, already_echelonized)
   4555 def subspace(self, gens, check=True, already_echelonized=False):
   4556     """
   4557     Return the subspace of ``self`` spanned by the elements of gens.
   4558 
   (...)
   4596         ArithmeticError: argument gens (= [[1, 1, 0]]) does not generate a submodule of self
   4597     """
-> 4598     return self.submodule(gens, check=check, already_echelonized=already_echelonized)

File /ext/sage/9.7/src/sage/modules/free_module.py:1744, in Module_free_ambient.submodule(self, gens, check, already_echelonized)
   1742 if isinstance(gens, Module_free_ambient):
   1743     gens = gens.gens()
-> 1744 V = self.span(gens, check=check, already_echelonized=already_echelonized)
   1745 if check:
   1746     if not V.is_submodule(self):

File /ext/sage/9.7/src/sage/modules/free_module.py:1659, in Module_free_ambient.span(self, gens, base_ring, check, already_echelonized)
   1657     gens = gens.gens()
   1658 if base_ring is None or base_ring is self.base_ring():
-> 1659     return self._submodule_class(self.ambient_module(), gens, check=check, already_echelonized=already_echelonized)
   1661 # The base ring has changed
   1662 try:

File /ext/sage/9.7/src/sage/modules/free_module.py:7690, in FreeModule_submodule_field.__init__(self, ambient, gens, check, already_echelonized)
   7688 if is_FreeModule(gens):
   7689     gens = gens.gens()
-> 7690 FreeModule_submodule_with_basis_field.__init__(self, ambient, basis=gens, check=check,
   7691     echelonize=not already_echelonized, already_echelonized=already_echelonized)

File /ext/sage/9.7/src/sage/modules/free_module.py:7491, in FreeModule_submodule_with_basis_field.__init__(self, ambient, basis, check, echelonize, echelonized_basis, already_echelonized)
   7476 def __init__(self, ambient, basis, check=True,
   7477     echelonize=False, echelonized_basis=None, already_echelonized=False):
   7478     """
   7479     Create a vector space with given basis.
   7480 
   (...)
   7489         [4 5 6]
   7490     """
-> 7491     FreeModule_submodule_with_basis_pid.__init__(
   7492         self, ambient, basis=basis, check=check, echelonize=echelonize,
   7493         echelonized_basis=echelonized_basis, already_echelonized=already_echelonized)

File /ext/sage/9.7/src/sage/modules/free_module.py:6402, in FreeModule_submodule_with_basis_pid.__init__(self, ambient, basis, check, echelonize, echelonized_basis, already_echelonized)
   6400         basis = [V(x) for x in basis]
   6401     except TypeError:
-> 6402         raise TypeError("each element of basis must be in "
   6403                         "the ambient vector space")
   6405 if echelonize and not already_echelonized:
   6406     basis = self._echelonized_basis(ambient, basis)

TypeError: each element of basis must be in the ambient vector space
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV.subspace(vector([1, 2, 2]), vector([1, 1, 1]))[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50).transpose().kernel().basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(prec=50).transpose().kernel().basis()[?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix(prec=50).transpose().kernel().basis()

[?7h[?12l[?25h[?2004l[?7h[
(0, 0, 0, 0, 1, 0),
(0, 0, 0, 0, 0, 1)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50).transpose().kernel().basis()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix(prec=50).transpose().kernel().basis()[0]

[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, 0, 1, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50).transpose().kernel().basis()[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lj[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lker[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lbenius_kernel(C, prec=50)[?7h[?12l[?25h[?25l[?7l()[0][?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]^[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l).cordinates[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(frobenius_kernel(C, prec=50)[0]^p).cordinates[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: (frobenius_kernel(C, prec=50)[0]^p).coordinates() == vector(6*[0])

[?7h[?12l[?25h[?2004l[
(0, 0, 0, 0, 1, 0),
(0, 0, 0, 0, 0, 1)
]
[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(frobenius_kernel(C, prec=50)[0]^p).coordinates() == vector(6*[0])[?7h[?12l[?25h[?25l[?7l([][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (frobenius_kernel(C, prec=50)[0]^p).coordinates()

[?7h[?12l[?25h[?2004l[
(0, 0, 0, 0, 1, 0),
(0, 0, 0, 0, 0, 1)
]
[?7h[0, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(frobenius_kernel(C, prec=50)[0]^p).coordinates()[?7h[?12l[?25h[?25l[?7l() == vector(6*[0])[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: (frobenius_kernel(C, prec=50)[0]^p).coordinates() = 6*[0]

[?7h[?12l[?25h[?2004l  Input In [114]
    (frobenius_kernel(C, prec=Integer(50))[Integer(0)]**p).coordinates() = Integer(6)*[Integer(0)]
    ^
SyntaxError: cannot assign to function call here. Maybe you meant '==' instead of '='?

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(frobenius_kernel(C, prec=50)[0]^p).coordinates() = 6*[0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l= 6*[0][?7h[?12l[?25h[?25l[?7lsage: (frobenius_kernel(C, prec=50)[0]^p).coordinates() == 6*[0]

[?7h[?12l[?25h[?2004l[
(0, 0, 0, 0, 1, 0),
(0, 0, 0, 0, 0, 1)
]
[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(frobenius_kernel(C, prec=50)[0]^p).coordinates() == 6*[0][?7h[?12l[?25h[?25l[?7lsage: (frobenius_kernel(C, prec=50)[0]^p).coordinates() == 6*[0]

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

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [117], 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>:25, 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>:36, in __init__(self, C, list_of_fcts, prec)

TypeError: superelliptic_function.expansion_at_infty() got an unexpected keyword argument 'i'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq = 5[?7h[?12l[?25h[?25l[?7luadratic_form(parity_quadratic_form(v0, q))[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

[?7h[?12l[?25h[?2004l]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ltess.sage')[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l(ts.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

[?7h[?12l[?25h[?2004lsuperelliptic form coordinates test:
True
p-th root test:
True
---------------------------------------------------------------------------
ValueError                                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>:5, 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>:139, in pth_root(self)

ValueError: Function is not a p-th power.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

[?7h[?12l[?25h[?2004las_cover_test:
True
True
group_action_matrices_test:
True
True
True
dual_element_test:
True
True
True
True
True
True
True
True
True
True
True
True
True
True
True
True
True
True
True
True
True
True
True
True
True
ith_component_test:
True
ith ramification group test:
^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'
  """
^C
KeyboardInterrupt

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7lini.sage')[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l(t.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
File /ext/sage/9.7/src/sage/rings/infinity.py:1201, in InfinityRing_class._element_constructor_(self, x)
   1199 try:
   1200     # For example, RealField() implements this
-> 1201     if x.is_positive_infinity():
   1202         return self.gen(0)

AttributeError: 'int' object has no attribute 'is_positive_infinity'

During handling of the above exception, another exception occurred:

KeyboardInterrupt                         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>:25, 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>:44, in __init__(self, C, list_of_fcts, prec)

File <string>:134, in artin_schreier_transform(power_series, prec)

File <string>:17, in new_reverse(power_series, prec)

File /ext/sage/9.7/src/sage/structure/element.pyx:1356, in sage.structure.element.Element.__sub__()
   1354 cdef int cl = classify_elements(left, right)
   1355 if HAVE_SAME_PARENT(cl):
-> 1356     return (<Element>left)._sub_(right)
   1357 if BOTH_ARE_ELEMENT(cl):
   1358     return coercion_model.bin_op(left, right, sub)

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:792, in sage.rings.laurent_series_ring_element.LaurentSeries._sub_()
    790 # 1. Special case when one or the other is 0.
    791 if not right:
--> 792     return self.add_bigoh(right.prec())
    793 if not self:
    794     return -right.add_bigoh(self.prec())

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1334, in sage.rings.laurent_series_ring_element.LaurentSeries.prec()
   1332         8
   1333     """
-> 1334     return self.__u.prec() + self.__n
   1335 
   1336 def precision_absolute(self):

File /ext/sage/9.7/src/sage/structure/element.pyx:1241, in sage.structure.element.Element.__add__()
   1239 integer_check_long_py(right, &value, &err)
   1240 if not err:
-> 1241     return (<Element>left)._add_long(value)
   1242 integer_check_long_py(left, &value, &err)
   1243 if not err:

File /ext/sage/9.7/src/sage/structure/element.pyx:2388, in sage.structure.element.ModuleElement._add_long()
   2386     if n == 0:
   2387         return self
-> 2388     return coercion_model.bin_op(self, n, add)
   2389 
   2390 cpdef _sub_(self, other):

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: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/infinity.py:1201, in InfinityRing_class._element_constructor_(self, x)
   1198 else:
   1199     try:
   1200         # For example, RealField() implements this
-> 1201         if x.is_positive_infinity():
   1202             return self.gen(0)
   1203         if x.is_negative_infinity():

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

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

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[-1].f.function[?7h[?12l[?25h[?25l[?7lS.genus()[?7h[?12l[?25h[?25l[?7lsage: AS

[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 5 with the equations:
z0^5 - z0 = x^3 + x
z1^5 - z1 = x^2

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.genus()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS.

  AS.at_most_poles                       AS.cohomology_of_structure_sheaf_basis AS.exponent_of_different               AS.genus                               
 

  AS.at_most_poles_forms                 AS.de_rham_basis                       AS.exponent_of_different_prim          AS.group                               
 

  AS.base_ring                           AS.dx                                  AS.fct_field                           AS.height                              
>

  AS.characteristic                      AS.dx_series                           AS.functions                           AS.holomorphic_differentials_basis     
 

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

 AS.at_most_poles                      







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

 AS.at_most_poles                       AS.cohomology_of_structure_sheaf_basis[?7h[?12l[?25h[?25l[?7lexpnent_of_different

 AS.cohomology_of_structure_sheaf_basis AS.exponent_of_different              [?7h[?12l[?25h[?25l[?7lgenus

 AS.exponent_of_different               AS.genus                              [?7h[?12l[?25h[?25l[?7lith_ramification_gp

 cohomology_of_structure_sheaf_basisexpnent_of_different              genus                ith_ramification_gp

 derhambasi      exponent_of_different_primgroup                     jumps

<dx       fct_fieldheight   lift_o_de_rham

 dx_seris     functionholomorphic_differentials_basismagical_element                [?7h[?12l[?25h[?25l[?7lgenus

 AS.genus                               AS.ith_ramification_gp                [?7h[?12l[?25h[?25l[?7lrop

 AS.genus                              

 AS.group                              [?7h[?12l[?25h[?25l[?7lheight



 AS.group                              

 AS.height                             [?7h[?12l[?25h[?25l[?7lolomorphic_differentials_basis





 AS.height                             

 AS.holomorphic_differentials_basis    [?7h[?12l[?25h[?25l[?7l()









[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[(1) * dx,
 (z1) * dx,
 (z1^2) * dx,
 (z1^3) * dx,
 (z1^4) * dx,
 (z0) * dx,
 (z0*z1) * dx,
 (z0*z1^2) * dx,
 (z0*z1^3 - x*z1^2) * dx,
 (z0*z1^4 + 2*x*z1^3 + 2*x*z0^2) * dx,
 (z0^2) * dx,
 (z0^2*z1) * dx,
 (z0^2*z1^2 - x^2) * dx,
 (z0^2*z1^3 - z0^4 + 2*x*z0*z1^2 - 2*x^2*z1) * dx,
 (z0^2*z1^4 + z0^4*z1 + x*z0*z1^3 + x*z0^3 + x^2*z1^2) * dx,
 (z0^3 - x*z1^2) * dx,
 (z0^3*z1 - 2*x*z1^3 + x*z0^2) * dx,
 (z0^3*z1^2 - x*z1^4 + 2*x*z0^2*z1 - 2*x^2*z0) * dx,
 (x) * dx,
 (x*z1) * dx,
 (x*z0) * dx,
 (x*z0*z1 - x^2) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb.function[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbAS.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7lbAS.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7lbAS.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7l AS.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7l=AS.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7l AS.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7lsage: bbb = AS.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb = AS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[5].cartier().coornates()[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7lsage: bbb[9[

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

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

 

 [?7h[?12l[?25h[?25l[?7lbbb = AS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[5].cartier().coornates()[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: bbb[9]

[?7h[?12l[?25h[?2004l[?7h(z0*z1^4 + 2*x*z1^3 + 2*x*z0^2) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[9][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: bbb[9].monomials()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [9], in <cell line: 1>()
----> 1 bbb[Integer(9)].monomials()

AttributeError: 'as_form' object has no attribute 'monomials'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[9].monomials()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lfmonomials()[?7h[?12l[?25h[?25l[?7lomonomials()[?7h[?12l[?25h[?25l[?7lrmonomials()[?7h[?12l[?25h[?25l[?7lmonomials()[?7h[?12l[?25h[?25l[?7l.monomials()[?7h[?12l[?25h[?25l[?7lsage: bbb[9].form.monomials()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [10], in <cell line: 1>()
----> 1 bbb[Integer(9)].form.monomials()

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.fraction_field_element.FractionFieldElement' object has no attribute 'monomials'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[9].form.monomials()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(RxyzQ, Rxyz, x, y, z)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lsage: (RxyzQ, Rxyz, x, y, z) = AS.fct_field

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(RxyzQ, Rxyz, x, y, z) = AS.fct_field[?7h[?12l[?25h[?25l[?7lbbb[9].form.monomials()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRb[9].form.monomials()[?7h[?12l[?25h[?25l[?7lxb[9].form.monomials()[?7h[?12l[?25h[?25l[?7lyb[9].form.monomials()[?7h[?12l[?25h[?25l[?7lzb[9].form.monomials()[?7h[?12l[?25h[?25l[?7l(b[9].form.monomials()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().monomials()[?7h[?12l[?25h[?25l[?7lsage: Rxyz(bbb[9].form).monomials()

[?7h[?12l[?25h[?2004l[?7h[z0*z1^4, x*z1^3, x*z0^2]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxyz(bbb[9].form).monomials()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmonomials(ccc)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxyz(bbb[9].form).monomials()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmRxyz(b[9].form).monomials()[0][?7h[?12l[?25h[?25l[?7l Rxyz(b[9].form).monomials()[0][?7h[?12l[?25h[?25l[?7l=Rxyz(b[9].form).monomials()[0][?7h[?12l[?25h[?25l[?7l Rxyz(b[9].form).monomials()[0][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: m = Rxyz(bbb[9].form).monomials()[0]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm = Rxyz(bbb[9].form).monomials()[0][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lsage: m.

  m.abs                    m.base_extend            m.change_ring            m.content                m.denominator            m.divides                 

  m.add_m_mul_q            m.base_ring              m.coefficient            m.content_ideal          m.derivative             m.dump                    

  m.additive_order         m.cartesian_product      m.coefficients           m.degree                 m.dict                   m.dumps                  >

  m.args                   m.category               m.constant_coefficient   m.degrees                m.discriminant           m.exponents               

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

 m.abs                   







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

 m.abs                    m.base_extend           [?7h[?12l[?25h[?25l[?7lchang_rig

 m.base_extend            m.change_ring           [?7h[?12l[?25h[?25l[?7lontent

 m.change_ring            m.content               [?7h[?12l[?25h[?25l[?7ldeominator

 m.content                m.denominator           [?7h[?12l[?25h[?25l[?7lcotent

 m.content                m.denominator           [?7h[?12l[?25h[?25l[?7lhange_ring

 m.change_ring            m.content               [?7h[?12l[?25h[?25l[?7lontent

 m.change_ring            m.content               [?7h[?12l[?25h[?25l[?7l_ideal

 m.content               

 m.content_ideal         [?7h[?12l[?25h[?25l[?7ldegre



 m.content_ideal         

 m.degree                [?7h[?12l[?25h[?25l[?7l(









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

  std_grading=                                 AA                                           AbelianGroup                                  

  x=                                           AS                                           AbelianGroupMorphism                          

  %%!                                          AS1                                          AbelianGroupWithValues                       >

  A                                            AS2                                          AbelianVariety                                [?7h[?12l[?25h[?25l[?7lz







[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: m.degree(z0)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [14], in <cell line: 1>()
----> 1 m.degree(z0)

NameError: name 'z0' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm.degree(z0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[0)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: m.degree(z[0])

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm.degree(z[0])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l1])[?7h[?12l[?25h[?25l[?7lsage: m.degree(z[1])

[?7h[?12l[?25h[?2004l[?7h4
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [17], 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>:25, 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>:15, in <module>

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

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [18], 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>:26, 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>:15, in <module>

File <string>:16, in cartier(omega)

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

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [19], 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>:26, 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>:15, in <module>

File <string>:17, in cartier(omega)

File <string>:17, in <dictcomp>(.0)

TypeError: unsupported operand type(s) for -: 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular' and 'superelliptic_function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: z[0]

[?7h[?12l[?25h[?2004l[?7hz0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[0][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltz[0][?7h[?12l[?25h[?25l[?7lyz[0][?7h[?12l[?25h[?25l[?7lpz[0][?7h[?12l[?25h[?25l[?7lez[0][?7h[?12l[?25h[?25l[?7ltype(z[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: type(z[0])

[?7h[?12l[?25h[?2004l[?7h<class 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular'>
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 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>:26, 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>:15, in <module>

File <string>:18, in cartier(omega)

File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute()
    941         5
    942      """
--> 943     return self.subs(in_dict,**kwds)
    944 
    945 cpdef _act_on_(self, x, bint self_on_left):

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs()
   3537     id_Delete(&to_id, _ring)
   3538     p_Delete(&_p, _ring)
-> 3539     raise TypeError("keys do not match self's parent")
   3540 try:
   3541     v = parent.coerce(v)

TypeError: keys do not match self's parent
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lMultivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [23], 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>:26, 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>:15, in <module>

File <string>:19, in cartier(omega)

File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute()
    941         5
    942      """
--> 943     return self.subs(in_dict,**kwds)
    944 
    945 cpdef _act_on_(self, x, bint self_on_left):

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs()
   3537     id_Delete(&to_id, _ring)
   3538     p_Delete(&_p, _ring)
-> 3539     raise TypeError("keys do not match self's parent")
   3540 try:
   3541     v = parent.coerce(v)

TypeError: keys do not match self's parent
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l!!! Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [24], 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>:26, 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>:15, in <module>

File <string>:19, in cartier(omega)

File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute()
    941         5
    942      """
--> 943     return self.subs(in_dict,**kwds)
    944 
    945 cpdef _act_on_(self, x, bint self_on_left):

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs()
   3537     id_Delete(&to_id, _ring)
   3538     p_Delete(&_p, _ring)
-> 3539     raise TypeError("keys do not match self's parent")
   3540 try:
   3541     v = parent.coerce(v)

TypeError: keys do not match self's parent
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l!!! Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
---------------------------------------------------------------------------
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>:26, 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>:15, in <module>

File <string>:19, in cartier(omega)

File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute()
    941         5
    942      """
--> 943     return self.subs(in_dict,**kwds)
    944 
    945 cpdef _act_on_(self, x, bint self_on_left):

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs()
   3537     id_Delete(&to_id, _ring)
   3538     p_Delete(&_p, _ring)
-> 3539     raise TypeError("keys do not match self's parent")
   3540 try:
   3541     v = parent.coerce(v)

TypeError: keys do not match self's parent
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50).transpose().kernel().basis()[0][?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basi()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lsage: C.height

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [26], in <cell line: 1>()
----> 1 C.height

AttributeError: 'superelliptic' object has no attribute 'height'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.height[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq = 5[?7h[?12l[?25h[?25l[?7luadratic_form(parity_quadratic_form(v0, q))[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

[?7h[?12l[?25h[?2004l
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l!!! Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
---------------------------------------------------------------------------
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>:26, 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>:15, in <module>

File <string>:19, in cartier(omega)

File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute()
    941         5
    942      """
--> 943     return self.subs(in_dict,**kwds)
    944 
    945 cpdef _act_on_(self, x, bint self_on_left):

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs()
   3537     id_Delete(&to_id, _ring)
   3538     p_Delete(&_p, _ring)
-> 3539     raise TypeError("keys do not match self's parent")
   3540 try:
   3541     v = parent.coerce(v)

TypeError: keys do not match self's parent
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l!!! Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
---------------------------------------------------------------------------
TypeError                                 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>:26, 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>:15, in <module>

File <string>:20, in cartier(omega)

File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute()
    941         5
    942      """
--> 943     return self.subs(in_dict,**kwds)
    944 
    945 cpdef _act_on_(self, x, bint self_on_left):

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs()
   3537     id_Delete(&to_id, _ring)
   3538     p_Delete(&_p, _ring)
-> 3539     raise TypeError("keys do not match self's parent")
   3540 try:
   3541     v = parent.coerce(v)

TypeError: keys do not match self's parent
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
!!! Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
---------------------------------------------------------------------------
TypeError                                 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>:26, 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>:15, in <module>

File <string>:21, in cartier(omega)

File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute()
    941         5
    942      """
--> 943     return self.subs(in_dict,**kwds)
    944 
    945 cpdef _act_on_(self, x, bint self_on_left):

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs()
   3537     id_Delete(&to_id, _ring)
   3538     p_Delete(&_p, _ring)
-> 3539     raise TypeError("keys do not match self's parent")
   3540 try:
   3541     v = parent.coerce(v)

TypeError: keys do not match self's parent
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq = 5[?7h[?12l[?25h[?25l[?7luadratic_form(parity_quadratic_form(v0, q))[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[17;1R^[[18;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;2R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[19;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[18;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[18;1R^[[20;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[20;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[19;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[18;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[18;1R^[[20;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

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

[?7h[?12l[?25h[?2004l{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
!!! Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
---------------------------------------------------------------------------
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>:26, 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>:15, in <module>

File <string>:21, in cartier(omega)

File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute()
    941         5
    942      """
--> 943     return self.subs(in_dict,**kwds)
    944 
    945 cpdef _act_on_(self, x, bint self_on_left):

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs()
   3537     id_Delete(&to_id, _ring)
   3538     p_Delete(&_p, _ring)
-> 3539     raise TypeError("keys do not match self's parent")
   3540 try:
   3541     v = parent.coerce(v)

TypeError: keys do not match self's parent
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.height[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfC.x[?7h[?12l[?25h[?25l[?7l C.x[?7h[?12l[?25h[?25l[?7l=C.x[?7h[?12l[?25h[?25l[?7l C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()x[?7h[?12l[?25h[?25l[?7l(x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: f = (C.x)*(C.z[1])

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [2], in <cell line: 1>()
----> 1 f = (C.x)*(C.z[Integer(1)])

NameError: name 'C' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = (C.x)*(C.z[1])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.x)*(C.z[1])[?7h[?12l[?25h[?25l[?7lA.x)*(C.z[1])[?7h[?12l[?25h[?25l[?7lS.x)*(C.z[1])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.z[1])[?7h[?12l[?25h[?25l[?7lA.z[1])[?7h[?12l[?25h[?25l[?7lS.z[1])[?7h[?12l[?25h[?25l[?7lsage: f = (AS.x)*(AS.z[1])

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = (AS.x)*(AS.z[1])[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l{[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]:[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]:[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l{}[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7lsage: f.substitute({x:x^2, y:x, z[0]:x, z[1]:x})

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [4], in <cell line: 1>()
----> 1 f.substitute({x:x**Integer(2), y:x, z[Integer(0)]:x, z[Integer(1)]:x})

AttributeError: 'as_function' object has no attribute 'substitute'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.substitute({x:x^2, y:x, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.substitute({x:x^2, y:x, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l = (AS.x)*(AS.z[1])[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsage: f = f.function

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l'bad' in str(E.local_data(3))[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = f.function[?7h[?12l[?25h[?25l[?7l.substitue({x:x^2, y:x, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7lsage: f.substitute({x:x^2, y:x, z[0]:x, z[1]:x})

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [6], in <cell line: 1>()
----> 1 f.substitute({x:x**Integer(2), y:x, z[Integer(0)]:x, z[Integer(1)]:x})

NameError: name 'z' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(RxyzQ, Rxyz, x, y, z) = C.fct_field[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.fct_field[?7h[?12l[?25h[?25l[?7lA.fct_field[?7h[?12l[?25h[?25l[?7lS.fct_field[?7h[?12l[?25h[?25l[?7lsage: (RxyzQ, Rxyz, x, y, z) = AS.fct_field

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(RxyzQ, Rxyz, x, y, z) = AS.fct_field[?7h[?12l[?25h[?25l[?7lf.substitute({:x^2, y:x, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7lsage: f.substitute({x:x^2, y:x, z[0]:x, z[1]:x})

[?7h[?12l[?25h[?2004l[?7hx^3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTraceback (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 [9] 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>:26 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>:14
    omega = AS.holomorphic_differentials_basis()[_sage_const_0 ]:
                                                                ^
SyntaxError: invalid syntax

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

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lnumerator(aaa[0].function)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: num

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxyz(bbb[9].form).monomials()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lnu[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: Rxyz(num)

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxyz(num)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l{)[?7h[?12l[?25h[?25l[?7l})[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7lx})[?7h[?12l[?25h[?25l[?7l:})[?7h[?12l[?25h[?25l[?7lx})[?7h[?12l[?25h[?25l[?7l^})[?7h[?12l[?25h[?25l[?7l2})[?7h[?12l[?25h[?25l[?7l,})[?7h[?12l[?25h[?25l[?7l })[?7h[?12l[?25h[?25l[?7ly})[?7h[?12l[?25h[?25l[?7l:})[?7h[?12l[?25h[?25l[?7ly})[?7h[?12l[?25h[?25l[?7l,})[?7h[?12l[?25h[?25l[?7l })[?7h[?12l[?25h[?25l[?7lz})[?7h[?12l[?25h[?25l[?7l:})[?7h[?12l[?25h[?25l[?7l})[?7h[?12l[?25h[?25l[?7l[})[?7h[?12l[?25h[?25l[?7l0})[?7h[?12l[?25h[?25l[?7l]})[?7h[?12l[?25h[?25l[?7l:})[?7h[?12l[?25h[?25l[?7lx})[?7h[?12l[?25h[?25l[?7l,})[?7h[?12l[?25h[?25l[?7l })[?7h[?12l[?25h[?25l[?7lz})[?7h[?12l[?25h[?25l[?7l[})[?7h[?12l[?25h[?25l[?7l1})[?7h[?12l[?25h[?25l[?7l]})[?7h[?12l[?25h[?25l[?7l:})[?7h[?12l[?25h[?25l[?7lx})[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: Rxyz(num).substitute({x:x^2, y:y, z[0]:x, z[1]:x})

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [13], in <cell line: 1>()
----> 1 Rxyz(num).substitute({x:x**Integer(2), y:y, z[Integer(0)]:x, z[Integer(1)]:x})

File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute()
    941         5
    942      """
--> 943     return self.subs(in_dict,**kwds)
    944 
    945 cpdef _act_on_(self, x, bint self_on_left):

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs()
   3537     id_Delete(&to_id, _ring)
   3538     p_Delete(&_p, _ring)
-> 3539     raise TypeError("keys do not match self's parent")
   3540 try:
   3541     v = parent.coerce(v)

TypeError: keys do not match self's parent
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[5][?7h[?12l[?25h[?25l[?7l = C.dx[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a = Rxyz(1)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = Rxyz(1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7larent(aaa[0].function)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: parent(a)

[?7h[?12l[?25h[?2004l[?7hMultivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(a)[?7h[?12l[?25h[?25l[?7la = Rxyz(1)[?7h[?12l[?25h[?25l[?7lRxyz(num).substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7l{}[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l{}[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7lsage: a.substitute({x:x^2, y:y, z[0]:x, z[1]:x})

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [16], in <cell line: 1>()
----> 1 a.substitute({x:x**Integer(2), y:y, z[Integer(0)]:x, z[Integer(1)]:x})

File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute()
    941         5
    942      """
--> 943     return self.subs(in_dict,**kwds)
    944 
    945 cpdef _act_on_(self, x, bint self_on_left):

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs()
   3537     id_Delete(&to_id, _ring)
   3538     p_Delete(&_p, _ring)
-> 3539     raise TypeError("keys do not match self's parent")
   3540 try:
   3541     v = parent.coerce(v)

TypeError: keys do not match self's parent
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(a)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: parent(a)

[?7h[?12l[?25h[?2004l[?7hMultivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(a)[?7h[?12l[?25h[?25l[?7la.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7l{}[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l{}[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l({}[?7h[?12l[?25h[?25l[?7l{[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: z = parent(a).gens()[2:]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz = parent(a).gens()[2:][?7h[?12l[?25h[?25l[?7lparent(a)[?7h[?12l[?25h[?25l[?7la.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7lsage: a.substitute({x:x^2, y:y, z[0]:x, z[1]:x})

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [19], in <cell line: 1>()
----> 1 a.substitute({x:x**Integer(2), y:y, z[Integer(0)]:x, z[Integer(1)]:x})

File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute()
    941         5
    942      """
--> 943     return self.subs(in_dict,**kwds)
    944 
    945 cpdef _act_on_(self, x, bint self_on_left):

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs()
   3537     id_Delete(&to_id, _ring)
   3538     p_Delete(&_p, _ring)
-> 3539     raise TypeError("keys do not match self's parent")
   3540 try:
   3541     v = parent.coerce(v)

TypeError: keys do not match self's parent
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lstr(E.local_data(2))[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lP1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l<[?7h[?12l[?25h[?25l[?7l>[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lX>[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lP[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: P.<X> = PolynomialRing(GF(p))

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lP.<X> = PolynomialRing(GF(p))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: P.<X> = PolynomialRing(GF(p), 1)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l = C_super.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lP[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A = P(1)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = P(1)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l{)[?7h[?12l[?25h[?25l[?7l})[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7lx})[?7h[?12l[?25h[?25l[?7l:})[?7h[?12l[?25h[?25l[?7lx})[?7h[?12l[?25h[?25l[?7l^})[?7h[?12l[?25h[?25l[?7l2})[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A.substitute({x:x^2})

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [23], in <cell line: 1>()
----> 1 A.substitute({x:x**Integer(2)})

File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute()
    941         5
    942      """
--> 943     return self.subs(in_dict,**kwds)
    944 
    945 cpdef _act_on_(self, x, bint self_on_left):

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs()
   3537     id_Delete(&to_id, _ring)
   3538     p_Delete(&_p, _ring)
-> 3539     raise TypeError("keys do not match self's parent")
   3540 try:
   3541     v = parent.coerce(v)

TypeError: keys do not match self's parent
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(a)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA.base_ring().order()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: parent(A)

[?7h[?12l[?25h[?2004l[?7hMultivariate Polynomial Ring in X over Finite Field of size 5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(A)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lA.substitute({x:x^2})[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7l{}[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^2})[?7h[?12l[?25h[?25l[?7lX^2})[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l:X^2})[?7h[?12l[?25h[?25l[?7lX:X^2})[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l{}[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A.substitute({X:X^2})

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.substitute({X:X^2})[?7h[?12l[?25h[?25l[?7lparent(A)[?7h[?12l[?25h[?25l[?7lA.substitute({x:x^2})[?7h[?12l[?25h[?25l[?7l = P(1)[?7h[?12l[?25h[?25l[?7lP.<X> = PolynomialRing(GF(p), 1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lasubstitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7lz = parent(a).gens()[2][?7h[?12l[?25h[?25l[?7la.substitute({x:x^2, yy, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lz = parent(a).gens()[2][?7h[?12l[?25h[?25l[?7la.substitute({x:x^2, yy, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7lP<X> = PolynomialRing(GF(p))[?7h[?12l[?25h[?25l[?7l, 1)[?7h[?12l[?25h[?25l[?7lA = P(1)[?7h[?12l[?25h[?25l[?7l.substitute({x:x^2})[?7h[?12l[?25h[?25l[?7lparent(A)[?7h[?12l[?25h[?25l[?7lA.substitute({X:X^2})[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y = C_super.x, C_super.y[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly = C_super.x, C_super.y[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: x, y = parent(a).gens[0:1]

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [26], in <cell line: 1>()
----> 1 x, y = parent(a).gens[Integer(0):Integer(1)]

TypeError: 'builtin_function_or_method' object is not subscriptable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y = parent(a).gens[0:1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: x, y = parent(a).gens[0:2]

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [27], in <cell line: 1>()
----> 1 x, y = parent(a).gens[Integer(0):Integer(2)]

TypeError: 'builtin_function_or_method' object is not subscriptable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y = parent(a).gens[0:2][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[],[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: x, y = parent(a).gens[0], parent(a).gens(1)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [28], in <cell line: 1>()
----> 1 x, y = parent(a).gens[Integer(0)], parent(a).gens(Integer(1))

TypeError: 'builtin_function_or_method' object is not subscriptable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y = parent(a).gens[0], parent(a).gens(1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([0], parent(a).gens(1)[?7h[?12l[?25h[?25l[?7l)[0], parent(a).gens(1)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: x, y = parent(a).gens()[0], parent(a).gens()[1]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y = parent(a).gens()[0], parent(a).gens()[1][?7h[?12l[?25h[?25l[?7l[0], parent(a).gens(1)[?7h[?12l[?25h[?25l[?7l[:2][?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lA.substitute({X:X^2})[?7h[?12l[?25h[?25l[?7lparent(A)[?7h[?12l[?25h[?25l[?7lA.substitute({x:x^2})[?7h[?12l[?25h[?25l[?7l = P(1)[?7h[?12l[?25h[?25l[?7lP.<X> = PolynomialRing(GF(p), 1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lasubstitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7lsage: a.substitute({x:x^2, y:y, z[0]:x, z[1]:x})

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
!!! Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [31], 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>:26, 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>:15, in <module>

File <string>:31, in cartier(omega)

File <string>:44, 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 'form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
!!! Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [32], 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>:26, 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>:15, in <module>

TypeError: cannot unpack non-iterable as_form object
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
!!! Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
(0) * dx
{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
!!! Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [33], 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>:26, 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>:15, in <module>

File <string>:24, in cartier(omega)

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:842, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
    840 if check:
    841     try:
--> 842         c = base_ring(c)
    843     except TypeError:
    844         p_Delete(&_p, _ring)

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:1654, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
   1652         raise ValueError("not integral")
   1653     if nmod_poly_degree(x._numer) > 0:
-> 1654         raise ValueError("not constant")
   1655 ans = IntegerMod_int.__new__(IntegerMod_int)
   1656 ans._parent = self.codomain()

ValueError: not constant
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
num 1
monomial 1
(0) * dx
{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
num z1
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [34], 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>:26, 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>:15, in <module>

File <string>:24, in cartier(omega)

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:842, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
    840 if check:
    841     try:
--> 842         c = base_ring(c)
    843     except TypeError:
    844         p_Delete(&_p, _ring)

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:1654, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
   1652         raise ValueError("not integral")
   1653     if nmod_poly_degree(x._numer) > 0:
-> 1654         raise ValueError("not constant")
   1655 ans = IntegerMod_int.__new__(IntegerMod_int)
   1656 ans._parent = self.codomain()

ValueError: not constant
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
num 1
monomials: [1]
monomial 1
(0) * dx
{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
num z1
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [35], 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>:26, 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>:15, in <module>

File <string>:24, in cartier(omega)

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:842, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
    840 if check:
    841     try:
--> 842         c = base_ring(c)
    843     except TypeError:
    844         p_Delete(&_p, _ring)

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:1654, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
   1652         raise ValueError("not integral")
   1653     if nmod_poly_degree(x._numer) > 0:
-> 1654         raise ValueError("not constant")
   1655 ans = IntegerMod_int.__new__(IntegerMod_int)
   1656 ans._parent = self.codomain()

ValueError: not constant
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm.degree(z[1])[?7h[?12l[?25h[?25l[?7lonomials(ccc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz = parent(a).gens()[2:][?7h[?12l[?25h[?25l[?7l[0][?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: z[1]

[?7h[?12l[?25h[?2004l[?7hz1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[1][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: z[1].monomials()

[?7h[?12l[?25h[?2004l[?7h[z1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxyz(num).substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxyz(num).substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: Rxyz(z[1])

[?7h[?12l[?25h[?2004l[?7hz1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
num 1
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [39], 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>:26, 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>:15, in <module>

File <string>:24, in cartier(omega)

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.finite_rings.integer_mod.IntegerMod_int' object has no attribute 'monomials'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
num 1
monomials: 1
monomial 1
(0) * dx
{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
num z1
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [40], 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>:26, 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>:15, in <module>

File <string>:24, in cartier(omega)

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:842, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
    840 if check:
    841     try:
--> 842         c = base_ring(c)
    843     except TypeError:
    844         p_Delete(&_p, _ring)

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:1654, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
   1652         raise ValueError("not integral")
   1653     if nmod_poly_degree(x._numer) > 0:
-> 1654         raise ValueError("not constant")
   1655 ans = IntegerMod_int.__new__(IntegerMod_int)
   1656 ans._parent = self.codomain()

ValueError: not constant
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
num, den 1 1
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [41], 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>:26, 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>:15, in <module>

File <string>:24, in cartier(omega)

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.finite_rings.integer_mod.IntegerMod_int' object has no attribute 'monomials'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
num, den 1 1
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [42], 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>:26, 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>:15, in <module>

File <string>:25, in cartier(omega)

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.finite_rings.integer_mod.IntegerMod_int' object has no attribute 'monomials'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
num, den 1 1
monomials: [1]
monomial 1
(0) * dx
z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
num, den z1 1
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [43], 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>:26, 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>:15, in <module>

File <string>:24, in cartier(omega)

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:842, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
    840 if check:
    841     try:
--> 842         c = base_ring(c)
    843     except TypeError:
    844         p_Delete(&_p, _ring)

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:1654, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
   1652         raise ValueError("not integral")
   1653     if nmod_poly_degree(x._numer) > 0:
-> 1654         raise ValueError("not constant")
   1655 ans = IntegerMod_int.__new__(IntegerMod_int)
   1656 ans._parent = self.codomain()

ValueError: not constant
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
num, den 1 1
monomials: [1]
monomial 1
(0) * dx
z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
num, den z1 1
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [44], 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>:26, 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>:15, in <module>

File <string>:25, in cartier(omega)

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:842, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
    840 if check:
    841     try:
--> 842         c = base_ring(c)
    843     except TypeError:
    844         p_Delete(&_p, _ring)

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:1654, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
   1652         raise ValueError("not integral")
   1653     if nmod_poly_degree(x._numer) > 0:
-> 1654         raise ValueError("not constant")
   1655 ans = IntegerMod_int.__new__(IntegerMod_int)
   1656 ans._parent = self.codomain()

ValueError: not constant
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
num, den 1 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
monomials: [1]
monomial 1
(0) * dx
z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
num, den z1 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
---------------------------------------------------------------------------
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>:26, 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>:15, in <module>

File <string>:25, in cartier(omega)

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:842, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
    840 if check:
    841     try:
--> 842         c = base_ring(c)
    843     except TypeError:
    844         p_Delete(&_p, _ring)

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:1654, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
   1652         raise ValueError("not integral")
   1653     if nmod_poly_degree(x._numer) > 0:
-> 1654         raise ValueError("not constant")
   1655 ans = IntegerMod_int.__new__(IntegerMod_int)
   1656 ans._parent = self.codomain()

ValueError: not constant
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
num, den 1 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
aaa: 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
monomials: [1]
monomial 1
(0) * dx
z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
num, den z1 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [46], 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>:26, 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>:15, in <module>

File <string>:25, in cartier(omega)

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:842, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
    840 if check:
    841     try:
--> 842         c = base_ring(c)
    843     except TypeError:
    844         p_Delete(&_p, _ring)

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:1654, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
   1652         raise ValueError("not integral")
   1653     if nmod_poly_degree(x._numer) > 0:
-> 1654         raise ValueError("not constant")
   1655 ans = IntegerMod_int.__new__(IntegerMod_int)
   1656 ans._parent = self.codomain()

ValueError: not constant
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
num, den 1 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
aaa: 1 Fraction Field of Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
---------------------------------------------------------------------------
AttributeError                            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>:26, 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>:15, in <module>

File <string>:27, in cartier(omega)

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.fraction_field_element.FractionFieldElement' object has no attribute 'monomials'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
num, den 1 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
aaa: 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
monomials: [1]
monomial 1
(0) * dx
z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
num, den z1 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
aaa: z1^5 - x^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
monomials: [z1^5, x^2]
monomial z1^5
monomial x^2
(0) * dx
z1^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
num, den z1^2 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
aaa: z1^10 - 2*x^2*z1^5 + x^4 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
monomials: [z1^10, x^2*z1^5, x^4]
monomial z1^10
monomial x^2*z1^5
monomial x^4
(1) * dx
z1^3 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
num, den z1^3 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
aaa: z1^15 + 2*x^2*z1^10 - 2*x^4*z1^5 - x^6 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
monomials: [z1^15, x^2*z1^10, x^4*z1^5, x^6]
monomial z1^15
monomial x^2*z1^10
monomial x^4*z1^5
monomial x^6
(-2*z1) * dx
z1^4 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
num, den z1^4 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
aaa: z1^20 + x^2*z1^15 + x^4*z1^10 + x^6*z1^5 + x^8 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
monomials: [z1^20, x^2*z1^15, x^4*z1^10, x^6*z1^5, x^8]
monomial z1^20
monomial x^2*z1^15
monomial x^4*z1^10
monomial x^6*z1^5
monomial x^8
(z1^2) * dx
z0 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
num, den z0 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
aaa: z0^5 - x^3 - x Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
monomials: [z0^5, x^3, x]
monomial z0^5
monomial x^3
monomial x
(0) * dx
z0*z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
num, den z0*z1 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
aaa: z0^5*z1^5 - x^3*z1^5 - x^2*z0^5 - x*z1^5 + x^5 + x^3 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
monomials: [z0^5*z1^5, x^3*z1^5, x^2*z0^5, x*z1^5, x^5, x^3]
monomial z0^5*z1^5
monomial x^3*z1^5
monomial x^2*z0^5
monomial x*z1^5
monomial x^5
monomial x^3
(0) * dx
z0*z1^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
num, den z0*z1^2 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
aaa: z0^5*z1^10 - x^3*z1^10 - 2*x^2*z0^5*z1^5 - x*z1^10 + 2*x^5*z1^5 + x^4*z0^5 + 2*x^3*z1^5 - x^7 - x^5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
monomials: [z0^5*z1^10, x^3*z1^10, x^2*z0^5*z1^5, x*z1^10, x^5*z1^5, x^4*z0^5, x^3*z1^5, x^7, x^5]
monomial z0^5*z1^10
monomial x^3*z1^10
monomial x^2*z0^5*z1^5
monomial x*z1^10
monomial x^5*z1^5
monomial x^4*z0^5
monomial x^3*z1^5
monomial x^7
monomial x^5
(z0) * dx
z0*z1^3 - x*z1^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
num, den z0*z1^3 - x*z1^2 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
aaa: z0^5*z1^15 - x^3*z1^15 + 2*x^2*z0^5*z1^10 - x*z1^15 - 2*x^5*z1^10 - 2*x^4*z0^5*z1^5 - 2*x^3*z1^10 + 2*x^7*z1^5 - x^6*z0^5 - x*z1^10 + 2*x^5*z1^5 + x^9 + 2*x^3*z1^5 + x^7 - x^5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
monomials: [z0^5*z1^15, x^3*z1^15, x^2*z0^5*z1^10, x*z1^15, x^5*z1^10, x^4*z0^5*z1^5, x^3*z1^10, x^7*z1^5, x^6*z0^5, x*z1^10, x^5*z1^5, x^9, x^3*z1^5, x^7, x^5]
monomial z0^5*z1^15
monomial x^3*z1^15
monomial x^2*z0^5*z1^10
monomial x*z1^15
monomial x^5*z1^10
monomial x^4*z0^5*z1^5
monomial x^3*z1^10
monomial x^7*z1^5
monomial x^6*z0^5
monomial x*z1^10
monomial x^5*z1^5
monomial x^9
monomial x^3*z1^5
monomial x^7
monomial x^5
(-2*z0*z1 + x) * dx
z0*z1^4 + 2*x*z1^3 + 2*x*z0^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
num, den z0*z1^4 + 2*x*z1^3 + 2*x*z0^2 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
aaa: z0^5*z1^20 - x^3*z1^20 + x^2*z0^5*z1^15 - x*z1^20 - x^5*z1^15 + x^4*z0^5*z1^10 - x^3*z1^15 - x^7*z1^10 + x^6*z0^5*z1^5 + 2*x*z1^15 - x^5*z1^10 - x^9*z1^5 + x^8*z0^5 - x^3*z1^10 - x^7*z1^5 - x^11 + 2*x*z0^10 + x^5*z1^5 - x^9 + x^4*z0^5 + x^2*z0^5 - x^5 + 2*x^3 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
monomials: [z0^5*z1^20, x^3*z1^20, x^2*z0^5*z1^15, x*z1^20, x^5*z1^15, x^4*z0^5*z1^10, x^3*z1^15, x^7*z1^10, x^6*z0^5*z1^5, x*z1^15, x^5*z1^10, x^9*z1^5, x^8*z0^5, x^3*z1^10, x^7*z1^5, x^11, x*z0^10, x^5*z1^5, x^9, x^4*z0^5, x^2*z0^5, x^5, x^3]
monomial z0^5*z1^20
monomial x^3*z1^20
monomial x^2*z0^5*z1^15
monomial x*z1^20
monomial x^5*z1^15
monomial x^4*z0^5*z1^10
monomial x^3*z1^15
monomial x^7*z1^10
monomial x^6*z0^5*z1^5
monomial x*z1^15
monomial x^5*z1^10
monomial x^9*z1^5
monomial x^8*z0^5
monomial x^3*z1^10
monomial x^7*z1^5
monomial x^11
monomial x*z0^10
monomial x^5*z1^5
monomial x^9
monomial x^4*z0^5
monomial x^2*z0^5
monomial x^5
monomial x^3
(z0*z1^2 - x*z1 - x + z0) * dx
z0^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
num, den z0^2 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
aaa: z0^10 - 2*x^3*z0^5 + x^6 - 2*x*z0^5 + 2*x^4 + x^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
monomials: [z0^10, x^3*z0^5, x^6, x*z0^5, x^4, x^2]
monomial z0^10
monomial x^3*z0^5
monomial x^6
monomial x*z0^5
monomial x^4
monomial x^2
(2) * dx
z0^2*z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
num, den z0^2*z1 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
aaa: z0^10*z1^5 - 2*x^3*z0^5*z1^5 - x^2*z0^10 + x^6*z1^5 - 2*x*z0^5*z1^5 + 2*x^5*z0^5 + 2*x^4*z1^5 - x^8 + 2*x^3*z0^5 + x^2*z1^5 - 2*x^6 - x^4 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
monomials: [z0^10*z1^5, x^3*z0^5*z1^5, x^2*z0^10, x^6*z1^5, x*z0^5*z1^5, x^5*z0^5, x^4*z1^5, x^8, x^3*z0^5, x^2*z1^5, x^6, x^4]
monomial z0^10*z1^5
monomial x^3*z0^5*z1^5
monomial x^2*z0^10
monomial x^6*z1^5
monomial x*z0^5*z1^5
monomial x^5*z0^5
monomial x^4*z1^5
monomial x^8
monomial x^3*z0^5
monomial x^2*z1^5
monomial x^6
monomial x^4
(2*z1 - 1) * dx
z0^2*z1^2 - x^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
num, den z0^2*z1^2 - x^2 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
aaa: z0^10*z1^10 - 2*x^3*z0^5*z1^10 - 2*x^2*z0^10*z1^5 + x^6*z1^10 - 2*x*z0^5*z1^10 - x^5*z0^5*z1^5 + x^4*z0^10 + 2*x^4*z1^10 - 2*x^8*z1^5 - x^3*z0^5*z1^5 - 2*x^7*z0^5 + x^2*z1^10 + x^6*z1^5 + x^10 - 2*x^5*z0^5 - 2*x^4*z1^5 + 2*x^8 + x^6 - x^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
monomials: [z0^10*z1^10, x^3*z0^5*z1^10, x^2*z0^10*z1^5, x^6*z1^10, x*z0^5*z1^10, x^5*z0^5*z1^5, x^4*z0^10, x^4*z1^10, x^8*z1^5, x^3*z0^5*z1^5, x^7*z0^5, x^2*z1^10, x^6*z1^5, x^10, x^5*z0^5, x^4*z1^5, x^8, x^6, x^2]
monomial z0^10*z1^10
monomial x^3*z0^5*z1^10
monomial x^2*z0^10*z1^5
monomial x^6*z1^10
monomial x*z0^5*z1^10
monomial x^5*z0^5*z1^5
monomial x^4*z0^10
monomial x^4*z1^10
monomial x^8*z1^5
monomial x^3*z0^5*z1^5
monomial x^7*z0^5
monomial x^2*z1^10
monomial x^6*z1^5
monomial x^10
monomial x^5*z0^5
monomial x^4*z1^5
monomial x^8
monomial x^6
monomial x^2
(z0^2 + 2*z1^2 - 2*z1) * dx
z0^2*z1^3 - z0^4 + 2*x*z0*z1^2 - 2*x^2*z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
num, den z0^2*z1^3 - z0^4 + 2*x*z0*z1^2 - 2*x^2*z1 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
aaa: z0^10*z1^15 - 2*x^3*z0^5*z1^15 + 2*x^2*z0^10*z1^10 + x^6*z1^15 - 2*x*z0^5*z1^15 - z0^20 + x^5*z0^5*z1^10 - 2*x^4*z0^10*z1^5 + 2*x^4*z1^15 - x^3*z0^15 + 2*x^8*z1^10 + x^3*z0^5*z1^10 - x^7*z0^5*z1^5 + x^2*z1^15 - 2*x^6*z0^10 - x*z0^15 - x^6*z1^10 + 2*x*z0^5*z1^10 - 2*x^10*z1^5 - x^5*z0^5*z1^5 + x^9*z0^5 - 2*x^4*z0^10 + x^8*z1^5 + x^3*z0^5*z1^5 - 2*x^12 - x^7*z0^5 - x^2*z0^10 - 2*x^2*z1^10 + 2*x^6*z1^5 - x^10 - x^5*z0^5 - x^4*z1^5 + x^8 - x^3*z0^5 - 2*x^2*z1^5 - x^6 + x^4 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
monomials: [z0^10*z1^15, x^3*z0^5*z1^15, x^2*z0^10*z1^10, x^6*z1^15, x*z0^5*z1^15, z0^20, x^5*z0^5*z1^10, x^4*z0^10*z1^5, x^4*z1^15, x^3*z0^15, x^8*z1^10, x^3*z0^5*z1^10, x^7*z0^5*z1^5, x^2*z1^15, x^6*z0^10, x*z0^15, x^6*z1^10, x*z0^5*z1^10, x^10*z1^5, x^5*z0^5*z1^5, x^9*z0^5, x^4*z0^10, x^8*z1^5, x^3*z0^5*z1^5, x^12, x^7*z0^5, x^2*z0^10, x^2*z1^10, x^6*z1^5, x^10, x^5*z0^5, x^4*z1^5, x^8, x^3*z0^5, x^2*z1^5, x^6, x^4]
monomial z0^10*z1^15
monomial x^3*z0^5*z1^15
monomial x^2*z0^10*z1^10
monomial x^6*z1^15
monomial x*z0^5*z1^15
monomial z0^20
monomial x^5*z0^5*z1^10
monomial x^4*z0^10*z1^5
monomial x^4*z1^15
monomial x^3*z0^15
monomial x^8*z1^10
monomial x^3*z0^5*z1^10
monomial x^7*z0^5*z1^5
monomial x^2*z1^15
monomial x^6*z0^10
monomial x*z0^15
monomial x^6*z1^10
monomial x*z0^5*z1^10
monomial x^10*z1^5
monomial x^5*z0^5*z1^5
monomial x^9*z0^5
monomial x^4*z0^10
monomial x^8*z1^5
monomial x^3*z0^5*z1^5
monomial x^12
monomial x^7*z0^5
monomial x^2*z0^10
monomial x^2*z1^10
monomial x^6*z1^5
monomial x^10
monomial x^5*z0^5
monomial x^4*z1^5
monomial x^8
monomial x^3*z0^5
monomial x^2*z1^5
monomial x^6
monomial x^4
(-2*z0^2*z1 + 2*z1^3 + x*z0 - 2*z0^2 - z1 + 1) * dx
z0^2*z1^4 + z0^4*z1 + x*z0*z1^3 + x*z0^3 + x^2*z1^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
num, den z0^2*z1^4 + z0^4*z1 + x*z0*z1^3 + x*z0^3 + x^2*z1^2 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
aaa: z0^10*z1^20 - 2*x^3*z0^5*z1^20 + x^2*z0^10*z1^15 + x^6*z1^20 - 2*x*z0^5*z1^20 + z0^20*z1^5 - 2*x^5*z0^5*z1^15 + x^4*z0^10*z1^10 + 2*x^4*z1^20 + x^3*z0^15*z1^5 + x^8*z1^15 - 2*x^3*z0^5*z1^15 - x^2*z0^20 - 2*x^7*z0^5*z1^10 + x^2*z1^20 + 2*x^6*z0^10*z1^5 + x*z0^15*z1^5 + 2*x^6*z1^15 + x*z0^5*z1^15 - x^5*z0^15 + x^10*z1^10 - 2*x^5*z0^5*z1^10 - x^9*z0^5*z1^5 + 2*x^4*z0^10*z1^5 - x^3*z0^15 + 2*x^8*z1^10 + 2*x^3*z0^5*z1^10 + 2*x^12*z1^5 + x^7*z0^5*z1^5 + x^2*z0^10*z1^5 - x^2*z1^15 + 2*x^11*z0^5 - 2*x^6*z0^10 + x*z0^15 - x^6*z1^10 + x^10*z1^5 + x^5*z0^5*z1^5 + x^4*z0^10 - 2*x^4*z1^10 - x^8*z1^5 + x^3*z0^5*z1^5 - 2*x^12 - x^7*z0^5 + 2*x^2*z0^10 + x^2*z1^10 + x^6*z1^5 - x^4*z1^5 - x^8 - 2*x^3*z0^5 + 2*x^6 - x^4 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
monomials: [z0^10*z1^20, x^3*z0^5*z1^20, x^2*z0^10*z1^15, x^6*z1^20, x*z0^5*z1^20, z0^20*z1^5, x^5*z0^5*z1^15, x^4*z0^10*z1^10, x^4*z1^20, x^3*z0^15*z1^5, x^8*z1^15, x^3*z0^5*z1^15, x^2*z0^20, x^7*z0^5*z1^10, x^2*z1^20, x^6*z0^10*z1^5, x*z0^15*z1^5, x^6*z1^15, x*z0^5*z1^15, x^5*z0^15, x^10*z1^10, x^5*z0^5*z1^10, x^9*z0^5*z1^5, x^4*z0^10*z1^5, x^3*z0^15, x^8*z1^10, x^3*z0^5*z1^10, x^12*z1^5, x^7*z0^5*z1^5, x^2*z0^10*z1^5, x^2*z1^15, x^11*z0^5, x^6*z0^10, x*z0^15, x^6*z1^10, x^10*z1^5, x^5*z0^5*z1^5, x^4*z0^10, x^4*z1^10, x^8*z1^5, x^3*z0^5*z1^5, x^12, x^7*z0^5, x^2*z0^10, x^2*z1^10, x^6*z1^5, x^4*z1^5, x^8, x^3*z0^5, x^6, x^4]
monomial z0^10*z1^20
monomial x^3*z0^5*z1^20
monomial x^2*z0^10*z1^15
monomial x^6*z1^20
monomial x*z0^5*z1^20
monomial z0^20*z1^5
monomial x^5*z0^5*z1^15
monomial x^4*z0^10*z1^10
monomial x^4*z1^20
monomial x^3*z0^15*z1^5
monomial x^8*z1^15
monomial x^3*z0^5*z1^15
monomial x^2*z0^20
monomial x^7*z0^5*z1^10
monomial x^2*z1^20
monomial x^6*z0^10*z1^5
monomial x*z0^15*z1^5
monomial x^6*z1^15
monomial x*z0^5*z1^15
monomial x^5*z0^15
monomial x^10*z1^10
monomial x^5*z0^5*z1^10
monomial x^9*z0^5*z1^5
monomial x^4*z0^10*z1^5
monomial x^3*z0^15
monomial x^8*z1^10
monomial x^3*z0^5*z1^10
monomial x^12*z1^5
monomial x^7*z0^5*z1^5
monomial x^2*z0^10*z1^5
monomial x^2*z1^15
monomial x^11*z0^5
monomial x^6*z0^10
monomial x*z0^15
monomial x^6*z1^10
monomial x^10*z1^5
monomial x^5*z0^5*z1^5
monomial x^4*z0^10
monomial x^4*z1^10
monomial x^8*z1^5
monomial x^3*z0^5*z1^5
monomial x^12
monomial x^7*z0^5
monomial x^2*z0^10
monomial x^2*z1^10
monomial x^6*z1^5
monomial x^4*z1^5
monomial x^8
monomial x^3*z0^5
monomial x^6
monomial x^4
(z0^2*z1^2 + 2*z1^4 - x*z0*z1 + 2*z0^2*z1 + z0^2 - 2*z1^2 - z1 - 1) * dx
z0^3 - x*z1^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
num, den z0^3 - x*z1^2 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
aaa: z0^15 + 2*x^3*z0^10 - 2*x^6*z0^5 + 2*x*z0^10 - x*z1^10 - x^9 + x^4*z0^5 + 2*x^3*z1^5 + 2*x^7 - 2*x^2*z0^5 + x^5 - x^3 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
monomials: [z0^15, x^3*z0^10, x^6*z0^5, x*z0^10, x*z1^10, x^9, x^4*z0^5, x^3*z1^5, x^7, x^2*z0^5, x^5, x^3]
monomial z0^15
monomial x^3*z0^10
monomial x^6*z0^5
monomial x*z0^10
monomial x*z1^10
monomial x^9
monomial x^4*z0^5
monomial x^3*z1^5
monomial x^7
monomial x^2*z0^5
monomial x^5
monomial x^3
(-x + z0) * dx
z0^3*z1 - 2*x*z1^3 + x*z0^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
num, den z0^3*z1 - 2*x*z1^3 + x*z0^2 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
aaa: z0^15*z1^5 + 2*x^3*z0^10*z1^5 - x^2*z0^15 - 2*x^6*z0^5*z1^5 + 2*x*z0^10*z1^5 - 2*x*z1^15 - 2*x^5*z0^10 - x^9*z1^5 + x^4*z0^5*z1^5 + 2*x^8*z0^5 - 2*x^3*z0^10 + x^3*z1^10 + 2*x^7*z1^5 - 2*x^2*z0^5*z1^5 + x^11 - x^6*z0^5 + x*z0^10 + x^5*z1^5 - 2*x^9 - x^3*z1^5 + x^7 - 2*x^2*z0^5 - 2*x^5 + x^3 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
monomials: [z0^15*z1^5, x^3*z0^10*z1^5, x^2*z0^15, x^6*z0^5*z1^5, x*z0^10*z1^5, x*z1^15, x^5*z0^10, x^9*z1^5, x^4*z0^5*z1^5, x^8*z0^5, x^3*z0^10, x^3*z1^10, x^7*z1^5, x^2*z0^5*z1^5, x^11, x^6*z0^5, x*z0^10, x^5*z1^5, x^9, x^3*z1^5, x^7, x^2*z0^5, x^5, x^3]
monomial z0^15*z1^5
monomial x^3*z0^10*z1^5
monomial x^2*z0^15
monomial x^6*z0^5*z1^5
monomial x*z0^10*z1^5
monomial x*z1^15
monomial x^5*z0^10
monomial x^9*z1^5
monomial x^4*z0^5*z1^5
monomial x^8*z0^5
monomial x^3*z0^10
monomial x^3*z1^10
monomial x^7*z1^5
monomial x^2*z0^5*z1^5
monomial x^11
monomial x^6*z0^5
monomial x*z0^10
monomial x^5*z1^5
monomial x^9
monomial x^3*z1^5
monomial x^7
monomial x^2*z0^5
monomial x^5
monomial x^3
(-x*z1 + z0*z1 - 2*x) * dx
z0^3*z1^2 - x*z1^4 + 2*x*z0^2*z1 - 2*x^2*z0 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
num, den z0^3*z1^2 - x*z1^4 + 2*x*z0^2*z1 - 2*x^2*z0 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
aaa: z0^15*z1^10 + 2*x^3*z0^10*z1^10 - 2*x^2*z0^15*z1^5 - 2*x^6*z0^5*z1^10 + 2*x*z0^10*z1^10 - x*z1^20 + x^5*z0^10*z1^5 + x^4*z0^15 - x^9*z1^10 + x^4*z0^5*z1^10 - x^8*z0^5*z1^5 + x^3*z0^10*z1^5 - x^3*z1^15 + 2*x^7*z0^10 + 2*x^7*z1^10 - 2*x^2*z0^5*z1^10 + 2*x^11*z1^5 - 2*x^6*z0^5*z1^5 + 2*x*z0^10*z1^5 - 2*x^10*z0^5 + 2*x^5*z0^10 + x^5*z1^10 + x^9*z1^5 - x^13 + x^8*z0^5 - 2*x^3*z0^10 - x^3*z1^10 + 2*x^7*z1^5 + x^2*z0^5*z1^5 + 2*x^11 + 2*x^6*z0^5 + x^5*z1^5 - x^9 - x^4*z0^5 + 2*x^3*z1^5 - 2*x^2*z0^5 + 2*x^3 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
monomials: [z0^15*z1^10, x^3*z0^10*z1^10, x^2*z0^15*z1^5, x^6*z0^5*z1^10, x*z0^10*z1^10, x*z1^20, x^5*z0^10*z1^5, x^4*z0^15, x^9*z1^10, x^4*z0^5*z1^10, x^8*z0^5*z1^5, x^3*z0^10*z1^5, x^3*z1^15, x^7*z0^10, x^7*z1^10, x^2*z0^5*z1^10, x^11*z1^5, x^6*z0^5*z1^5, x*z0^10*z1^5, x^10*z0^5, x^5*z0^10, x^5*z1^10, x^9*z1^5, x^13, x^8*z0^5, x^3*z0^10, x^3*z1^10, x^7*z1^5, x^2*z0^5*z1^5, x^11, x^6*z0^5, x^5*z1^5, x^9, x^4*z0^5, x^3*z1^5, x^2*z0^5, x^3]
monomial z0^15*z1^10
monomial x^3*z0^10*z1^10
monomial x^2*z0^15*z1^5
monomial x^6*z0^5*z1^10
monomial x*z0^10*z1^10
monomial x*z1^20
monomial x^5*z0^10*z1^5
monomial x^4*z0^15
monomial x^9*z1^10
monomial x^4*z0^5*z1^10
monomial x^8*z0^5*z1^5
monomial x^3*z0^10*z1^5
monomial x^3*z1^15
monomial x^7*z0^10
monomial x^7*z1^10
monomial x^2*z0^5*z1^10
monomial x^11*z1^5
monomial x^6*z0^5*z1^5
monomial x*z0^10*z1^5
monomial x^10*z0^5
monomial x^5*z0^10
monomial x^5*z1^10
monomial x^9*z1^5
monomial x^13
monomial x^8*z0^5
monomial x^3*z0^10
monomial x^3*z1^10
monomial x^7*z1^5
monomial x^2*z0^5*z1^5
monomial x^11
monomial x^6*z0^5
monomial x^5*z1^5
monomial x^9
monomial x^4*z0^5
monomial x^3*z1^5
monomial x^2*z0^5
monomial x^3
(z0^3 - x*z1^2 + z0*z1^2 + x*z1 - x - z0) * dx
x Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
num, den x 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
aaa: x Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
monomials: [x]
monomial x
(0) * dx
x*z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
num, den x*z1 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
aaa: x*z1^5 - x^3 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
monomials: [x*z1^5, x^3]
monomial x*z1^5
monomial x^3
(0) * dx
x*z0 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
num, den x*z0 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
aaa: x*z0^5 - x^4 - x^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
monomials: [x*z0^5, x^4, x^2]
monomial x*z0^5
monomial x^4
monomial x^2
(-1) * dx
x*z0*z1 - x^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
num, den x*z0*z1 - x^2 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
aaa: x*z0^5*z1^5 - x^4*z1^5 - x^3*z0^5 - x^2*z1^5 + x^6 + x^4 - x^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
monomials: [x*z0^5*z1^5, x^4*z1^5, x^3*z0^5, x^2*z1^5, x^6, x^4, x^2]
monomial x*z0^5*z1^5
monomial x^4*z1^5
monomial x^3*z0^5
monomial x^2*z1^5
monomial x^6
monomial x^4
monomial x^2
(-z1 + 1) * dx
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[?7h[?12l[?25h[?2004l1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
(0) * dx
z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
(0) * dx
z1^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
(1) * dx
z1^3 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
(-2*z1) * dx
z1^4 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
(z1^2) * dx
z0 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
(0) * dx
z0*z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
(0) * dx
z0*z1^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
(z0) * dx
z0*z1^3 - x*z1^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
(-2*z0*z1 + x) * dx
z0*z1^4 + 2*x*z1^3 + 2*x*z0^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
(z0*z1^2 - x*z1 - x + z0) * dx
z0^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
(2) * dx
z0^2*z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
(2*z1 - 1) * dx
z0^2*z1^2 - x^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
(z0^2 + 2*z1^2 - 2*z1) * dx
z0^2*z1^3 - z0^4 + 2*x*z0*z1^2 - 2*x^2*z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
(-2*z0^2*z1 + 2*z1^3 + x*z0 - 2*z0^2 - z1 + 1) * dx
z0^2*z1^4 + z0^4*z1 + x*z0*z1^3 + x*z0^3 + x^2*z1^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
(z0^2*z1^2 + 2*z1^4 - x*z0*z1 + 2*z0^2*z1 + z0^2 - 2*z1^2 - z1 - 1) * dx
z0^3 - x*z1^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
(-x + z0) * dx
z0^3*z1 - 2*x*z1^3 + x*z0^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
(-x*z1 + z0*z1 - 2*x) * dx
z0^3*z1^2 - x*z1^4 + 2*x*z0^2*z1 - 2*x^2*z0 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
(z0^3 - x*z1^2 + z0*z1^2 + x*z1 - x - z0) * dx
x Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
(0) * dx
x*z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
(0) * dx
x*z0 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
(-1) * dx
x*z0*z1 - x^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
(-z1 + 1) * dx
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[?7h[?12l[?25h[?2004l(0) * dx
(0) * dx
(1) * dx
(-2*z1) * dx
(z1^2) * dx
(0) * dx
(0) * dx
(z0) * dx
(-2*z0*z1 + x) * dx
(z0*z1^2 - x*z1 - x + z0) * dx
(2) * dx
(2*z1 - 1) * dx
(z0^2 + 2*z1^2 - 2*z1) * dx
(-2*z0^2*z1 + 2*z1^3 + x*z0 - 2*z0^2 - z1 + 1) * dx
(z0^2*z1^2 + 2*z1^4 - x*z0*z1 + 2*z0^2*z1 + z0^2 - 2*z1^2 - z1 - 1) * dx
(-x + z0) * dx
(-x*z1 + z0*z1 - 2*x) * dx
(z0^3 - x*z1^2 + z0*z1^2 + x*z1 - x - z0) * dx
(0) * dx
(0) * dx
(-1) * dx
(-z1 + 1) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.substitute({X:X^2})[?7h[?12l[?25h[?25l[?7lS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[(1) * dx,
 (z1) * dx,
 (z1^2) * dx,
 (z1^3) * dx,
 (z1^4) * dx,
 (z0) * dx,
 (z0*z1) * dx,
 (z0*z1^2) * dx,
 (z0*z1^3 - x*z1^2) * dx,
 (z0*z1^4 + 2*x*z1^3 + 2*x*z0^2) * dx,
 (z0^2) * dx,
 (z0^2*z1) * dx,
 (z0^2*z1^2 - x^2) * dx,
 (z0^2*z1^3 - z0^4 + 2*x*z0*z1^2 - 2*x^2*z1) * dx,
 (z0^2*z1^4 + z0^4*z1 + x*z0*z1^3 + x*z0^3 + x^2*z1^2) * dx,
 (z0^3 - x*z1^2) * dx,
 (z0^3*z1 - 2*x*z1^3 + x*z0^2) * dx,
 (z0^3*z1^2 - x*z1^4 + 2*x*z0^2*z1 - 2*x^2*z0) * dx,
 (x) * dx,
 (x*z1) * dx,
 (x*z0) * dx,
 (x*z0*z1 - x^2) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(0) * dx
(0) * dx
(1) * dx
(-2*z1) * dx
(z1^2) * dx
(0) * dx
(0) * dx
(z0) * dx
(-2*z0*z1 + x) * dx
(z0*z1^2 - x*z1 - x + z0) * dx
(2) * dx
(2*z1 - 1) * dx
(z0^2 + 2*z1^2 - 2*z1) * dx
(-2*z0^2*z1 + 2*z1^3 + x*z0 - 2*z0^2 - z1 + 1) * dx
(z0^2*z1^2 + 2*z1^4 - x*z0*z1 + 2*z0^2*z1 + z0^2 - 2*z1^2 - z1 - 1) * dx
(-x + z0) * dx
(-x*z1 + z0*z1 - 2*x) * dx
(z0^3 - x*z1^2 + z0*z1^2 + x*z1 - x - z0) * dx
(0) * dx
(0) * dx
(-1) * dx
(-z1 + 1) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(0) * dx
(0) * dx
(1) * dx
(-2*z1) * dx
(z1^2) * dx
(0) * dx
(0) * dx
(z0) * dx
(-2*z0*z1 + x) * dx
(z0*z1^2 - x*z1 - x + z0) * dx
(2) * dx
(2*z1 - 1) * dx
(z0^2 + 2*z1^2 - 2*z1) * dx
(-2*z0^2*z1 + 2*z1^3 + x*z0 - 2*z0^2 - z1 + 1) * dx
(z0^2*z1^2 + 2*z1^4 - x*z0*z1 + 2*z0^2*z1 + z0^2 - 2*z1^2 - z1 - 1) * dx
(-x + z0) * dx
(-x*z1 + z0*z1 - 2*x) * dx
(z0^3 - x*z1^2 + z0*z1^2 + x*z1 - x - z0) * dx
(0) * dx
(0) * dx
(-1) * dx
(-z1 + 1) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 4 4 0 0]
[2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 3 2 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[1 4 0 2 0 0 0 0 0 0 3 3 0 0 0 0 0 0 0 0 1 0]
[4 4 3 0 2 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 4]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 3 4 0 0]
[0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 1 0 0 4 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus()

[?7h[?12l[?25h[?2004l[?7h22
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[9].form.monomials()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lsage: bbb

[?7h[?12l[?25h[?2004l[?7h[(1) * dx,
 (z1) * dx,
 (z1^2) * dx,
 (z1^3) * dx,
 (z1^4) * dx,
 (z0) * dx,
 (z0*z1) * dx,
 (z0*z1^2) * dx,
 (z0*z1^3 - x*z1^2) * dx,
 (z0*z1^4 + 2*x*z1^3 + 2*x*z0^2) * dx,
 (z0^2) * dx,
 (z0^2*z1) * dx,
 (z0^2*z1^2 - x^2) * dx,
 (z0^2*z1^3 - z0^4 + 2*x*z0*z1^2 - 2*x^2*z1) * dx,
 (z0^2*z1^4 + z0^4*z1 + x*z0*z1^3 + x*z0^3 + x^2*z1^2) * dx,
 (z0^3 - x*z1^2) * dx,
 (z0^3*z1 - 2*x*z1^3 + x*z0^2) * dx,
 (z0^3*z1^2 - x*z1^4 + 2*x*z0^2*z1 - 2*x^2*z0) * dx,
 (x) * dx,
 (x*z1) * dx,
 (x*z0) * dx,
 (x*z0*z1 - x^2) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l.function[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[9].form.monomials()[?7h[?12l[?25h[?25l[?7l0catier().coordinates()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].cartier().coordinates()[?7h[?12l[?25h[?25l[?7lsage: bbb[0].cartier().coordinates()

[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[0 0 1 0 0 0 0 0 0 0 2 4 0 1 4 0 0 0 0 0 4 1]
[0 0 0 3 0 0 0 0 0 0 0 2 3 4 4 0 0 0 0 0 0 4]
[0 0 0 0 1 0 0 0 0 0 0 0 2 0 3 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 4 0 0 0 0]
[0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 3 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 3 2 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 4 0 0 0 0 0 4 3 4 0 0 0 0]
[0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 4 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l4
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [59], 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>:26, 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>:17, in cartier_matrix(AS)

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 'genus'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS

[?7h[?12l[?25h[?2004l[?7h(Z/p)-cover of Superelliptic curve with the equation y^2 = x^3 + 1 over Finite Field of size 5 with the equation:
 z^5 - z = x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.genus()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus()

[?7h[?12l[?25h[?2004l[?7h7
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l4
4
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltests.sage')[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

 tensor        tests.sage    text3d       

 tensor_signed tetrahedron                

 tests         text                       



 [?7h[?12l[?25h[?25l[?7l(sts.sage')





[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

[?7h[?12l[?25h[?2004lCartier test:
Increase precision.
Increase precision.
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Input In [63], 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>:23, 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>:155, in cartier_matrix(self)

File /ext/sage/9.7/src/sage/matrix/matrix0.pyx:1504, in sage.matrix.matrix0.Matrix.__setitem__()
   1502         raise IndexError("value does not have the right number of columns")
   1503     elif single_col and row_list_len != len(value_list):
-> 1504         raise IndexError("value does not have the right number of rows")
   1505 else:
   1506     if row_list_len != len(value_list):

IndexError: value does not have the right number of rows
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

[?7h[?12l[?25h[?2004lCartier test:
Increase precision.
Increase precision.
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Input In [64], 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>:23, 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>:155, in cartier_matrix(self)

File /ext/sage/9.7/src/sage/matrix/matrix0.pyx:1504, in sage.matrix.matrix0.Matrix.__setitem__()
   1502         raise IndexError("value does not have the right number of columns")
   1503     elif single_col and row_list_len != len(value_list):
-> 1504         raise IndexError("value does not have the right number of rows")
   1505 else:
   1506     if row_list_len != len(value_list):

IndexError: value does not have the right number of rows
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7load('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

[?7h[?12l[?25h[?2004lCartier test:
True
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l = E.frobenius_matrix_hypellfrob()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lQ[?7h[?12l[?25h[?25l[?7lQ[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[],[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: M = matrix(QQ, [[1, 1], [0, 0]])

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM = matrix(QQ, [[1, 1], [0, 0]])[?7h[?12l[?25h[?25l[?7l.jordan_form()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: M.image()

[?7h[?12l[?25h[?2004l[?7hVector space of degree 2 and dimension 1 over Rational Field
Basis matrix:
[1 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM.image()[?7h[?12l[?25h[?25l[?7lsage: M

[?7h[?12l[?25h[?2004l[?7h[1 1]
[0 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l.image()[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: M.kernel()

[?7h[?12l[?25h[?2004l[?7hVector space of degree 2 and dimension 1 over Rational Field
Basis matrix:
[0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM.kernel()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7limag()[?7h[?12l[?25h[?25l[?7lmage()[?7h[?12l[?25h[?25l[?7lsage: M.image()

[?7h[?12l[?25h[?2004l[?7hVector space of degree 2 and dimension 1 over Rational Field
Basis matrix:
[1 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM.image()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltimage()[?7h[?12l[?25h[?25l[?7lrimage()[?7h[?12l[?25h[?25l[?7laimage()[?7h[?12l[?25h[?25l[?7lnimage()[?7h[?12l[?25h[?25l[?7lsimage()[?7h[?12l[?25h[?25l[?7lpimage()[?7h[?12l[?25h[?25l[?7loimage()[?7h[?12l[?25h[?25l[?7lsimage()[?7h[?12l[?25h[?25l[?7leimage()[?7h[?12l[?25h[?25l[?7l(image()[?7h[?12l[?25h[?25l[?7l()image()[?7h[?12l[?25h[?25l[?7l().image()[?7h[?12l[?25h[?25l[?7lsage: M.transpose().image()

[?7h[?12l[?25h[?2004l[?7hVector space of degree 2 and dimension 1 over Rational Field
Basis matrix:
[1 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM.transpose().image()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: M.transpose().image().basis()

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

[?7h[?12l[?25h[?2004lTrue True True
[
RModule M of dimension 3 over GF(2)
]
{
[0 0 1]
[1 1 1]
[1 0 0],
[1 1 1]
[0 0 1]
[0 1 0]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTrue True True
[
RModule M of dimension 3 over GF(2)
]
{
[0 0 1]
[1 1 1]
[1 0 0],
[1 1 1]
[0 0 1]
[0 1 0]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.height[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 + x + 1, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x^3 + x + 1, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupe[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRax.<x> = PolynomialRing(Ra)[?7h[?12l[?25h[?25l[?7l.<x> =PolynomialRing(QQ)[?7h[?12l[?25h[?25l[?7l<[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l>[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= PolynomialRing(QQ)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lG)[?7h[?12l[?25h[?25l[?7lF)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: R.<x> = PolynomialRing(GF(3))

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR.<x> = PolynomialRing(GF(3))[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.height[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 + x + 1, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l superelliptic(x^3 + x + 1, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l-, 2)[?7h[?12l[?25h[?25l[?7lx, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l x, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.height[?7h[?12l[?25h[?25l[?7ldx.cartier()[?7h[?12l[?25h[?25l[?7le_rham_basis()[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in range(1, n):[?7h[?12l[?25h[?25l[?7l =a[n]*x^ + a[0][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic_function(C, 1/x)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in range(1, n):[?7h[?12l[?25h[?25l[?7l =a[n]*x^ + a[0][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic_function(C, 1/x)[?7h[?12l[?25h[?25l[?7luperelliptic_function(C, 1/x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7ly)[?7h[?12l[?25h[?25l[?7l/)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: f = superelliptic_function(C, y/x)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [5], in <cell line: 1>()
----> 1 f = superelliptic_function(C, y/x)

NameError: name 'y' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = superelliptic_function(C, y/x)[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lR.<x> = PoynomalRing(GF(3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l,> = PolynomialRing(GF(3)[?7h[?12l[?25h[?25l[?7l > = PolynomialRing(GF(3)[?7h[?12l[?25h[?25l[?7ly> = PolynomialRing(GF(3)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx.<x, y> = PolynomialRing(GF(3)[?7h[?12l[?25h[?25l[?7ly.<x, y> = PolynomialRing(GF(3)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: Rxy.<x, y> = PolynomialRing(GF(3), 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxy.<x, y> = PolynomialRing(GF(3), 2)[?7h[?12l[?25h[?25l[?7lf = superelliptic_functio(C, y/x)[?7h[?12l[?25h[?25l[?7lsage: f = superelliptic_function(C, y/x)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldimension_of_RHS = p*gY + (len(list_of_m) - 1)*(p-1) + sum(sum(i*alpha(i, m, p) for i in range(1, p)) for m in list_of_m)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = superelliptic_function(C, y/x)[?7h[?12l[?25h[?25l[?7l.substitute({x:x^2, y:x, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f.diffn()

[?7h[?12l[?25h[?2004l[?7h((-x^2 - 1)/(x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.expnsion_at_infty()[1][?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().pth_root()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l/*(C.dx)[?7h[?12l[?25h[?25l[?7lC*(C.dx)[?7h[?12l[?25h[?25l[?7l.*(C.dx)[?7h[?12l[?25h[?25l[?7ly*(C.dx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y*(C.dx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()*(C.dx)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.x)^2/(C.y)*(C.dx)

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

[?7h[?12l[?25h[?2004l[?7ht^-4 + 1 + O(t^6)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()





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

[?7h[?12l[?25h[?2004l  Input In [11]
    C.
      ^
SyntaxError: invalid syntax

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[?7h[?12l[?25h[?2004l[?7h(1/(x^3 + 2*x))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y)^(-1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((C.y)^(-1)).diffn()

[?7h[?12l[?25h[?2004l[?7h((-1)/(x^3*y - x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x[?7h[?12l[?25h[?25l[?7l1C.x[?7h[?12l[?25h[?25l[?7l/C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((1/C.x).difn()[?7h[?12l[?25h[?25l[?7l)(1/C.x).difn()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l/C.x).difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x).difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l^).difn()[?7h[?12l[?25h[?25l[?7l).difn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()^.difn()[?7h[?12l[?25h[?25l[?7l(.difn()[?7h[?12l[?25h[?25l[?7l().difn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l-).difn()[?7h[?12l[?25h[?25l[?7l1).difn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()).difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l((C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l*((C.x)^(-1)).difn()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC)*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7lx)*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7l.)*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7l)*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7l.)*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7lx)*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()^*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7l(*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7l-*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7l2*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7l()*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.x)^(-2)*((C.x)^(-1)).diffn()

[?7h[?12l[?25h[?2004l[?7h((-1)/x^4) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.diffn()[?7h[?12l[?25h[?25l[?7lfff.cartier()[?7h[?12l[?25h[?25l[?7l = x^3 - x + 2[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ff = superellitptic_function(C, y/x^2)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [15], in <cell line: 1>()
----> 1 ff = superellitptic_function(C, y/x**Integer(2))

NameError: name 'superellitptic_function' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = superellitptic_function(C, y/x^2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lptic_function(C, y/x^2)[?7h[?12l[?25h[?25l[?7lsage: ff = superelliptic_function(C, y/x^2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = superelliptic_function(C, y/x^2)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.dicriminant()%8[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ff.diffn()

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

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
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>:25, 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>:43, in <module>

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

File <string>:113, in degree_of_rational_fctn(f, F)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:554, in 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):
--> 554     raise TypeError("base_ring {!r} must be a ring".format(base_ring))
    556 n = -1  # Unknown number of variables
    557 names = None  # Unknown variable names

TypeError: base_ring 3 must be a ring
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 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>:25, 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>

TypeError: bad operand type for unary -: 'superelliptic_function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 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>:25, 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 /ext/sage/9.7/src/sage/rings/integer.pyx:1769, in sage.rings.integer.Integer.__add__()
   1767         return y
   1768 
-> 1769     return coercion_model.bin_op(left, right, operator.add)
   1770 
   1771 cpdef _add_(self, right):

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 +: 'Integer Ring' and '<class '__main__.superelliptic_function'>'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: C.one

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.one[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: loa

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [5], in <cell line: 1>()
----> 1 loa

NameError: name 'loa' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lloa[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lloa[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx
t^-40 + O(t^-30)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx
t^-40 + O(t^-30)
---------------------------------------------------------------------------
NameError                                 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>:25, 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>

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

[?7h[?12l[?25h[?2004l((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx
t^-40 + O(t^-30)
(2*x^15 + 2*x^13 + x^12 + x^10 + 2*x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2, 2*x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx
t^-40 + O(t^-30)
(2*x^15 + 2*x^13 + x^12 + x^10 + 2*x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2, 2*x)
(2*x^12 + x^10 + x^9 + x^8 + 2*x^7 + x^6 + x^5 + x^4 + x^2 + 2*x + 1, x^2 + x + 2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx
t^-40 + O(t^-30)
[2, 1, x^2 + 2*x + 2, 2*x^2 + 2*x + 1, x^2 + 1, x^2 + x + 2, 2*x]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: omega

[?7h[?12l[?25h[?2004l[?7h((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.one[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.xpansion_at_infty()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)^(-2)*((C.x)^(-1)).diffn()[?7h[?12l[?25h[?25l[?7l)^(-2)*((C.x)^(-1)).diffn()[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()y[?7h[?12l[?25h[?25l[?7l(y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: (C.x)^(11)/(C.y)^3*C.dx

[?7h[?12l[?25h[?2004l[?7h(x^11/y^3) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x)^(11)/(C.y)^3*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x)^(1)/(C.y)^3*C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((C.x)^(11)/(C.y)^3*C.dx).expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2*t^-40 + O(t^-30)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x)^(11)/(C.y)^3*C.dx).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x)^(11)/(C.y)^3*C.dx[?7h[?12l[?25h[?25l[?7lomega[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lomega[?7h[?12l[?25h[?25l[?7l(C.x)^(11)/(C.y)^3*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x)^(11)/(C.y)^3*C.dx).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo((C.x)^(1)/(C.y)^3*C.dx)[?7h[?12l[?25h[?25l[?7lm((C.x)^(1)/(C.y)^3*C.dx)[?7h[?12l[?25h[?25l[?7l1((C.x)^(1)/(C.y)^3*C.dx)[?7h[?12l[?25h[?25l[?7l ((C.x)^(1)/(C.y)^3*C.dx)[?7h[?12l[?25h[?25l[?7l=((C.x)^(1)/(C.y)^3*C.dx)[?7h[?12l[?25h[?25l[?7l ((C.x)^(1)/(C.y)^3*C.dx)[?7h[?12l[?25h[?25l[?7lsage: om1 = ((C.x)^(11)/(C.y)^3*C.dx)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = ((C.x)^(11)/(C.y)^3*C.dx)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: om1.is_regular_on_U

 om1.is_regular_on_U0    

 om1.is_regular_on_Uinfty





 [?7h[?12l[?25h[?25l[?7l0

 om1.is_regular_on_U0    



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





[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.is_regular_on_U0()

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lom1.is_regular_on_U0()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: om1

[?7h[?12l[?25h[?2004l[?7h(x^11/y^3) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7lom1[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.is_regular_on_U0()[?7h[?12l[?25h[?25l[?7lj[?7h[?12l[?25h[?25l[?7lth_component[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.jth_component(0)

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.jth_component(0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om1.jth_component(1)

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.jth_component(1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7lsage: om1.jth_component(2)

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.jth_component(2)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.cartier()

[?7h[?12l[?25h[?2004l[?7h(x^3/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: om1

[?7h[?12l[?25h[?2004l[?7h(x^11/y^3) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.cartier()[?7h[?12l[?25h[?25l[?7ljth_component(2)[?7h[?12l[?25h[?25l[?7lth_component(2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7lsage: om1.jth_component(3)

[?7h[?12l[?25h[?2004l[?7hx^11
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y = parent(a).gens()[0], parent(a).gens()[1][?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l11.[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: x^11.quo_rem(x^3 - x)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [24], in <cell line: 1>()
----> 1 x**Integer(11).quo_rem(x**Integer(3) - x)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_template.pxi:592, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_template.__pow__()
    590 cdef long e
    591 try:
--> 592     e = ee
    593 except OverflowError:
    594     return Polynomial.__pow__(self, ee, modulus)

TypeError: an integer is required
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx^11.quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^1.quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(11).quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: (x^11).quo_rem(x^3 - x)

[?7h[?12l[?25h[?2004l[?7h(x^8 + x^6 + x^4 + x^2 + 1, x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = Ra.gens()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc_expansion[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(x^11, x^3 - x)

[?7h[?12l[?25h[?2004l[?7h[x^2, 0, x^2 + 1, x]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.one[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lheight[?7h[?12l[?25h[?25l[?7lolomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx
t^-40 + O(t^-30)
[2, 1, x^2 + 2*x + 2, 2*x^2 + 2*x + 1, x^2 + 1, x^2 + x + 2, 2*x]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS

[?7h[?12l[?25h[?2004l[?7h(Z/p)-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equation:
 z^3 - z = x^4
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.genus()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.cartier_matrix()

[?7h[?12l[?25h[?2004l[?7h[0 0 0]
[0 0 0]
[0 0 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cartier_matrix()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: (AS.x)^(-1)*AS.dx

[?7h[?12l[?25h[?2004l[?7h(1/x) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.x)^(-1)*AS.dx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((AS.x)^(-1)*AS.dx)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((AS.x)^(-1)*AS.dx).cartier()

[?7h[?12l[?25h[?2004l[?7h(1/x) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.diffn()[?7h[?12l[?25h[?25l[?7lor  i range(1, n):[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: for b in AS.holomorphic_differentials_basis():

....: [?7h[?12l[?25h[?25l[?7lprint(ffff.cartier())[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:     print(b.cartier())

....: [?7h[?12l[?25h[?25l[?7lsage: for b in AS.holomorphic_differentials_basis():

....:     print(b.cartier())

....: 

[?7h[?12l[?25h[?2004l(0) * dx
(0) * dx
(0) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cartier_matrix()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcartier_matrix()[?7h[?12l[?25h[?25l[?7lsage: AS.cartier_matrix()

[?7h[?12l[?25h[?2004l[?7h[0 0 0 1]
[0 0 0 0]
[0 2 0 0]
[0 0 0 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cartier_matrix()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lker[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lel[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lccc.monomials()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr_kernel[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: cartier_kernel(AS)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [36], in <cell line: 1>()
----> 1 cartier_kernel(AS)

File <string>:16, in cartier_kernel(C, prec)

TypeError: as_cover.cartier_matrix() got an unexpected keyword argument 'prec'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cartier_matrix()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcartier_matrix()[?7h[?12l[?25h[?25l[?7lsage: AS.cartier_matrix()

[?7h[?12l[?25h[?2004l[?7h[0 0 0 1]
[0 0 0 0]
[0 2 0 0]
[0 0 0 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcartier_kernel(AS)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ltier_kernel(AS)[?7h[?12l[?25h[?25l[?7lsage: cartier_kernel(AS)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [39], in <cell line: 1>()
----> 1 cartier_kernel(AS)

File <string>:24, in cartier_kernel(C, prec)

File <string>:23, in __add__(self, other)

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

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcartier_kernel(AS)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ltier_kernel(AS)[?7h[?12l[?25h[?25l[?7lsage: cartier_kernel(AS)

[?7h[?12l[?25h[?2004l[?7h[(1) * dx, (x) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcartier_kernel(AS)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lier_kernel(AS)[?7h[?12l[?25h[?25l[?7lsage: cartier_kernel(AS)

[?7h[?12l[?25h[?2004l[?7h[(1) * dx, (x) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcartier_kernel(AS)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lier_kernel(AS)[?7h[?12l[?25h[?25l[?7lsage: cartier_kernel(AS)

[?7h[?12l[?25h[?2004l[?7h[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[(1) * dx, (x) * dx, (x^3) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[(1) * dx, (x) * dx, (x^3) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[(1) * dx, (x) * dx, (x^3) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[(1) * dx, (x^2 + z0) * dx, (x) * dx, (x^3) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ltess.sage')[?7h[?12l[?25h[?25l[?7l(ests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx]
superelliptic p rank test:
---------------------------------------------------------------------------
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: 'p'

During handling of the above exception, another exception occurred:

AttributeError                            Traceback (most recent call last)
Input In [51], 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>:7, 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>:5, in <module>

File /ext/sage/9.7/src/sage/structure/category_object.pyx:833, in sage.structure.category_object.CategoryObject.__getattr__()
    831         AttributeError: 'PrimeNumbers_with_category' object has no attribute 'sadfasdf'
    832     """
--> 833     return self.getattr_from_category(name)
    834 
    835 cdef getattr_from_category(self, name):

File /ext/sage/9.7/src/sage/structure/category_object.pyx:848, in sage.structure.category_object.CategoryObject.getattr_from_category()
    846     cls = self._category.parent_class
    847 
--> 848 attr = getattr_from_other_class(self, cls, name)
    849 self.__cached_methods[name] = attr
    850 return attr

File /ext/sage/9.7/src/sage/cpython/getattr.pyx:356, in sage.cpython.getattr.getattr_from_other_class()
    354     dummy_error_message.cls = type(self)
    355     dummy_error_message.name = name
--> 356     raise AttributeError(dummy_error_message)
    357 cdef PyObject* attr = instance_getattr(cls, name)
    358 if attr is NULL:

AttributeError: 'HyperellipticCurve_FiniteField_with_category' object has no attribute 'p'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx]
superelliptic p rank test:
2
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [52], 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>:7, 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>:6, in <module>

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

[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx]
superelliptic p rank test:
2
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [53], 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>:7, 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>

File <string>:170, in p_rank(self)

File /ext/sage/9.7/src/sage/matrix/special.py:922, in identity_matrix(ring, n, sparse)
    920     n = ring
    921     ring = ZZ
--> 922 return matrix_space.MatrixSpace(ring, n, n, sparse)(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/matrix/matrix_space.py:561, in MatrixSpace.__classcall__(cls, base_ring, nrows, ncols, sparse, implementation, **kwds)
    516 """
    517 Normalize the arguments to call the ``__init__`` constructor.
    518 
   (...)
    558     False
    559 """
    560 if base_ring not in _Rings:
--> 561     raise TypeError("base_ring (=%s) must be a ring"%base_ring)
    562 nrows = int(nrows)
    563 if ncols is None:

TypeError: base_ring (=3) must be a ring
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx^11.quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: x

[?7h[?12l[?25h[?2004l[?7hx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprint(f^2)[?7h[?12l[?25h[?25l[?7larent(A)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: parent(x)

[?7h[?12l[?25h[?2004l[?7hUnivariate Polynomial Ring in x over Finite Field of size 67
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l?superelliptic_cech[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lsage: ?superelliptic

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
OSError                                   Traceback (most recent call last)
Input In [56], in <cell line: 1>()
----> 1 get_ipython().run_line_magic('pinfo', 'superelliptic')

File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:2305, in InteractiveShell.run_line_magic(self, magic_name, line, _stack_depth)
   2303     kwargs['local_ns'] = self.get_local_scope(stack_depth)
   2304 with self.builtin_trap:
-> 2305     result = fn(*args, **kwargs)
   2306 return result

File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/magics/namespace.py:58, in NamespaceMagics.pinfo(self, parameter_s, namespaces)
     56     self.psearch(oname)
     57 else:
---> 58     self.shell._inspect('pinfo', oname, detail_level=detail_level,
     59                         namespaces=namespaces)

File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:1685, in InteractiveShell._inspect(self, meth, oname, namespaces, **kw)
   1683     pmethod(info.obj, oname, formatter)
   1684 elif meth == 'pinfo':
-> 1685     pmethod(
   1686         info.obj,
   1687         oname,
   1688         formatter,
   1689         info,
   1690         enable_html_pager=self.enable_html_pager,
   1691         **kw,
   1692     )
   1693 else:
   1694     pmethod(info.obj, oname)

File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/oinspect.py:698, in Inspector.pinfo(self, obj, oname, formatter, info, detail_level, enable_html_pager, omit_sections)
    665 def pinfo(
    666     self,
    667     obj,
   (...)
    673     omit_sections=(),
    674 ):
    675     """Show detailed information about an object.
    676 
    677     Optional arguments:
   (...)
    696     - omit_sections: set of section keys and titles to omit
    697     """
--> 698     info = self._get_info(
    699         obj, oname, formatter, info, detail_level, omit_sections=omit_sections
    700     )
    701     if not enable_html_pager:
    702         del info['text/html']

File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/oinspect.py:591, in Inspector._get_info(self, obj, oname, formatter, info, detail_level, omit_sections)
    571 def _get_info(
    572     self, obj, oname="", formatter=None, info=None, detail_level=0, omit_sections=()
    573 ):
    574     """Retrieve an info dict and format it.
    575 
    576     Parameters
   (...)
    588         Titles or keys to omit from output (can be set, tuple, etc., anything supporting `in`)
    589     """
--> 591     info = self.info(obj, oname=oname, info=info, detail_level=detail_level)
    593     _mime = {
    594         'text/plain': [],
    595         'text/html': '',
    596     }
    598     def append_field(bundle, title:str, key:str, formatter=None):

File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/oinspect.py:762, in Inspector.info(self, obj, oname, info, detail_level)
    760             ds += "\nDocstring:\n" + obj.__doc__
    761 else:
--> 762     ds = getdoc(obj)
    763     if ds is None:
    764         ds = '<no docstring>'

File /ext/sage/9.7/src/sage/misc/lazy_import.pyx:391, in sage.misc.lazy_import.LazyImport.__call__()
    389         True
    390     """
--> 391     return self.get_object()(*args, **kwds)
    392 
    393 def __repr__(self):

File /ext/sage/9.7/src/sage/misc/sageinspect.py:2107, in sage_getdoc(obj, obj_name, embedded)
   2105 r = sage_getdoc_original(obj)
   2106 s = sage.misc.sagedoc.format(r, embedded=embedded)
-> 2107 f = sage_getfile(obj)
   2108 if f and os.path.exists(f):
   2109     from sage.doctest.control import skipfile

File /ext/sage/9.7/src/sage/misc/sageinspect.py:1414, in sage_getfile(obj)
   1412 # No go? fall back to inspect.
   1413 try:
-> 1414     sourcefile = inspect.getabsfile(obj)
   1415 except TypeError: # this happens for Python builtins
   1416     return ''

File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/inspect.py:844, in getabsfile(object, _filename)
    839 """Return an absolute path to the source or compiled file for an object.
    840 
    841 The idea is for each object to have a unique origin, so this routine
    842 normalizes the result as much as possible."""
    843 if _filename is None:
--> 844     _filename = getsourcefile(object) or getfile(object)
    845 return os.path.normcase(os.path.abspath(_filename))

File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/inspect.py:817, in getsourcefile(object)
    813 def getsourcefile(object):
    814     """Return the filename that can be used to locate an object's source.
    815     Return None if no way can be identified to get the source.
    816     """
--> 817     filename = getfile(object)
    818     all_bytecode_suffixes = importlib.machinery.DEBUG_BYTECODE_SUFFIXES[:]
    819     all_bytecode_suffixes += importlib.machinery.OPTIMIZED_BYTECODE_SUFFIXES[:]

File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/inspect.py:785, in getfile(object)
    783             return module.__file__
    784         if object.__module__ == '__main__':
--> 785             raise OSError('source code not available')
    786     raise TypeError('{!r} is a built-in class'.format(object))
    787 if ismethod(object):

OSError: source code not available
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lstr(E.local_data(2))[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lsage: superelliptic

 superelliptic          superelliptic_drw_form

 superelliptic/         superelliptic_form    

 superelliptic_cech     superelliptic_function



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

 superelliptic         





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







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

 superelliptic          superelliptic_drw_form

 superelliptic/         superelliptic_form    

 superelliptic_cech     superelliptic_function[?7h[?12l[?25h[?25l[?7ll





[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupe[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx]
superelliptic p rank test:
2
[ 0 39  0]
[19  0 29]
[ 0 21  0]
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [57], 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>:7, 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>:170, in p_rank(self)

File /ext/sage/9.7/src/sage/matrix/special.py:922, in identity_matrix(ring, n, sparse)
    920     n = ring
    921     ring = ZZ
--> 922 return matrix_space.MatrixSpace(ring, n, n, sparse)(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/matrix/matrix_space.py:561, in MatrixSpace.__classcall__(cls, base_ring, nrows, ncols, sparse, implementation, **kwds)
    516 """
    517 Normalize the arguments to call the ``__init__`` constructor.
    518 
   (...)
    558     False
    559 """
    560 if base_ring not in _Rings:
--> 561     raise TypeError("base_ring (=%s) must be a ring"%base_ring)
    562 nrows = int(nrows)
    563 if ncols is None:

TypeError: base_ring (=3) must be a ring
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cartier_matrix()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.one[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.genus()

[?7h[?12l[?25h[?2004l[?7h3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lisinstance(C_super.x, superelliptic_function)[?7h[?12l[?25h[?25l[?7lid[?7h[?12l[?25h[?25l[?7lide[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: identity_matrix(3)

[?7h[?12l[?25h[?2004l[?7h[1 0 0]
[0 1 0]
[0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx]
superelliptic p rank test:
2
[ 0 39  0]
[19  0 29]
[ 0 21  0]
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [60], 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>:7, 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 /ext/sage/9.7/src/sage/matrix/special.py:922, in identity_matrix(ring, n, sparse)
    920     n = ring
    921     ring = ZZ
--> 922 return matrix_space.MatrixSpace(ring, n, n, sparse)(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/matrix/matrix_space.py:561, in MatrixSpace.__classcall__(cls, base_ring, nrows, ncols, sparse, implementation, **kwds)
    516 """
    517 Normalize the arguments to call the ``__init__`` constructor.
    518 
   (...)
    558     False
    559 """
    560 if base_ring not in _Rings:
--> 561     raise TypeError("base_ring (=%s) must be a ring"%base_ring)
    562 nrows = int(nrows)
    563 if ncols is None:

TypeError: base_ring (=2*x^18 + x^15 + x^14 + x^11) must be a ring
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lidentity_matrix(3)[?7h[?12l[?25h[?25l[?7lid[?7h[?12l[?25h[?25l[?7lide[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ltity_matrix(3)[?7h[?12l[?25h[?25l[?7lsage: identity_matrix(3)

[?7h[?12l[?25h[?2004l[?7h[1 0 0]
[0 1 0]
[0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgX = (two_gX_minus_2+2)/2[?7h[?12l[?25h[?25l[?7lsage: g

[?7h[?12l[?25h[?2004l[?7h2*x^18 + x^15 + x^14 + x^11
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lhight[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.genus()

[?7h[?12l[?25h[?2004l[?7h3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx]
superelliptic p rank test:
2
[ 0 39  0]
[19  0 29]
[ 0 21  0]
[1 0 0]
[0 1 0]
[0 0 1]
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [64], 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>:7, 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>:9, in <module>

File <string>:170, in p_rank(self)

File /ext/sage/9.7/src/sage/matrix/special.py:922, in identity_matrix(ring, n, sparse)
    920     n = ring
    921     ring = ZZ
--> 922 return matrix_space.MatrixSpace(ring, n, n, sparse)(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/matrix/matrix_space.py:561, in MatrixSpace.__classcall__(cls, base_ring, nrows, ncols, sparse, implementation, **kwds)
    516 """
    517 Normalize the arguments to call the ``__init__`` constructor.
    518 
   (...)
    558     False
    559 """
    560 if base_ring not in _Rings:
--> 561     raise TypeError("base_ring (=%s) must be a ring"%base_ring)
    562 nrows = int(nrows)
    563 if ncols is None:

TypeError: base_ring (=3) must be a ring
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx]
superelliptic p rank test:
2
[66 39  0]
[19 66 29]
[ 0 21 66]
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [65], 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>:7, 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>:170, in p_rank(self)

File /ext/sage/9.7/src/sage/matrix/special.py:922, in identity_matrix(ring, n, sparse)
    920     n = ring
    921     ring = ZZ
--> 922 return matrix_space.MatrixSpace(ring, n, n, sparse)(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/matrix/matrix_space.py:561, in MatrixSpace.__classcall__(cls, base_ring, nrows, ncols, sparse, implementation, **kwds)
    516 """
    517 Normalize the arguments to call the ``__init__`` constructor.
    518 
   (...)
    558     False
    559 """
    560 if base_ring not in _Rings:
--> 561     raise TypeError("base_ring (=%s) must be a ring"%base_ring)
    562 nrows = int(nrows)
    563 if ncols is None:

TypeError: base_ring (=3) must be a ring
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx]
superelliptic p rank test:
2
[66 39  0]
[19 66 29]
[ 0 21 66]
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [66], 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>:7, 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>:170, in p_rank(self)

File /ext/sage/9.7/src/sage/matrix/special.py:922, in identity_matrix(ring, n, sparse)
    920     n = ring
    921     ring = ZZ
--> 922 return matrix_space.MatrixSpace(ring, n, n, sparse)(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/matrix/matrix_space.py:561, in MatrixSpace.__classcall__(cls, base_ring, nrows, ncols, sparse, implementation, **kwds)
    516 """
    517 Normalize the arguments to call the ``__init__`` constructor.
    518 
   (...)
    558     False
    559 """
    560 if base_ring not in _Rings:
--> 561     raise TypeError("base_ring (=%s) must be a ring"%base_ring)
    562 nrows = int(nrows)
    563 if ncols is None:

TypeError: base_ring (=3) must be a ring
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l?superelliptic[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lid[?7h[?12l[?25h[?25l[?7lide[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: ?identity_matrix

[?7h[?12l[?25h[?2004l[?1049h[?1h=
Signature:      identity_matrix(ring, n=0, sparse=False)
Docstring:     
   This function is available as identity_matrix(...) and
   matrix.identity(...).

   Return the n x n identity matrix over the given ring.

   The default ring is the integers.

   EXAMPLES:

      sage: M = identity_matrix(QQ, 2); M
      [1 0]
      [0 1]
      sage: M.parent()
      Full MatrixSpace of 2 by 2 dense matrices over Rational Field
      sage: M = identity_matrix(2); M
      [1 0]
      [0 1]
      sage: M.parent()
      Full MatrixSpace of 2 by 2 dense matrices over Integer Ring
      sage: M.is_mutable()
      True
      sage: M = identity_matrix(3, sparse=True); M
      [1 0 0]
      [0 1 0]
:
      [0 0 1]
:
      sage: M.parent()
:
      Full MatrixSpace of 3 by 3 sparse matrices over Integer Ring
:
      sage: M.is_mutable()
:
      True
:
Init docstring: Initialize self.  See help(type(self)) for accurate signature.
:
File:           /ext/sage/9.7/src/sage/matrix/special.py
:
Type:           function
:

(END)

(END)

(END)

(END)
M   The default ring is the integers.
M
M   Return the n x n identity matrix over the given ring.
M
M   matrix.identity(...).
M   This function is available as identity_matrix(...) and
MDocstring:     
MSignature:      identity_matrix(ring, n=0, sparse=False)

:
 ::ww
:
      [0 0 1]
:
 ::qq
[?1l>[?1049l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx]
superelliptic p rank test:
2
[66 39  0]
[19 66 29]
[ 0 21 66]
0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.a_number()

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lX[?7h[?12l[?25h[?25l[?7lsage: X

[?7h[?12l[?25h[?2004l[?7hHyperelliptic Curve over Finite Field of size 67 defined by y^2 = x^7 + x^3 + x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lX[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lnumber[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: X.a_number()

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx]
a-number test:
True
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7lini.sage')[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l(t.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 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>:25, 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>:10, in <module>

TypeError: 'function' object cannot be interpreted as an integer
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [74], 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>:25, 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 /ext/sage/9.7/src/sage/misc/functional.py:639, in symbolic_prod(expression, *args, **kwds)
    637 from .misc_c import prod as c_prod
    638 if hasattr(expression, 'prod'):
--> 639     return expression.prod(*args, **kwds)
    640 elif len(args) <= 1:
    641     return c_prod(expression, *args)

TypeError: Monoids.ParentMethods.prod() takes 2 positional arguments but 7 were given
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [75], 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>:25, 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 /ext/sage/9.7/src/sage/misc/functional.py:639, in symbolic_prod(expression, *args, **kwds)
    637 from .misc_c import prod as c_prod
    638 if hasattr(expression, 'prod'):
--> 639     return expression.prod(*args, **kwds)
    640 elif len(args) <= 1:
    641     return c_prod(expression, *args)

TypeError: Monoids.ParentMethods.prod() takes 2 positional arguments but 7 were given
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [76], 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>:25, 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 /ext/sage/9.7/src/sage/misc/functional.py:639, in symbolic_prod(expression, *args, **kwds)
    637 from .misc_c import prod as c_prod
    638 if hasattr(expression, 'prod'):
--> 639     return expression.prod(*args, **kwds)
    640 elif len(args) <= 1:
    641     return c_prod(expression, *args)

TypeError: Monoids.ParentMethods.prod() takes 2 positional arguments but 7 were given
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [77], 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>:25, 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 /ext/sage/9.7/src/sage/misc/functional.py:639, in symbolic_prod(expression, *args, **kwds)
    637 from .misc_c import prod as c_prod
    638 if hasattr(expression, 'prod'):
--> 639     return expression.prod(*args, **kwds)
    640 elif len(args) <= 1:
    641     return c_prod(expression, *args)

TypeError: Monoids.ParentMethods.prod() takes 2 positional arguments but 7 were given
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l(0, 0, 0, 0, 0, 0, 0)
(0, 0, 0, 0, 0, 0, 0) x^7
x^7
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [78], 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>:25, 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>:23, in <module>

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

[?7h[?12l[?25h[?2004l(0, 0, 0, 0, 0, 0, 0)
(0, 0, 0, 0, 0, 0, 0) x^7
x^7
x^7 -2
(0, 0, 0, 0, 0, 0, 1)
(0, 0, 0, 0, 0, 0, 1) x^7
x^7
x^7 -2
(0, 0, 0, 0, 0, 0, 2)
(0, 0, 0, 0, 0, 0, 2) x^7
x^7
x^7 -2
(0, 0, 0, 0, 0, 1, 0)
(0, 0, 0, 0, 0, 1, 0) x^7
x^7 + x^5
x^7 + x^5 -3
(0, 0, 0, 0, 0, 1, 1)
(0, 0, 0, 0, 0, 1, 1) x^7
x^7 + x^5
x^7 + x^5 -3
(0, 0, 0, 0, 0, 1, 2)
(0, 0, 0, 0, 0, 1, 2) x^7
x^7 + x^5
x^7 + x^5 -3
(0, 0, 0, 0, 0, 2, 0)
(0, 0, 0, 0, 0, 2, 0) x^7
x^7 + 2*x^5
x^7 + 2*x^5 -3
(0, 0, 0, 0, 0, 2, 1)
(0, 0, 0, 0, 0, 2, 1) x^7
x^7 + 2*x^5
x^7 + 2*x^5 -3
(0, 0, 0, 0, 0, 2, 2)
(0, 0, 0, 0, 0, 2, 2) x^7
x^7 + 2*x^5
x^7 + 2*x^5 -3
(0, 0, 0, 0, 1, 0, 0)
(0, 0, 0, 0, 1, 0, 0) x^7
x^7 + x^4
x^7 + x^4 -2
(0, 0, 0, 0, 1, 0, 1)
(0, 0, 0, 0, 1, 0, 1) x^7
x^7 + x^4
x^7 + x^4 -2
(0, 0, 0, 0, 1, 0, 2)
(0, 0, 0, 0, 1, 0, 2) x^7
x^7 + x^4
x^7 + x^4 -2
(0, 0, 0, 0, 1, 1, 0)
(0, 0, 0, 0, 1, 1, 0) x^7
x^7 + x^5 + x^4
x^7 + x^5 + x^4 -3
(0, 0, 0, 0, 1, 1, 1)
(0, 0, 0, 0, 1, 1, 1) x^7
x^7 + x^5 + x^4
^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)
Input In [79], 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>:25, 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>:44, in __init__(self, C, list_of_fcts, prec)

File <string>:167, in artin_schreier_transform(power_series, prec)

File <string>:12, in new_reverse(power_series, prec)

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1831, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
   1829 if x:
   1830     raise ValueError("must not specify %s keyword and positional argument" % name)
-> 1831 a = self(kwds[name])
   1832 del kwds[name]
   1833 try:

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1852, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
   1850         x = x[0]
   1851 
-> 1852     return self.__u(*x)*(x[0]**self.__n)
   1853 
   1854 def __pari__(self):

File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:365, in sage.rings.power_series_poly.PowerSeries_poly.__call__()
    363         x[0] = a
    364         x = tuple(x)
--> 365     return self.__f(x)
    366 
    367 def _unsafe_mutate(self, i, value):

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:898, in sage.rings.polynomial.polynomial_element.Polynomial.__call__()
    896             return result
    897         pol._compiled = CompiledPolynomialFunction(pol.list())
--> 898     return pol._compiled.eval(a)
    899 
    900 def compose_trunc(self, Polynomial other, long n):

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:125, in sage.rings.polynomial.polynomial_compiled.CompiledPolynomialFunction.eval()
    123 cdef object temp
    124 try:
--> 125     pd_eval(self._dag, x, self._coeffs)  #see further down
    126     temp = self._dag.value               #for an explanation
    127     pd_clean(self._dag)                  #of these 3 lines

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
    352     if pd.value is None:
--> 353         pd.eval(vars, coeffs)
    354     pd.hits += 1
    355 

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
    505 
    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507         pd_eval(self.left, vars, coeffs)
    508         pd_eval(self.right, vars, coeffs)
    509         self.value = self.left.value * self.right.value + coeffs[self.index]

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
    352     if pd.value is None:
--> 353         pd.eval(vars, coeffs)
    354     pd.hits += 1
    355 

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
    505 
    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507         pd_eval(self.left, vars, coeffs)
    508         pd_eval(self.right, vars, coeffs)
    509         self.value = self.left.value * self.right.value + coeffs[self.index]

    [... skipping similar frames: sage.rings.polynomial.polynomial_compiled.pd_eval at line 353 (42 times), sage.rings.polynomial.polynomial_compiled.abc_pd.eval at line 507 (41 times)]

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
    505 
    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507         pd_eval(self.left, vars, coeffs)
    508         pd_eval(self.right, vars, coeffs)
    509         self.value = self.left.value * self.right.value + coeffs[self.index]

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
    352     if pd.value is None:
--> 353         pd.eval(vars, coeffs)
    354     pd.hits += 1
    355 

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:509, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
    507 pd_eval(self.left, vars, coeffs)
    508 pd_eval(self.right, vars, coeffs)
--> 509 self.value = self.left.value * self.right.value + coeffs[self.index]
    510 pd_clean(self.left)
    511 pd_clean(self.right)

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

[?7h[?12l[?25h[?2004lx^7
x^7 -2
x^7
x^7 -2
x^7
x^7 -2
x^7 + x^5
x^7 + x^5 -3
x^7 + x^5
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [80], 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>:25, 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>:313, in a_number(self)

File <string>:155, in cartier_matrix(self, prec)

File <string>:70, in coordinates(self, basis)

File <string>:137, in holomorphic_differentials_basis(self, threshold)

File <string>:423, in holomorphic_combinations(S)

File <string>:45, in __add__(self, other)

File <string>:10, in __init__(self, 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 /ext/sage/9.7/src/sage/rings/polynomial/term_order.py:796, in TermOrder.__init__(self, name, n, force)
    794         self._singular_str = singular_name_mapping.get(name,name)
    795         self._macaulay2_str = macaulay2_name_mapping.get(name,name)
--> 796         self._magma_str = magma_name_mapping.get(name,name)
    797 else: # len(block_names) > 1, and hence block order represented by a string
    798     length = 0

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

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

[?7h[?12l[?25h[?2004lx^7
x^7 4
x^7
x^7 4
x^7
x^7 4
x^7 + x^5
x^7 + x^5 3
x^7 + x^5
x^7 + x^5 3
x^7 + x^5
x^7 + x^5 3
x^7 + 2*x^5
x^7 + 2*x^5 3
x^7 + 2*x^5
x^7 + 2*x^5 3
x^7 + 2*x^5
x^7 + 2*x^5 3
x^7 + x^4
x^7 + x^4 4
x^7 + x^4
x^7 + x^4 4
x^7 + x^4
x^7 + x^4 4
x^7 + x^5 + x^4
x^7 + x^5 + x^4 3
x^7 + x^5 + x^4
x^7 + x^5 + x^4 3
x^7 + x^5 + x^4
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [81], 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>:25, 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>:313, in a_number(self)

File <string>:155, in cartier_matrix(self, prec)

File <string>:139, in cartier(self)

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

File <string>:15, in __add__(self, other)

File <string>:217, in reduction(C, g)

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:649, in PolynomialRing(base_ring, *args, **kwds)
    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:683, in _single_variate(base_ring, name, sparse, implementation, order)
    681 # "implementation" must be last
    682 key = [base_ring, name, sparse, implementation]
--> 683 R = _get_from_cache(key)
    684 if R is not None:
    685     return R

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:668, in _get_from_cache(key)
    666 def _get_from_cache(key):
    667     key = tuple(key)
--> 668     return _cache.get(key)

File /ext/sage/9.7/src/sage/misc/weak_dict.pyx:662, in sage.misc.weak_dict.WeakValueDictionary.get()
    660 
    661         """
--> 662         cdef PyObject * wr = PyDict_GetItemWithError(self, k)
    663         if wr == NULL:
    664             return d

File /ext/sage/9.7/src/sage/rings/fraction_field.py:783, in FractionField_generic.__hash__(self)
    769 """
    770 Compute the hash of ``self``.
    771 
   (...)
    779     True
    780 """
    781 # to avoid having exactly the same hash as the base ring,
    782 # we change this hash using a random number
--> 783 return hash(self._R) ^ 147068341996611

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

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

[?7h[?12l[?25h[?2004lx^7 4
x^7 4
x^7 4
x^7 + x^5 3
x^7 + x^5 3
x^7 + x^5 3
x^7 + 2*x^5 3
x^7 + 2*x^5 3
x^7 + 2*x^5 3
x^7 + x^4 4
x^7 + x^4 4
x^7 + x^4 4
x^7 + x^5 + x^4 3
x^7 + x^5 + x^4 3
x^7 + x^5 + x^4 3
x^7 + 2*x^5 + x^4 3
x^7 + 2*x^5 + x^4 3
x^7 + 2*x^5 + x^4 3
x^7 + 2*x^4 4
x^7 + 2*x^4 4
x^7 + 2*x^4 4
x^7 + x^5 + 2*x^4 3
x^7 + x^5 + 2*x^4 3
x^7 + x^5 + 2*x^4 3
x^7 + 2*x^5 + 2*x^4 3
x^7 + 2*x^5 + 2*x^4 3
x^7 + 2*x^5 + 2*x^4 3
x^7 4
x^7 4
x^7 4
x^7 + x^5 3
x^7 + x^5 3
x^7 + x^5 3
x^7 + 2*x^5 3
x^7 + 2*x^5 3
x^7 + 2*x^5 3
x^7 + x^4 4
x^7 + x^4 4
x^7 + x^4 4
x^7 + x^5 + x^4 3
x^7 + x^5 + x^4 3
x^7 + x^5 + x^4 3
x^7 + 2*x^5 + x^4 3
x^7 + 2*x^5 + x^4 3
x^7 + 2*x^5 + x^4 3
x^7 + 2*x^4 4
x^7 + 2*x^4 4
x^7 + 2*x^4 4
x^7 + x^5 + 2*x^4 3
x^7 + x^5 + 2*x^4 3
x^7 + x^5 + 2*x^4 3
x^7 + 2*x^5 + 2*x^4 3
x^7 + 2*x^5 + 2*x^4 3
x^7 + 2*x^5 + 2*x^4 3
x^7 4
x^7 4
x^7 4
x^7 + x^5 3
x^7 + x^5 3
x^7 + x^5 3
x^7 + 2*x^5 3
x^7 + 2*x^5 3
x^7 + 2*x^5 3
x^7 + x^4 4
x^7 + x^4 4
x^7 + x^4 4
x^7 + x^5 + x^4 3
x^7 + x^5 + x^4 3
x^7 + x^5 + x^4 3
x^7 + 2*x^5 + x^4 3
x^7 + 2*x^5 + x^4 3
x^7 + 2*x^5 + x^4 3
x^7 + 2*x^4 4
x^7 + 2*x^4 4
x^7 + 2*x^4 4
x^7 + x^5 + 2*x^4 3
x^7 + x^5 + 2*x^4 3
x^7 + x^5 + 2*x^4 3
x^7 + 2*x^5 + 2*x^4 3
x^7 + 2*x^5 + 2*x^4 3
x^7 + 2*x^5 + 2*x^4 3
x^7 + x^2 4
x^7 + x^2 4
x^7 + x^2 4
x^7 + x^5 + x^2 3
x^7 + x^5 + x^2 3
x^7 + x^5 + x^2 3
x^7 + 2*x^5 + x^2 3
x^7 + 2*x^5 + x^2 3
x^7 + 2*x^5 + x^2 3
x^7 + x^4 + x^2 4
x^7 + x^4 + x^2 4
x^7 + x^4 + x^2 4
x^7 + x^5 + x^4 + x^2 3
x^7 + x^5 + x^4 + x^2 3
x^7 + x^5 + x^4 + x^2 3
x^7 + 2*x^5 + x^4 + x^2 3
x^7 + 2*x^5 + x^4 + x^2 3
x^7 + 2*x^5 + x^4 + x^2 3
x^7 + 2*x^4 + x^2 4
x^7 + 2*x^4 + x^2 4
x^7 + 2*x^4 + x^2 4
x^7 + x^5 + 2*x^4 + x^2 3
x^7 + x^5 + 2*x^4 + x^2 3
x^7 + x^5 + 2*x^4 + x^2 3
x^7 + 2*x^5 + 2*x^4 + x^2 3
x^7 + 2*x^5 + 2*x^4 + x^2 3
x^7 + 2*x^5 + 2*x^4 + x^2 3
x^7 + x^2 4
x^7 + x^2 4
x^7 + x^2 4
x^7 + x^5 + x^2 3
x^7 + x^5 + x^2 3
x^7 + x^5 + x^2 3
x^7 + 2*x^5 + x^2 3
x^7 + 2*x^5 + x^2 3
x^7 + 2*x^5 + x^2 3
x^7 + x^4 + x^2 4
x^7 + x^4 + x^2 4
x^7 + x^4 + x^2 4
x^7 + x^5 + x^4 + x^2 3
x^7 + x^5 + x^4 + x^2 3
x^7 + x^5 + x^4 + x^2 3
x^7 + 2*x^5 + x^4 + x^2 3
x^7 + 2*x^5 + x^4 + x^2 3
x^7 + 2*x^5 + x^4 + x^2 3
x^7 + 2*x^4 + x^2 4
x^7 + 2*x^4 + x^2 4
x^7 + 2*x^4 + x^2 4
x^7 + x^5 + 2*x^4 + x^2 3
x^7 + x^5 + 2*x^4 + x^2 3
x^7 + x^5 + 2*x^4 + x^2 3
x^7 + 2*x^5 + 2*x^4 + x^2 3
x^7 + 2*x^5 + 2*x^4 + x^2 3
x^7 + 2*x^5 + 2*x^4 + x^2 3
x^7 + x^2 4
x^7 + x^2 4
x^7 + x^2 4
x^7 + x^5 + x^2 3
x^7 + x^5 + x^2 3
x^7 + x^5 + x^2 3
x^7 + 2*x^5 + x^2 3
x^7 + 2*x^5 + x^2 3
x^7 + 2*x^5 + x^2 3
x^7 + x^4 + x^2 4
x^7 + x^4 + x^2 4
x^7 + x^4 + x^2 4
x^7 + x^5 + x^4 + x^2 3
x^7 + x^5 + x^4 + x^2 3
x^7 + x^5 + x^4 + x^2 3
x^7 + 2*x^5 + x^4 + x^2 3
x^7 + 2*x^5 + x^4 + x^2 3
x^7 + 2*x^5 + x^4 + x^2 3
x^7 + 2*x^4 + x^2 4
x^7 + 2*x^4 + x^2 4
x^7 + 2*x^4 + x^2 4
x^7 + x^5 + 2*x^4 + x^2 3
x^7 + x^5 + 2*x^4 + x^2 3
^C---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Input In [82], 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>:25, 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>:44, in __init__(self, C, list_of_fcts, prec)

File <string>:167, in artin_schreier_transform(power_series, prec)

File <string>:12, in new_reverse(power_series, prec)

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1831, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
   1829 if x:
   1830     raise ValueError("must not specify %s keyword and positional argument" % name)
-> 1831 a = self(kwds[name])
   1832 del kwds[name]
   1833 try:

File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1852, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
   1850         x = x[0]
   1851 
-> 1852     return self.__u(*x)*(x[0]**self.__n)
   1853 
   1854 def __pari__(self):

File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:365, in sage.rings.power_series_poly.PowerSeries_poly.__call__()
    363         x[0] = a
    364         x = tuple(x)
--> 365     return self.__f(x)
    366 
    367 def _unsafe_mutate(self, i, value):

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:898, in sage.rings.polynomial.polynomial_element.Polynomial.__call__()
    896             return result
    897         pol._compiled = CompiledPolynomialFunction(pol.list())
--> 898     return pol._compiled.eval(a)
    899 
    900 def compose_trunc(self, Polynomial other, long n):

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:125, in sage.rings.polynomial.polynomial_compiled.CompiledPolynomialFunction.eval()
    123 cdef object temp
    124 try:
--> 125     pd_eval(self._dag, x, self._coeffs)  #see further down
    126     temp = self._dag.value               #for an explanation
    127     pd_clean(self._dag)                  #of these 3 lines

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
    352     if pd.value is None:
--> 353         pd.eval(vars, coeffs)
    354     pd.hits += 1
    355 

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
    505 
    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507         pd_eval(self.left, vars, coeffs)
    508         pd_eval(self.right, vars, coeffs)
    509         self.value = self.left.value * self.right.value + coeffs[self.index]

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
    352     if pd.value is None:
--> 353         pd.eval(vars, coeffs)
    354     pd.hits += 1
    355 

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
    505 
    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507         pd_eval(self.left, vars, coeffs)
    508         pd_eval(self.right, vars, coeffs)
    509         self.value = self.left.value * self.right.value + coeffs[self.index]

    [... skipping similar frames: sage.rings.polynomial.polynomial_compiled.pd_eval at line 353 (9 times), sage.rings.polynomial.polynomial_compiled.abc_pd.eval at line 507 (8 times)]

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
    505 
    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507         pd_eval(self.left, vars, coeffs)
    508         pd_eval(self.right, vars, coeffs)
    509         self.value = self.left.value * self.right.value + coeffs[self.index]

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
    352     if pd.value is None:
--> 353         pd.eval(vars, coeffs)
    354     pd.hits += 1
    355 

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:509, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
    507 pd_eval(self.left, vars, coeffs)
    508 pd_eval(self.right, vars, coeffs)
--> 509 self.value = self.left.value * self.right.value + coeffs[self.index]
    510 pd_clean(self.left)
    511 pd_clean(self.right)

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: 
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.a_number()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^1 = x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(x)[?7h[?12l[?25h[?25l[?7lsage: p

[?7h[?12l[?25h[?2004l[?7h3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.a_nmber()[?7h[?12l[?25h[?25l[?7lbasis_of_cohomology()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lring[?7h[?12l[?25h[?25l[?7lsage: C.base_ring

[?7h[?12l[?25h[?2004l[?7hFinite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.base_ring[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)^(-1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf(C.y[?7h[?12l[?25h[?25l[?7lf(C.y[?7h[?12l[?25h[?25l[?7l (C.y[?7h[?12l[?25h[?25l[?7l=(C.y[?7h[?12l[?25h[?25l[?7l (C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: ff = (C.y)^3/(C.x)^3

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = (C.y)^3/(C.x)^3[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: ff

[?7h[?12l[?25h[?2004l[?7h((x^2 + 2)/x^2)*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((AS.x)^(-1)*AS.dx).cartier()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((AS.x)^(-1)*AS.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.x)^(11)/(C.y)^3*C.dx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly-[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: (C.y)/(C.x)^2

[?7h[?12l[?25h[?2004l[?7h1/x^2*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y)/(C.x)^2[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.y)/(C.x)^2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((C.y)/(C.x)^2).expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht + O(t^21)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: 5/3-3

[?7h[?12l[?25h[?2004l[?7h-4/3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l7%3[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: 7/3-3

[?7h[?12l[?25h[?2004l[?7h-2/3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.base_ring[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C/y)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7ly)^3/[?7h[?12l[?25h[?25l[?7l.y)^3/[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7lsage: (C.y)^3/(C.x)^4

[?7h[?12l[?25h[?2004l[?7h((x^2 + 2)/x^3)*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y)^3/(C.x)^4[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.y)^3/(C.x)^4)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((C.y)^3/(C.x)^4).expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-1 + O(t^19)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.y)^3/(C.x)^4).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y)^3/(C.x)^4[?7h[?12l[?25h[?25l[?7l(C.y)^3/(C.x)^4).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.y)^3/(C.x)^4).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf((C.y)^3/(C.x)^4)[?7h[?12l[?25h[?25l[?7lf((C.y)^3/(C.x)^4)[?7h[?12l[?25h[?25l[?7l ((C.y)^3/(C.x)^4)[?7h[?12l[?25h[?25l[?7l=((C.y)^3/(C.x)^4)[?7h[?12l[?25h[?25l[?7l ((C.y)^3/(C.x)^4)[?7h[?12l[?25h[?25l[?7lsage: ff = ((C.y)^3/(C.x)^4)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = ((C.y)^3/(C.x)^4)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: ff

[?7h[?12l[?25h[?2004l[?7h((x^2 + 2)/x^3)*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff[?7h[?12l[?25h[?25l[?7l = ((C.y)^3/(C.x)^4)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7lsage: ff = ((C.y)^3/(C.x)^2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = ((C.y)^3/(C.x)^2)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion_at_infty[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ff.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-5 + 2*t^-1 + 2*t^3 + 2*t^7 + t^11 + O(t^15)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: ff

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

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.base_ring[?7h[?12l[?25h[?25l[?7lfrobenus_matrix(prec=50).transpose().kernel().basis()[0][?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(prec=50).transpose().kernel().basis()[0][?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lobenius_matrix(prec=50).transpose().kernel().basis()[0][?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix(prec=50).transpose().kernel().basis()[0]

[?7h[?12l[?25h[?2004l[?7h(1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50).transpose().kernel().basis()[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix(prec=50)

[?7h[?12l[?25h[?2004l[?7h[0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR.<x> = PolynomialRing(ZZ)[?7h[?12l[?25h[?25l[?7lsage: R.<x> = PolynomialRing(ZZ)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff[?7h[?12l[?25h[?25l[?7l = superelliptic_function(C, y/x)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx^n + a[0][?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3-x[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: f = x^3 - x

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR.<x> = PolynomialRing(ZZ)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM = hypellfrob(p, 1, f)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 1, f)[?7h[?12l[?25h[?25l[?7l3, 1, f)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: M = hypellfrob(3, 1, f)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [105], in <cell line: 1>()
----> 1 M = hypellfrob(Integer(3), Integer(1), f)

NameError: name 'hypellfrob' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrom sage.schemes.hyperelliptic_curves.hypellfrob import hypellfrob[?7h[?12l[?25h[?25l[?7lsage: from sage.schemes.hyperelliptic_curves.hypellfrob import hypellfrob

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrom sage.schemes.hyperelliptic_curves.hypellfrob import hypellfrob[?7h[?12l[?25h[?25l[?7lM = hypellfrob(3, 1, f)[?7h[?12l[?25h[?25l[?7lsage: M = hypellfrob(3, 1, f)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [107], in <cell line: 1>()
----> 1 M = hypellfrob(Integer(3), Integer(1), f)

File /ext/sage/9.7/src/sage/schemes/hyperelliptic_curves/hypellfrob.pyx:238, in sage.schemes.hyperelliptic_curves.hypellfrob.hypellfrob()
    236 bound = (len(Q) - 1) * (2*N - 1)
    237 if p <= bound:
--> 238     raise ValueError("In the current implementation, p must be greater "
    239                      "than (2g+1)(2N-1) = %s" % bound)
    240 

ValueError: In the current implementation, p must be greater than (2g+1)(2N-1) = 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lsage: g

[?7h[?12l[?25h[?2004l[?7h((2*x^4 + 2*x^2 + 2)/x^3)*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.discriminant().factor()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates()

[?7h[?12l[?25h[?2004l[?7h[1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lbase_rng[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.frobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7lcartier_matrix()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.

  C.a_number                               C.basis_of_cohomology                    C.degrees_de_rham0                        

  C.base_ring                              C.cartier_matrix                         C.degrees_de_rham1                        

  C.basis_de_rham_degrees                  C.characteristic                         C.degrees_holomorphic_differentials      >

  C.basis_holomorphic_differentials_degree C.de_rham_basis                          C.dr_frobenius_matrix                     

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

 C.a_number                              







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

 C.a_number                               C.basis_of_cohomology                   [?7h[?12l[?25h[?25l[?7l()









[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.basis_of_cohomology()

[?7h[?12l[?25h[?2004l[?7h[2/x*y]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: gg = (C.y)/(C.x)

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



 [?7h[?12l[?25h[?25l[?7lgg = (C.y)/(C.x)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7log^8*[?7h[?12l[?25h[?25l[?7lmg^8*[?7h[?12l[?25h[?25l[?7l g^8*[?7h[?12l[?25h[?25l[?7l=g^8*[?7h[?12l[?25h[?25l[?7l g^8*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lfn[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om = gg^8*gg.diffn()

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

 [?7h[?12l[?25h[?25l[?7lom = gg^8*gg.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.expansion_at_ifty()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: om.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2*t^-10 + 2*t^-6 + t^-2 + O(1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7lsage: om.expansion_at_infty(prec = 30)

[?7h[?12l[?25h[?2004l[?7h2*t^-10 + 2*t^-6 + t^-2 + t^2 + 2*t^6 + t^10 + O(t^20)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7lsage: v

[?7h[?12l[?25h[?2004l[?7h1/x^2*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.basis_of_cohomology()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lY[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lv)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7ly)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: C.y*v*(v - C.y)

[?7h[?12l[?25h[?2004l[?7h((2*x^4 + 2*x^2 + 2)/x^3)*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.expansion_at_infty(prec = 30)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

[?7h[?12l[?25h[?2004l[?7h((-x^10 + x^6 + x^4 - 1)/(x^5*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y*v*(v - C.y)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7lx.cartier()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx[?7h[?12l[?25h[?25l[?7l.C.dx[?7h[?12l[?25h[?25l[?7lxC.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.xC.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*C.dx[?7h[?12l[?25h[?25l[?7lC.dx[?7h[?12l[?25h[?25l[?7l.C.dx[?7h[?12l[?25h[?25l[?7lyC.dx[?7h[?12l[?25h[?25l[?7l()C.dx[?7h[?12l[?25h[?25l[?7l()^C.dx[?7h[?12l[?25h[?25l[?7l(C.dx[?7h[?12l[?25h[?25l[?7l-C.dx[?7h[?12l[?25h[?25l[?7l1C.dx[?7h[?12l[?25h[?25l[?7l()C.dx[?7h[?12l[?25h[?25l[?7l()*C.dx[?7h[?12l[?25h[?25l[?7lsage: (C.x*C.y)^(-1)*C.dx

[?7h[?12l[?25h[?2004l[?7h(1/(x*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x*C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo(C.x*C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7lm(C.x*C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l1(C.x*C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l (C.x*C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l=(C.x*C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l (C.x*C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om1 = (C.x*C.y)^(-1)*C.dx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = (C.x*C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.jth_component(3[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^2 + t^6 + O(t^12)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[1]
3*X^18 + 2*X^16 + 2*X^14 + 8*X^10 - 2*X^9 - 4*X^8 + 6*X^7 + 4*X^6 - 6*X^5 + 2*X^4 + 2*X^3 + 2*X^2 - 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y*v*(v - C.y)[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.y*v*(v - C.y)[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

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

[?7h[?12l[?25h[?2004l0 dx
[1]
3*X^18 + 2*X^16 + 2*X^14 + 8*X^10 - 2*X^9 - 4*X^8 + 6*X^7 + 4*X^6 - 6*X^5 + 2*X^4 + 2*X^3 + 2*X^2 - 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l((x^3 - x^2 - x + 1)/(x^3*y)) dx
[1]
3*X^18 + 2*X^16 + 2*X^14 + 8*X^10 - 2*X^9 - 4*X^8 + 6*X^7 + 4*X^6 - 6*X^5 + 2*X^4 + 2*X^3 + 2*X^2 - 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l0 dx
[1]
3*X^18 + 2*X^16 + 2*X^14 + 8*X^10 - 2*X^9 - 4*X^8 + 6*X^7 + 4*X^6 - 6*X^5 + 2*X^4 + 2*X^3 + 2*X^2 - 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l0 dx
[1]
3*X^18 + 2*X^16 - X^15 + 2*X^14 + 3*X^13 + 2*X^12 - 3*X^11 + 2*X^10 - X^9 + 2*X^8 + 6*X^7 + 2*X^6 - 6*X^5 + 2*X^4 + 2*X^3 + 2*X^2 - 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l0 dx
[1]
3*X^18 + 2*X^16 - 2*X^15 + 2*X^14 + 6*X^13 + 2*X^12 - 6*X^11 + 2*X^10 - 2*X^9 + 2*X^8 + 12*X^7 + 2*X^6 - 12*X^5 + 2*X^4 + 4*X^3 + 2*X^2 - 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l0 dx
[1]
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x*C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()%[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: (-10)%3

[?7h[?12l[?25h[?2004l[?7h2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-10)%3[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()%[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7lsage: (3/2)%9

[?7h[?12l[?25h[?2004l[?7h6
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(3/2)%9[?7h[?12l[?25h[?25l[?7lC.x*C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.x/C.y).expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht + t^5 + 2*t^9 + 2*t^13 + t^17 + O(t^21)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1621228612.factor()[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7lsage: 19/3-4

[?7h[?12l[?25h[?2004l[?7h7/3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l19/3-4[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7lsage: 17/3-4

[?7h[?12l[?25h[?2004l[?7h5/3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l17/3-4[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7lsage: 13/3-4

[?7h[?12l[?25h[?2004l[?7h1/3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l13/3-4[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7lsage: 11/3-4

[?7h[?12l[?25h[?2004l[?7h-1/3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l7/3-3[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7lsage: 7/3-4

[?7h[?12l[?25h[?2004l[?7h-5/3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l5/3-3[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7lsage: 5/3-4

[?7h[?12l[?25h[?2004l[?7h-7/3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l0 dx
[1]
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
[0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l0 dx
[1]
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
[0]
[0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor m in range(1, p^2):[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion_at_infty[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f2.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-11 + 2*t^-7 + 2*t^-3 + t + 2*t^5 + O(t^9)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: f2

[?7h[?12l[?25h[?2004l[?7h(x^8/(x^4 + x^2 + 1))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf2[?7h[?12l[?25h[?25l[?7l1 = superelliptic_function(C_super, 1)[?7h[?12l[?25h[?25l[?7lsage: f1

[?7h[?12l[?25h[?2004l[?7h((x^10 + 2*x^2 + 2)/(x^6 + 2*x^4))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg = (C.y)/(C.x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRHS = ceil(m*(k+1)/p) - ceil(m*k/p)[?7h[?12l[?25h[?25l[?7lxy.<x, y> = PolynomialRing(GF(3), 2)[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.<x> = PolynomialRing(QQ)[?7h[?12l[?25h[?25l[?7l<[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l>[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lP[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lynomialRing(QQ)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lG)[?7h[?12l[?25h[?25l[?7lF)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: Rx.<x> = PolynomialRing(GF(3))

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx.<x> = PolynomialRing(GF(3))[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg = (C.y)/(C.x)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp = 5[?7h[?12l[?25h[?25l[?7lrint(LHS == RHS)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l8)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l4)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l+)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l+)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: print((x^8).quo_rem(x^4 + x^2 + 1))

[?7h[?12l[?25h[?2004l(x^4 + 2*x^2, x^2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x/C.y).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()^(11)/(C.y)^3*C.dx[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l2/(C.y)*(C.dx)[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(C.x)^2*C.y/(C.y)^4 + (C.y)^2 + 1)[?7h[?12l[?25h[?25l[?7lg(C.x)^2*C.y/(C.y)^4 + (C.y)^2 + 1)[?7h[?12l[?25h[?25l[?7l (C.x)^2*C.y/(C.y)^4 + (C.y)^2 + 1)[?7h[?12l[?25h[?25l[?7l=(C.x)^2*C.y/(C.y)^4 + (C.y)^2 + 1)[?7h[?12l[?25h[?25l[?7l (C.x)^2*C.y/(C.y)^4 + (C.y)^2 + 1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: gg = (C.x)^2*C.y/((C.y)^4 + (C.y)^2 + 1)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [26], in <cell line: 1>()
----> 1 gg = (C.x)**Integer(2)*C.y/((C.y)**Integer(4) + (C.y)**Integer(2) + Integer(1))

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

[?7h[?12l[?25h[?2004l0 dx
[1]
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
[0]
[0]
t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
---------------------------------------------------------------------------
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>:25, 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>:14, in <module>

NameError: name 'g' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1[?7h[?12l[?25h[?25l[?7lor m in range(1, p^2):[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: forma

[?7h[?12l[?25h[?2004l[?7h((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lforma[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsion_at_infty[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: forma.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2*t^-8 + 2*t^-4 + O(t^2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lforma.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7lsage: forma.expansion_at_infty(prec=30)

[?7h[?12l[?25h[?2004l[?7h2*t^-8 + 2*t^-4 + 2*t^4 + 2*t^8 + O(t^22)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lforma.expansion_at_infty(prec=30)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: forma

[?7h[?12l[?25h[?2004l[?7h((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTraceback (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 [6] 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>:25 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>:14
    forma2 = ((xx**_sage_const_4  + xx**_sage_const_2  + C.one)/(xx**_sage_const_6 *C.y)) C.dx
                                                                                          ^
SyntaxError: invalid syntax

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

[?7h[?12l[?25h[?2004l((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
((x^4 + x^2 + 1)/(x^6*y)) dx
---------------------------------------------------------------------------
NameError                                 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>:25, 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>

NameError: name 'g' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lforma[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: forma1

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [8], in <cell line: 1>()
----> 1 forma1

NameError: name 'forma1' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lforma1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: forma2

[?7h[?12l[?25h[?2004l[?7h((x^4 + x^2 + 1)/(x^6*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lforma2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lion_at_infty[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: forma2.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^4 + t^8 + O(t^14)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lforma2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: forma2

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

[?7h[?12l[?25h[?2004l((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
((x^4 + x^2 + 1)/(x^6*y)) dx
---------------------------------------------------------------------------
NameError                                 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>:25, 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>

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

[?7h[?12l[?25h[?2004l((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
((x^4 + x^2 + 1)/(x^6*y)) dx
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
[0]
[0]
t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [13], 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>:25, 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>: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'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
((x^4 + x^2 + 1)/(x^6*y)) dx
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
[0]
[0]
t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
((x^10 - x^6 + 1)/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x/C.y).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lx^11)quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (x^10 - x^6 + 1).quo_rem(x^2 - 1)

[?7h[?12l[?25h[?2004l[?7h(x^8 + x^6, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^10 - x^6 + 1).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l^).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l8).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l+).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7lx).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l^).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l6).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l - 1)[?7h[?12l[?25h[?25l[?7l3 - 1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7lsage: (x^8+x^6).quo_rem(x^3 - x)

[?7h[?12l[?25h[?2004l[?7h(x^5 + 2*x^3 + 2*x, 2*x^2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion(x^11, x^3 - x)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc_expansion(x^11, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l8, x^3 - x)[?7h[?12l[?25h[?25l[?7l , x^3 - x)[?7h[?12l[?25h[?25l[?7l+, x^3 - x)[?7h[?12l[?25h[?25l[?7l , x^3 - x)[?7h[?12l[?25h[?25l[?7lx, x^3 - x)[?7h[?12l[?25h[?25l[?7l^, x^3 - x)[?7h[?12l[?25h[?25l[?7l6, x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(x^8 + x^6, x^3 - x)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [17], in <cell line: 1>()
----> 1 adic_expansion(x**Integer(8) + x**Integer(6), x**Integer(3) - x)

NameError: name 'adic_expansion' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lfty/[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft

 drafty/draft.sage  drafty/draft4.sage

 drafty/draft2.sage drafty/draft5.sage

 drafty/draft3.sage drafty/draft6.sage



 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.sage

 drafty/draft.sage 





 <unknown> [?7h[?12l[?25h[?25l[?7l2.sage

 drafty/draft.sage 

 drafty/draft2.sage[?7h[?12l[?25h[?25l[?7l3



 drafty/draft2.sage

 drafty/draft3.sage[?7h[?12l[?25h[?25l[?7l4

 drafty/draft4.sage



 drafty/draft3.sage[?7h[?12l[?25h[?25l[?7l5

 drafty/draft4.sage

 drafty/draft5.sage[?7h[?12l[?25h[?25l[?7l'







[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft5.sage')

[?7h[?12l[?25h[?2004l((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx
t^-40 + O(t^-30)
[2, 1, x^2 + 2*x + 2, 2*x^2 + 2*x + 1, x^2 + 1, x^2 + x + 2, 2*x]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

 [?7h[?12l[?25h[?25l[?7lload('drafty/draft5.sage')[?7h[?12l[?25h[?25l[?7ladic_expansion(x^8 + x^6, x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(x^8 + x^6, x^3 - x)

[?7h[?12l[?25h[?2004l[?7h[x^2, 2*x, 2*x^2]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft5.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7l(nit.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
((x^4 + x^2 + 1)/(x^6*y)) dx
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
[0]
[0]
t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
((x^10 - x^6 + 1)/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: xx^11/(C.y)^3*C.dx

[?7h[?12l[?25h[?2004l[?7h(x^10/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx^11/(C.y)^3*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx^11/(C.y)^3*C.dx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: xx^9*C.y*C.y*C.y.diffn()

[?7h[?12l[?25h[?2004l[?7h((x^12 - x^10)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

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

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

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

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

[?7h[?12l[?25h[?2004l0 dx
((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
((x^4 + x^2 + 1)/(x^6*y)) dx
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
[0]
[0]
t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
((x^10 - x^6 + 1)/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l11/3-4[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7lsage: 19/3-4

[?7h[?12l[?25h[?2004l[?7h7/3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l19/3-4[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l/3-4[?7h[?12l[?25h[?25l[?7lsage: 17/3-4

[?7h[?12l[?25h[?2004l[?7h5/3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l17/3-4[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l/3-4[?7h[?12l[?25h[?25l[?7lsage: 13/3-4

[?7h[?12l[?25h[?2004l[?7h1/3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l13/3-4[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l/3-4[?7h[?12l[?25h[?25l[?7lsage: 11/3-4

[?7h[?12l[?25h[?2004l[?7h-1/3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l7/3-4[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l3-4[?7h[?12l[?25h[?25l[?7lsage: 7/3-4

[?7h[?12l[?25h[?2004l[?7h-5/3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l5/3-4[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l3-4[?7h[?12l[?25h[?25l[?7lsage: 5/3-4

[?7h[?12l[?25h[?2004l[?7h-7/3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l0 dx
((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
f2 ((-x^6 - 1)/(x^2*y - y)) dx
((x^4 + x^2 + 1)/(x^6*y)) dx
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
[0]
[0]
t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
((x^10 - x^6 + 1)/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lega[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lforma2[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: forma

[?7h[?12l[?25h[?2004l[?7h((-x^6 - 1)/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lforma[?7h[?12l[?25h[?25l[?7l.expansion_at_infty(prec=30)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lpansion_at_infty(prec=30)[?7h[?12l[?25h[?25l[?7lsage: forma.expansion_at_infty(prec=30)

[?7h[?12l[?25h[?2004l[?7h2*t^-8 + 2*t^-4 + 2*t^4 + 2*t^8 + t^16 + t^20 + O(t^22)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lforma.expansion_at_infty(prec=30)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l0 dx
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
f2 ((-x^6 - 1)/(x^2*y - y)) dx
((x^4 + x^2 + 1)/(x^6*y)) dx
[0]
[0]
t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
((x^10 - x^6 + 1)/(x^2*y - y)) dx
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [11], 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>:25, 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>:31, in <module>

File /ext/sage/9.7/src/sage/structure/element.pyx:4496, in sage.structure.element.coerce_binop.new_method()
   4494     return method(self, other, *args, **kwargs)
   4495 else:
-> 4496     a, b = coercion_model.canonical_coercion(self, other)
   4497     if a is self:
   4498         return method(a, b, *args, **kwargs)

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: 'Univariate Polynomial Ring in x over Finite Field of size 3' and 'Univariate Polynomial Ring in X over Rational Field'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l0 dx
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
f2 ((-x^6 - 1)/(x^2*y - y)) dx
((x^4 + x^2 + 1)/(x^6*y)) dx
[0]
[0]
t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
((x^10 - x^6 + 1)/(x^2*y - y)) dx
(x^7 + x, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^8+x^6).quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (x^7+x).quo_rem(x^3 - x)

[?7h[?12l[?25h[?2004l[?7h(x^4 + x^2 + 1, 2*x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg = (C.x)^2*C.y/((C.y)^4 + (C.y)^2 + 1)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg = (C.x)^2*C.y/((C.y)^4 + (C.y)^2 + 1)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lforma.expansion_at_infty(prec=30)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lff.cartier()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: ffffff = (xx^10 + 2*xx^8 + xx^4 + 2*xx^2)/yy^3

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lffffff = (xx^10 + 2*xx^8 + xx^4 + 2*xx^2)/yy^3[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion_at_infty[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ffffff.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-11 + t^-7 + 2*t^-3 + 2*t + t^5 + O(t^9)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lffffff.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ldinates[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ffffff.coordinates()

[?7h[?12l[?25h[?2004l[?7h[0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lffffff.coordinates()[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7l = (xx^10 + 2*xx^8 + xx^4 + 2*xx^2)/yy^3[?7h[?12l[?25h[?25l[?7l(x^7+x).quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7lffffff = (xx^10 + 2*xx^8 + xx^4 + 2*xx^2)/yy^3[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lffffff.coordinates()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: fg = (xx^7+xx)/yy

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfg = (xx^7+xx)/yy[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion_at_infty[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fg.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-11 + t^-7 + 2*t^-3 + 2*t + t^5 + O(t^9)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7linates[?7h[?12l[?25h[?25l[?7l*()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fg.coordinates()

[?7h[?12l[?25h[?2004l[?7h[0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfg.coordinates()[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7l = (xx^7+xx)/yy[?7h[?12l[?25h[?25l[?7lfffff.coordinates()[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7l = (xx^10 + 2*xx^8 + xx^4 + 2*xx^2)/yy^3[?7h[?12l[?25h[?25l[?7l(x^7+x).quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: (x^7+x).quo_rem(x^3 - x)

[?7h[?12l[?25h[?2004l[?7h(x^4 + x^2 + 1, 2*x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfg.coordinates()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l = (xx^7+xx)/yy[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fg = xx*yy/(xx^3 - xx)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfg = xx*yy/(xx^3 - xx)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ldinates()[?7h[?12l[?25h[?25l[?7lsage: fg.coordinates()

[?7h[?12l[?25h[?2004l[?7h[0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfg.coordinates()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: fg.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht + t^5 + 2*t^9 + 2*t^13 + t^17 + O(t^21)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l0 dx
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
f2 ((-x^6 - 1)/(x^2*y - y)) dx
((x^4 + x^2 + 1)/(x^6*y)) dx
[0]
[0]
t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
((x^10 - x^6 + 1)/(x^2*y - y)) dx
(x^7 + x, 0)
((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
((-x^6 - 1)/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^7+x).quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7l-10)%3[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l - 1[?7h[?12l[?25h[?25l[?7l2 - 1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (-x^6 - 1).quo_rem(x^2 - 1)

[?7h[?12l[?25h[?2004l[?7h(2*x^4 + 2*x^2 + 2, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1;3S[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l0 dx
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
f2 ((-x^6 - 1)/(x^2*y - y)) dx
((x^4 + x^2 + 1)/(x^6*y)) dx
[0]
[0]
t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
((x^10 - x^6 + 1)/(x^2*y - y)) dx
(x^7 + x, 0)
((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
((-x^6 - 1)/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ldrafty/draft5.sage')[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l(afty/draft5.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft5.sage')

[?7h[?12l[?25h[?2004l((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx
t^-40 + O(t^-30)
[2, 1, x^2 + 2*x + 2, 2*x^2 + 2*x + 1, x^2 + 1, x^2 + x + 2, 2*x]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()+[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: G = 2*x^9*(x^3 - x)+2*x^4+2*x^2+2

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG = 2*x^9*(x^3 - x)+2*x^4+2*x^2+2[?7h[?12l[?25h[?25l[?7lsage: G

[?7h[?12l[?25h[?2004l[?7h2*x^12 + x^10 + 2*x^4 + 2*x^2 + 2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion(x^9*(x^3-x)^2 - x^4 - x^2 - 1, x^3 - x)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc_expansion(x^9*(x^3-x)^2 - x^4 - x^2 - 1, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l(), x^3 - x)[?7h[?12l[?25h[?25l[?7l(, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7lG, x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(G, x^3 - x)

[?7h[?12l[?25h[?2004l[?7h[2, 0, 2, x, x^2 + 2]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7lsage: G

[?7h[?12l[?25h[?2004l[?7h2*x^12 + x^10 + 2*x^4 + 2*x^2 + 2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7l = 2*x^9*(x^3 - x)+2*x^4+2*x^2+2[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy(aaa[0].function).denominator()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l\[?7h[?12l[?25h[?25l[?7lsage: G1 = G - 2*x^4 + 2*x^6\

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG1 = G - 2*x^4 + 2*x^6\[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion(G, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1, x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(G1, x^3 - x)

[?7h[?12l[?25h[?2004l[?7h[2, 0, 1, 0, x^2 + 2]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion(G1, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7lx, x^3 - x)[?7h[?12l[?25h[?25l[?7l^, x^3 - x)[?7h[?12l[?25h[?25l[?7l4, x^3 - x)[?7h[?12l[?25h[?25l[?7l , x^3 - x)[?7h[?12l[?25h[?25l[?7l+, x^3 - x)[?7h[?12l[?25h[?25l[?7l , x^3 - x)[?7h[?12l[?25h[?25l[?7lx, x^3 - x)[?7h[?12l[?25h[?25l[?7l^, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l , x^3 - x)[?7h[?12l[?25h[?25l[?7lx, x^3 - x)[?7h[?12l[?25h[?25l[?7l^, x^3 - x)[?7h[?12l[?25h[?25l[?7l2, x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(x^4 + x^2, x^3 - x)

[?7h[?12l[?25h[?2004l[?7h[x, 2*x^2]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx9y2 + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lGx9y2 + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l x9y2 + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l=x9y2 + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l x9y2 + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^9y2 + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l* + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l( + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7lx + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l^ + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l3 + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l- + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7lx + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l() + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^4 + x2 + 1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^2 + 1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: G = x^9*(x^3 - x) + x^4 + x^2 + 1

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG = x^9*(x^3 - x) + x^4 + x^2 + 1[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7lsage: G(x+1) - G

[?7h[?12l[?25h[?2004l[?7h2*x^3 + 2*x + 2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG(x+1) - G[?7h[?12l[?25h[?25l[?7l1 = G2*x^4 + 2*x^6\[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l2x4 + 2x2 + 2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*x2 + 2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^2 + 2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*x4 + 2*x^2 + 2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^4 + 2*x^2 + 2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: G1 = 2*x^4 + 2*x^2 + 2

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG1 = 2*x^4 + 2*x^2 + 2[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7lsage: G1(x+1) - G

[?7h[?12l[?25h[?2004l[?7h2*x^12 + x^10 + x^4 + 2*x^3 + x^2 + 2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG1(x+1) - G[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: G1(x+1) - G1

[?7h[?12l[?25h[?2004l[?7h2*x^3 + 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg = (C.x)^2*C.y/((C.y)^4 + (C.y)^2 + 1)[?7h[?12l[?25h[?25l[?7l = len(Ifactors)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly^3/(x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g = yy^3/(xx*(xx+1)^2)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [15], in <cell line: 1>()
----> 1 g = yy**Integer(3)/(xx*(xx+Integer(1))**Integer(2))

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'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^3/(xx*(xx+1)^2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)^2)[?7h[?12l[?25h[?25l[?7lC)^2)[?7h[?12l[?25h[?25l[?7l.)^2)[?7h[?12l[?25h[?25l[?7lo)^2)[?7h[?12l[?25h[?25l[?7ln)^2)[?7h[?12l[?25h[?25l[?7le)^2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g = yy^3/(xx*(xx+C.one)^2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^3/(xx*(xx+C.one)^2)[?7h[?12l[?25h[?25l[?7l.coordinates)[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates()

[?7h[?12l[?25h[?2004l[?7h[0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = yy^3/(xx*xx+C.one)^2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l2*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: g = yy^3/(xx^2*(xx+C.one))

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates()

[?7h[?12l[?25h[?2004l[?7h[0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7l = yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g = yy/xx - yy/(xx+1)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [20], in <cell line: 1>()
----> 1 g = yy/xx - yy/(xx+Integer(1))

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'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy/xx - yy/(xx+1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lC1)[?7h[?12l[?25h[?25l[?7l.1)[?7h[?12l[?25h[?25l[?7l.o1)[?7h[?12l[?25h[?25l[?7ln1)[?7h[?12l[?25h[?25l[?7le1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: g = yy/xx - yy/(xx+C.one)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy/xx - yy/(xx+C.one)[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates()

[?7h[?12l[?25h[?2004l[?7h[0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7lsage: g

[?7h[?12l[?25h[?2004l[?7h(1/(x^2 + x))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsion_at_infty[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^5 + 2*t^9 + t^17 + O(t^25)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7l = yy/xx - yy/(xx+C.one)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7l = yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7lsage: g = yy^3/(xx^2*(xx+C.one))

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7lsage: g

[?7h[?12l[?25h[?2004l[?7h(1/(x^3 + x^2))*y^3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l = yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g = yy^3/(xx*(xx+C.one)^2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^3/(xx*(xx+C.one)^2)[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates()

[?7h[?12l[?25h[?2004l[?7h[0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: g.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^3 + t^7 + t^15 + 2*t^19 + O(t^23)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: g

[?7h[?12l[?25h[?2004l[?7h(1/(x^3 + 2*x^2 + x))*y^3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^4 = x^3 + 2*x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft5.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('drafty/draft5.sage')[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lini[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l'drafty/draft5.sage')[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l(t.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l0 dx
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
f2 ((-x^6 - 1)/(x^2*y - y)) dx
((x^4 + x^2 + 1)/(x^6*y)) dx
[0]
[0]
t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
((x^10 - x^6 + 1)/(x^2*y - y)) dx
(x^7 + x, 0)
((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
((-x^6 - 1)/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7l = yy^3/(xx*(xx+C.one)^2)[?7h[?12l[?25h[?25l[?7l()\[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g = yy^3/(xx*(xx+C.one)^2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^3/(xx*(xx+C.one)^2)[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates()

[?7h[?12l[?25h[?2004l[?7h[2]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7l = yy^3/(xx*(xx+C.one)^2)[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7l = yy^3/(xx*(xx+C.one)^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7lsage: g = yy^3/(xx^2*(xx+C.one))

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates()

[?7h[?12l[?25h[?2004l[?7h[1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7l = yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7l = yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lyy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy^3/(xx*(xx+C.one)^2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l y^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l+ y^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-y^3/(x^2*(x+C.one) + y^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l y^3/(x^2*(x+C.one) + y^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g = - yy^3/(xx^2*(xx+C.one)) + yy^3/(xx*(xx+C.one)^2)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [38], in <cell line: 1>()
----> 1 g = - yy**Integer(3)/(xx**Integer(2)*(xx+C.one)) + yy**Integer(3)/(xx*(xx+C.one)**Integer(2))

TypeError: bad operand type for unary -: 'superelliptic_function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = - yy^3/(xx^2*(xx+C.one)) + yy^3/(xx*(xx+C.one)^2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l()y^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l(()y^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l(y^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()-[?7h[?12l[?25h[?25l[?7lyy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7lsage: g = yy^3/(xx*(xx+C.one)^2)-yy^3/(xx^2*(xx+C.one))

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^3/(xx*(xx+C.one)^2)-yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7l.coordinates)[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates()

[?7h[?12l[?25h[?2004l[?7h[1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7lsage: g

[?7h[?12l[?25h[?2004l[?7h((2*x + 1)/(x^2 + x))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx.<x> = PolynomialRing(GF(3))[?7h[?12l[?25h[?25l[?7l.<x> = PolynomialRing(ZZ)[?7h[?12l[?25h[?25l[?7l<[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l>[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lP[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7llRing(ZZ)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lG)[?7h[?12l[?25h[?25l[?7lF)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: R.<x> = PolynomialRing(GF(3))

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l = yy^3/(xx*(xx+C.one)^2)-yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: g = 2*x^4 + 2*x^2 + 2

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = 2*x^4 + 2*x^2 + 2[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lsage: g(x+1) - g

[?7h[?12l[?25h[?2004l[?7h2*x^3 + 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(x+1) - g[?7h[?12l[?25h[?25l[?7l = 2*x^4 + 2*x^2 + 2[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx^(f.degree())*f(1/x)[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: g = x^4 +x^2 + 1

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = x^4 +x^2 + 1[?7h[?12l[?25h[?25l[?7l(x+1) - g[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1) - g[?7h[?12l[?25h[?25l[?7lsage: g(x+1) - g

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

[?7h[?12l[?25h[?2004l0 dx
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
f2 ((-x^6 - 1)/(x^2*y - y)) dx
((x^4 + x^2 + 1)/(x^6*y)) dx
[0]
[0]
t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
((x^10 - x^6 + 1)/(x^2*y - y)) dx
(x^7 + x, 0)
((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
((-x^6 - 1)/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(x+1) - g[?7h[?12l[?25h[?25l[?7l = x^4 +x^2 + 1[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lyy^3/(xx*(xx+C.one)^2)-yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/xx - yy/(xx+C.one)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx^4 +x^2 + 1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(x+1) - g[?7h[?12l[?25h[?25l[?7l = x^4 +x^2 + 1[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy^3/(xx*(xx+C.one)^2)-yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/xx - yy/(xx+C.one)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l - yy/(xx+C.one)[?7h[?12l[?25h[?25l[?7lsage: g = yy/xx - yy/(xx+C.one)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy/xx - yy/(xx+C.one)[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: g.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht + 2*t^3 + t^5 + 2*t^9 + 2*t^13 + t^17 + O(t^21)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = yy/xx - yy/(xx+C.one)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lyy/xx - yy/(xx+C.one)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly/(x+C.one)[?7h[?12l[?25h[?25l[?7ly/(x+C.one)[?7h[?12l[?25h[?25l[?7ly/(x+C.one)[?7h[?12l[?25h[?25l[?7ly/(x+C.one)[?7h[?12l[?25h[?25l[?7ly/(x+C.one)[?7h[?12l[?25h[?25l[?7ly/(x+C.one)[?7h[?12l[?25h[?25l[?7l/(x+C.one)[?7h[?12l[?25h[?25l[?7l/(x+C.one)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^/(x+C.one)[?7h[?12l[?25h[?25l[?7l2/(x+C.one)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()&[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: g = yy^2/(xx+C.one)^2 * y/x - yy/(xx+C.one) * yy^2/xx^2

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [9], in <cell line: 1>()
----> 1 g = yy**Integer(2)/(xx+C.one)**Integer(2) * y/x - yy/(xx+C.one) * yy**Integer(2)/xx**Integer(2)

NameError: name 'y' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^2/(xx+C.one)^2 * y/x - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly/x - y/(x+C.one) * y^2/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx - y/(x+C.one) * y^2/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7l.expansion_at_ifty()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: g.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2*t^-1 + 2*t + 2*t^5 + t^7 + t^9 + t^11 + t^13 + 2*t^15 + 2*t^17 + O(t^19)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates()

[?7h[?12l[?25h[?2004l[?7h[1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7lsage: g

[?7h[?12l[?25h[?2004l[?7h((2*x + 1)/(x^2 + x))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: g - yy/xxx

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [14], in <cell line: 1>()
----> 1 g - yy/xxx

NameError: name 'xxx' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg - yy/xxx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g - yy/xx

[?7h[?12l[?25h[?2004l[?7h(1/(x + 1))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg - yy/xx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(g - y/x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg - yy/xxx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l y/x[?7h[?12l[?25h[?25l[?7l+ y/x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g + yy/xx

[?7h[?12l[?25h[?2004l[?7h(2/(x^2 + x))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg + yy/xx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(g + y/x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (g + yy/xx).expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2*t + t^3 + 2*t^5 + t^9 + t^13 + 2*t^17 + O(t^21)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgy/x[?7h[?12l[?25h[?25l[?7lgy/x[?7h[?12l[?25h[?25l[?7l y/x[?7h[?12l[?25h[?25l[?7l=y/x[?7h[?12l[?25h[?25l[?7l y/x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: gg = yy/xx - yy/(xx + C.one)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg = yy/xx - yy/(xx + C.one)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lansion_at_infty[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: gg.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht + 2*t^3 + t^5 + 2*t^9 + 2*t^13 + t^17 + O(t^21)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: g

[?7h[?12l[?25h[?2004l[?7h((2*x + 1)/(x^2 + x))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + yy/xx[?7h[?12l[?25h[?25l[?7l=^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ly^2/(x+1)^2 \cdot y/x - y/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly^2/(x+1)^2 \cdot y/x - y/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lx+1)^2 \cdot y/x - y/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l y/x - y/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l y/x - y/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l y/x - y/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l y/x - y/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l y/x - y/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l* y/x - y/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly/x - y/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx - y/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7ly/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lx+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7lC) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l.) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7lo) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7ln) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7le) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l y^2/x^2[?7h[?12l[?25h[?25l[?7l y^2/x^2[?7h[?12l[?25h[?25l[?7l y^2/x^2[?7h[?12l[?25h[?25l[?7l y^2/x^2[?7h[?12l[?25h[?25l[?7l y^2/x^2[?7h[?12l[?25h[?25l[?7l* y^2/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly^2/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g = yy^2/(xx+1)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [21], in <cell line: 1>()
----> 1 g = yy**Integer(2)/(xx+Integer(1))**Integer(2) * yy/xx - yy/(xx+C.one) * yy**Integer(2)/xx**Integer(2)

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'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^2/(xx+1)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)^2 * y/x - y/(x+C.one) * y^2/x^2[?7h[?12l[?25h[?25l[?7lC)^2 * y/x - y/(x+C.one) * y^2/x^2[?7h[?12l[?25h[?25l[?7l.)^2 * y/x - y/(x+C.one) * y^2/x^2[?7h[?12l[?25h[?25l[?7lo)^2 * y/x - y/(x+C.one) * y^2/x^2[?7h[?12l[?25h[?25l[?7ln)^2 * y/x - y/(x+C.one) * y^2/x^2[?7h[?12l[?25h[?25l[?7le)^2 * y/x - y/(x+C.one) * y^2/x^2[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2

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

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lordinates()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates()

[?7h[?12l[?25h[?2004l[?7h[1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7l = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7l+/xx[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lyy/xx[?7h[?12l[?25h[?25l[?7lsage: g + yy/xx

[?7h[?12l[?25h[?2004l[?7h(2/(x^2 + x))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg + yy/xx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(g + y/x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: (g + yy/xx).expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2*t + t^3 + 2*t^5 + t^9 + t^13 + 2*t^17 + O(t^21)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(g + yy/xx).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lx^7+x).quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7lsage: (x+1)^5 - x^5

[?7h[?12l[?25h[?2004l[?7h2*x^4 + x^3 + x^2 + 2*x + 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ldrafty/draft5.sage')[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l(afty/draft5.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft5.sage')

[?7h[?12l[?25h[?2004l((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx
t^-40 + O(t^-30)
[2, 1, x^2 + 2*x + 2, 2*x^2 + 2*x + 1, x^2 + 1, x^2 + x + 2, 2*x]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2x^4 + x^3 + x^2 + 2x - x^3 (x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg2x^4 + x^3 + x^2 + 2x - x^3 (x^3 - x)[?7h[?12l[?25h[?25l[?7l 2x^4 + x^3 + x^2 + 2x - x^3 (x^3 - x)[?7h[?12l[?25h[?25l[?7l=2x^4 + x^3 + x^2 + 2x - x^3 (x^3 - x)[?7h[?12l[?25h[?25l[?7l 2x^4 + x^3 + x^2 + 2x - x^3 (x^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*x^4 + x^3 + x^2 + 2x - x^3 (x^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*x - x^3 (x^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l* (x^3 - x)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g = 2*x^4 + x^3 + x^2 + 2*x - x^3* (x^3 - x)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = 2*x^4 + x^3 + x^2 + 2*x - x^3* (x^3 - x)[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion(x^4 + x^2, x^3 - x)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lic_expansion(x^4 + x^2, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7lg, x^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(g, x^3 - x)

[?7h[?12l[?25h[?2004l[?7h[2, x + 1, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: yy/xx

[?7h[?12l[?25h[?2004l[?7h1/x*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy/xx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^/x[?7h[?12l[?25h[?25l[?7l3/x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgy^3/x^3[?7h[?12l[?25h[?25l[?7l y^3/x^3[?7h[?12l[?25h[?25l[?7l=y^3/x^3[?7h[?12l[?25h[?25l[?7l y^3/x^3[?7h[?12l[?25h[?25l[?7lsage: g = yy^3/xx^3

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^3/xx^3[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates()

[?7h[?12l[?25h[?2004l[?7h[0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lpansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: g.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^3 + O(t^23)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^4 = x^3 + 2*x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft5.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('drafty/draft5.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft5.sage')

[?7h[?12l[?25h[?2004l((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx
t^-40 + O(t^-30)
[2, 1, x^2 + 2*x + 2, 2*x^2 + 2*x + 1, x^2 + 1, x^2 + x + 2, 2*x]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft5.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l(t.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l0 dx
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
f2 ((-x^6 - 1)/(x^2*y - y)) dx
((x^4 + x^2 + 1)/(x^6*y)) dx
[0]
[0]
t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
((x^10 - x^6 + 1)/(x^2*y - y)) dx
(x^7 + x, 0)
((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
((-x^6 - 1)/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ldrafty/draft5.sage')[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7l = yy^3/xx^3[?7h[?12l[?25h[?25l[?7lsage: g = yy^3/xx^3

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^3/xx^3[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: g.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7ht^-3 + t + 2*t^5 + 2*t^9 + t^13 + O(t^17)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates()

[?7h[?12l[?25h[?2004l[?7h[0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7lsage: g

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





 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l = hypellfrob(3, 1, f)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR.<x> = PolynomialRing(GF(3))[?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: R9 = Integers(9)

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



 [?7h[?12l[?25h[?25l[?7lM = hypellfrob(3, 1, f)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lmatrix(QQ, [[1, 1], [0, 0]])[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[[][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l7]][?7h[?12l[?25h[?25l[?7l,]][?7h[?12l[?25h[?25l[?7l ]][?7h[?12l[?25h[?25l[?7l4]][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l,][?7h[?12l[?25h[?25l[?7l ][?7h[?12l[?25h[?25l[?7l[[][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l3]][?7h[?12l[?25h[?25l[?7l,]][?7h[?12l[?25h[?25l[?7l ]][?7h[?12l[?25h[?25l[?7l4]][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: M = matrix(R9, [[7, 4], [3, 4]])

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

 [?7h[?12l[?25h[?25l[?7lM = matrix(R9, [[7, 4], [3, 4]])[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: M^3

[?7h[?12l[?25h[?2004l[?7h[1 6]
[0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM^3[?7h[?12l[?25h[?25l[?7l.transpose().image().basis()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: M.determinant()

[?7h[?12l[?25h[?2004l[?7h7
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM.determinant()[?7h[?12l[?25h[?25l[?7l^3[?7h[?12l[?25h[?25l[?7l = matrix(R9, [[7, 4], [3, 4]])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l8]])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: M = matrix(R9, [[7, 4], [3, 8]])

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM = matrix(R9, [[7, 4], [3, 8]])[?7h[?12l[?25h[?25l[?7l^3[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: M^3

[?7h[?12l[?25h[?2004l[?7h[4 4]
[3 5]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = matrix(R9, [[7, 4], [3, 8]])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l4]])[?7h[?12l[?25h[?25l[?7lsage: M = matrix(R9, [[7, 4], [3, 4]])

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM = matrix(R9, [[7, 4], [3, 4]])[?7h[?12l[?25h[?25l[?7l^3[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: M^3

[?7h[?12l[?25h[?2004l[?7h[1 6]
[0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx^9*C.y*C.y*C.y.diffn()[?7h[?12l[?25h[?25l[?7lsage: x

[?7h[?12l[?25h[?2004l[?7hx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x+1)^5 - x^5[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+1)^5 - x^5[?7h[?12l[?25h[?25l[?7lsage: (x+1)^5 - x^5

[?7h[?12l[?25h[?2004l[?7h2*x^4 + x^3 + x^2 + 2*x + 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2+2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = yy/xx - yy/(xx + C.one)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2x^4 + x^3 + x^2 + 2x + x^3 (x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l* (x^3 - x)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(x^3 - x)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*x + x^3*(x^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*x^4 + x^3 + x^2 + 2*x + x^3*(x^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: gg = 2*x^4 + x^3 + x^2 + 2*x + x^3*(x^3 - x)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg = 2*x^4 + x^3 + x^2 + 2*x + x^3*(x^3 - x)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lsage: gg

[?7h[?12l[?25h[?2004l[?7hx^6 + x^4 + x^3 + x^2 + 2*x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion(g, x^3 - x)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc_expansion(g, x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(g, x^3 - x)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [54], in <cell line: 1>()
----> 1 adic_expansion(g, x**Integer(3) - x)

File <string>:17, in adic_expansion(g, h)

AttributeError: 'superelliptic_function' object has no attribute 'degree'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion(g, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg, x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(gg, x^3 - x)

[?7h[?12l[?25h[?2004l[?7h[1, 1, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM^3[?7h[?12l[?25h[?25l[?7l = matrix(R9, [[7, 4], [3, 4]])[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l matrix(R9, [[7, 4], [3, 4]])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l], [3, 4])[?7h[?12l[?25h[?25l[?7l], [3, 4])[?7h[?12l[?25h[?25l[?7l], [3, 4])[?7h[?12l[?25h[?25l[?7l], [3, 4])[?7h[?12l[?25h[?25l[?7l4], [3, 4])[?7h[?12l[?25h[?25l[?7l,], [3, 4])[?7h[?12l[?25h[?25l[?7l ], [3, 4])[?7h[?12l[?25h[?25l[?7l4], [3, 4])[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l6]])[?7h[?12l[?25h[?25l[?7l,]])[?7h[?12l[?25h[?25l[?7l ]])[?7h[?12l[?25h[?25l[?7l3]])[?7h[?12l[?25h[?25l[?7l4]])[?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l4]])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: M = matrix(R9, [[4, 4], [6, 4]])

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM = matrix(R9, [[4, 4], [6, 4]])[?7h[?12l[?25h[?25l[?7l^3[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: M^3

[?7h[?12l[?25h[?2004l[?7h[1 0]
[0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM^3[?7h[?12l[?25h[?25l[?7l = matrix(R9, [[4, 4], [6, 4]])[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lid[?7h[?12l[?25h[?25l[?7lide[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM - iden[?7h[?12l[?25h[?25l[?7l1M - iden[?7h[?12l[?25h[?25l[?7l M - iden[?7h[?12l[?25h[?25l[?7l=M - iden[?7h[?12l[?25h[?25l[?7l M - iden[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: M1 = M - identity_matrix(3)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [58], in <cell line: 1>()
----> 1 M1 = M - identity_matrix(Integer(3))

File /ext/sage/9.7/src/sage/structure/element.pyx:1358, in sage.structure.element.Element.__sub__()
   1356     return (<Element>left)._sub_(right)
   1357 if BOTH_ARE_ELEMENT(cl):
-> 1358     return coercion_model.bin_op(left, right, sub)
   1359 
   1360 try:

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 -: 'Full MatrixSpace of 2 by 2 dense matrices over Ring of integers modulo 9' and 'Full MatrixSpace of 3 by 3 dense matrices over Integer Ring'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM1 = M - identity_matrix(3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lG3)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7lR3)[?7h[?12l[?25h[?25l[?7l93)[?7h[?12l[?25h[?25l[?7l,3)[?7h[?12l[?25h[?25l[?7l 3)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: M1 = M - identity_matrix(R9, 3)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [59], in <cell line: 1>()
----> 1 M1 = M - identity_matrix(R9, Integer(3))

File /ext/sage/9.7/src/sage/structure/element.pyx:1358, in sage.structure.element.Element.__sub__()
   1356     return (<Element>left)._sub_(right)
   1357 if BOTH_ARE_ELEMENT(cl):
-> 1358     return coercion_model.bin_op(left, right, sub)
   1359 
   1360 try:

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 -: 'Full MatrixSpace of 2 by 2 dense matrices over Ring of integers modulo 9' and 'Full MatrixSpace of 3 by 3 dense matrices over Ring of integers modulo 9'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM1 = M - identity_matrix(R9, 3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7lsage: M1 = M - identity_matrix(R9, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM1 = M - identity_matrix(R9, 2)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: M1.kernel()

[?7h[?12l[?25h[?2004lsage/matrix/matrix_modn_dense_template.pxi:1: DeprecationWarning: invalid escape sequence '\Z'
  """
sage/matrix/matrix_modn_dense_template.pxi:1: DeprecationWarning: invalid escape sequence '\Z'
  """
---------------------------------------------------------------------------
NotImplementedError                       Traceback (most recent call last)
Input In [61], in <cell line: 1>()
----> 1 M1.kernel()

File /ext/sage/9.7/src/sage/matrix/matrix2.pyx:5032, in sage.matrix.matrix2.Matrix.left_kernel()
   5030 
   5031         tm = verbose("computing left kernel for %sx%s matrix" % (self.nrows(), self.ncols()),level=1)
-> 5032         K = self.transpose().right_kernel(*args, **kwds)
   5033         self.cache('left_kernel', K)
   5034         verbose("done computing left kernel for %sx%s matrix" % (self.nrows(), self.ncols()),level=1,t=tm)

File /ext/sage/9.7/src/sage/matrix/matrix2.pyx:4870, in sage.matrix.matrix2.Matrix.right_kernel()
   4868 
   4869         # Go get the kernel matrix, this is where it all happens
-> 4870         M = self.right_kernel_matrix(*args, **kwds)
   4871 
   4872         ambient = R**self.ncols()

File /ext/sage/9.7/src/sage/matrix/matrix_modn_dense_template.pxi:1897, in sage.matrix.matrix_modn_dense_float.Matrix_modn_dense_template.right_kernel_matrix()
   1895 """
   1896 if self.fetch('in_echelon_form') is None:
-> 1897     self = self.echelon_form(algorithm=algorithm)
   1898 
   1899 cdef Py_ssize_t r = self.rank()

File /ext/sage/9.7/src/sage/matrix/matrix2.pyx:7729, in sage.matrix.matrix2.Matrix.echelon_form()
   7727     v = E.echelonize(cutoff=cutoff, **kwds)
   7728 else:
-> 7729     v = E.echelonize(algorithm = algorithm, cutoff=cutoff, **kwds)
   7730 E.set_immutable()  # so we can cache the echelon form.
   7731 self.cache('echelon_form', E)

File /ext/sage/9.7/src/sage/matrix/matrix_modn_dense_template.pxi:1725, in sage.matrix.matrix_modn_dense_float.Matrix_modn_dense_template.echelonize()
   1723 
   1724         if not self.base_ring().is_field():
-> 1725             raise NotImplementedError("Echelon form not implemented over '%s'."%self.base_ring())
   1726 
   1727         if algorithm == 'linbox':

NotImplementedError: Echelon form not implemented over 'Ring of integers modulo 9'.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM1.kernel()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: M1

[?7h[?12l[?25h[?2004l[?7h[3 4]
[6 3]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.kernel()[?7h[?12l[?25h[?25l[?7lsage: M1.kernel()

  M1.C                                 M1.QR                                M1.add_multiple_of_row               M1.adjoint_classical                  

  M1.H                                 M1.T                                 M1.add_to_entry                      M1.adjugate                           

  M1.LLL_gram                          M1.act_on_polynomial                 M1.additive_order                    M1.anticommutator                    >

  M1.LU                                M1.add_multiple_of_column            M1.adjoint                           M1.antitranspose                      

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

 M1.C                                







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

 M1.C                                 M1.QR                               [?7h[?12l[?25h[?25l[?7ladd_multiple_of_row

 M1.QR                                M1.add_multiple_of_row              [?7h[?12l[?25h[?25l[?7ljoint_classical

 M1.add_multiple_of_row               M1.adjoint_classical                [?7h[?12l[?25h[?25l[?7lpply_map

 QRadd_multiple_of_rowjoint_classical  pply_map        

 Tadd_to_entryjugat    pply_morphism

<acton_polynomialdditive_order   ntcommutatos_bipartite_graph

 add_multiple_of_columnjoint               ntitransposes_sum_of_permutations[?7h[?12l[?25h[?25l[?7lugment

add_multiple_of_rowjoint_classical  pply_map        ugment  

add_to_entryjugat    pply_morphismutomorphism_of_rows_and_columns

dditive_order   ntcommutatos_bipartite_graphbase_extend       

joint               ntitransposes_sum_of_permutationsbase_ring             [?7h[?12l[?25h[?25l[?7lblock_ldlt

joint_classical  pply_map        ugment  block_ldlt

jugat    pply_morphismutomorphism_of_rows_and_columnsblock_sum                        

ntcommutatos_bipartite_graphbase_extend       crtesian_product

ntitransposes_sum_of_permutationsbase_ring             ctgory [?7h[?12l[?25h[?25l[?7lchange_ring

pply_map        ugment  block_ldltchange_ring

pply_morphismutomorphism_of_rows_and_columnsblock_sum                        characteristic_polynomial

s_bipartite_graphbase_extend       crtesian_productharpoly         

s_sum_of_permutationsbase_ring             ctgory holesk[?7h[?12l[?25h[?25l[?7loefficiet

ugment  block_ldltchange_ringoefficiet

utomorphism_of_rows_and_columnsblock_sum                        characteristic_polynomialoefficients             

base_extend       crtesian_productharpoly         olumn  

base_ring             ctgory holeskolumn_ambient_module[?7h[?12l[?25h[?25l[?7lr









[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: M1.rank()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NotImplementedError                       Traceback (most recent call last)
Input In [63], in <cell line: 1>()
----> 1 M1.rank()

File /ext/sage/9.7/src/sage/matrix/matrix_modn_dense_template.pxi:2159, in sage.matrix.matrix_modn_dense_float.Matrix_modn_dense_template.rank()
   2157         # linbox is very buggy for p=2, but this code should never
   2158         # be called since p=2 is handled via M4RI
-> 2159         return Matrix_dense.rank(self)
   2160 
   2161 def determinant(self):

File /ext/sage/9.7/src/sage/matrix/matrix0.pyx:4643, in sage.matrix.matrix0.Matrix.rank()
   4641 if self._nrows == 0 or self._ncols == 0:
   4642     return 0
-> 4643 r = len(self.pivots())
   4644 self.cache('rank', r)
   4645 return r

File /ext/sage/9.7/src/sage/matrix/matrix0.pyx:4600, in sage.matrix.matrix0.Matrix.pivots()
   4598 x = self.fetch('pivots')
   4599 if not x is None: return tuple(x)
-> 4600 self.echelon_form()
   4601 x = self.fetch('pivots')
   4602 if x is None:

File /ext/sage/9.7/src/sage/matrix/matrix2.pyx:7727, in sage.matrix.matrix2.Matrix.echelon_form()
   7725 E = self.__copy__()
   7726 if algorithm == 'default':
-> 7727     v = E.echelonize(cutoff=cutoff, **kwds)
   7728 else:
   7729     v = E.echelonize(algorithm = algorithm, cutoff=cutoff, **kwds)

File /ext/sage/9.7/src/sage/matrix/matrix_modn_dense_template.pxi:1725, in sage.matrix.matrix_modn_dense_float.Matrix_modn_dense_template.echelonize()
   1723 
   1724         if not self.base_ring().is_field():
-> 1725             raise NotImplementedError("Echelon form not implemented over '%s'."%self.base_ring())
   1726 
   1727         if algorithm == 'linbox':

NotImplementedError: Echelon form not implemented over 'Ring of integers modulo 9'.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM1.rank()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: M1

[?7h[?12l[?25h[?2004l[?7h[3 4]
[6 3]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lorma.expansionat_infty(prec=30)[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l m in range(1, p^2):[?7h[?12l[?25h[?25l[?7lalista2:[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lrange(0, 10):[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lrange[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: for a in range(3):

....: [?7h[?12l[?25h[?25l[?7lf += a[i]*x^i[?7h[?12l[?25h[?25l[?7lor B in range(-10, 30):[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lb0, 10):[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lrange[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7l....:     for b in range(3):

....: [?7h[?12l[?25h[?25l[?7lfor k in range(1, p-1):[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lrange[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7l....:         for c in range(3):

....: [?7h[?12l[?25h[?25l[?7lpass[?7h[?12l[?25h[?25l[?7lrint(e, f, g)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lif not(LHS == RHS):[?7h[?12l[?25h[?25l[?7lif[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l....:             if 0 == 1:

....: [?7h[?12l[?25h[?25l[?7lprint(m, k)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l....:                 print(1)

....: [?7h[?12l[?25h[?25l[?7lsage: for a in range(3):

....:     for b in range(3):

....:         for c in range(3):

....:             if 0 == 1:

....:                 print(1)

....: 

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

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7list_of_m = [m for m in list_of_m if m%p != 0][?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7llist[?7h[?12l[?25h[?25l[?7llista = ['a', 'b','c'][?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: lista = []

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llista = [][?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: licznik = 0

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llicznik = 0[?7h[?12l[?25h[?25l[?7lsta =[][?7h[?12l[?25h[?25l[?7lsage: for a in range(3):

....:     for b in range(3):

....:         for c in range(3):

....:             if 0 == 1:

....:                 print(1)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = d/(e*g)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lrange[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7l

....: [?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1 + 3*a[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[],[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l....:                 M = matrix(R9, [[1 + 3*a, 1+3*b], [3*c, 1+3*d]])

....: [?7h[?12l[?25h[?25l[?7lif e == 3:[?7h[?12l[?25h[?25l[?7lif[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lind[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldetity_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lntity_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7l....:                 if M^3 == identity_matrix(R9, 2):

....: [?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l....:                     licznik += 1

....: [?7h[?12l[?25h[?25l[?7lsage: for a in range(3):

....:     for b in range(3):

....:         for c in range(3):

....:             for d in range(3):

....:                 M = matrix(R9, [[1 + 3*a, 1+3*b], [3*c, 1+3*d]])

....:                 if M^3 == identity_matrix(R9, 2):

....:                     licznik += 1

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7lsage: 3^4

[?7h[?12l[?25h[?2004l[?7h81
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llicznik = 0[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lnik = 0[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7lsage: licznik

[?7h[?12l[?25h[?2004l[?7h27
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM1[?7h[?12l[?25h[?25l[?7lsage: M

[?7h[?12l[?25h[?2004l[?7h[7 7]
[6 7]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg[?7h[?12l[?25h[?25l[?7l = yy^3/xx^3[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l2*x^4 + x^3 + x^2 + 2*x - x^3* (x^3 - x)[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l+ x^3 + x^2 + 2*x - x^3* (x^3 - x)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*x^2 + 2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx^2 + 2[?7h[?12l[?25h[?25l[?7lsage: g = 2*x^4 + 2*x^2 + 2

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = 2*x^4 + 2*x^2 + 2[?7h[?12l[?25h[?25l[?7l(x+1) - g[?7h[?12l[?25h[?25l[?7lx+1) - g[?7h[?12l[?25h[?25l[?7lsage: g(x+1) - g

[?7h[?12l[?25h[?2004l[?7h2*x^3 + 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy/xx[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: v = yy/xx^2

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy/xx[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7lsage: yy*v^2 - yy^2*v

[?7h[?12l[?25h[?2004l[?7h((2*x^4 + 2*x^2 + 2)/x^3)*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy*v^2 - yy^2*v[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lhy*v^2 - y^2*v[?7h[?12l[?25h[?25l[?7l y*v^2 - y^2*v[?7h[?12l[?25h[?25l[?7l=y*v^2 - y^2*v[?7h[?12l[?25h[?25l[?7l y*v^2 - y^2*v[?7h[?12l[?25h[?25l[?7lsage: h = yy*v^2 - yy^2*v

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh = yy*v^2 - yy^2*v[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ldinates[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: h.coordinates()

[?7h[?12l[?25h[?2004l[?7h[1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy*v^2 - yy^2*v[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: yx = yy/xx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyx = yy/xx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: yx^8*yx.diffn()

[?7h[?12l[?25h[?2004l[?7h((-x^10 + x^6 + x^4 - 1)/(x^5*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh.coordinates()[?7h[?12l[?25h[?25l[?7lsage: h

[?7h[?12l[?25h[?2004l[?7h((2*x^4 + 2*x^2 + 2)/x^3)*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(x+1) - g[?7h[?12l[?25h[?25l[?7l = 2*x^4 + 2*x^2 + 2[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lyy^3/xx^3[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2(x+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7l/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7lsage: g = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g

[?7h[?12l[?25h[?2004l[?7h((2*x + 1)/(x^2 + x))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/xx - yy/(xx+C.one)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: g = yy/xx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy/xx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7lsage: g = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: g1 = g + yy/xx

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg1 = g + yy/xx[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: g1

[?7h[?12l[?25h[?2004l[?7h(2/(x^2 + x))*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lansion_at_infty[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g1.expansion_at_infty()

[?7h[?12l[?25h[?2004l[?7h2*t + t^3 + 2*t^5 + t^9 + t^13 + 2*t^17 + O(t^21)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ M = msasage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19                     │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l = matrix(R9, [[4, 4], [6, 4]])[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lmatrix(R9, [[4, 4], [6, 4]])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, [4, 4], [6, 4])[?7h[?12l[?25h[?25l[?7l, [4, 4], [6, 4])[?7h[?12l[?25h[?25l[?7lQ, [4, 4], [6, 4])[?7h[?12l[?25h[?25l[?7lQ, [4, 4], [6, 4])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l], [6, 4])[?7h[?12l[?25h[?25l[?7l], [6, 4])[?7h[?12l[?25h[?25l[?7l], [6, 4])[?7h[?12l[?25h[?25l[?7l], [6, 4])[?7h[?12l[?25h[?25l[?7l-], [6, 4])[?7h[?12l[?25h[?25l[?7l1], [6, 4])[?7h[?12l[?25h[?25l[?7l,], [6, 4])[?7h[?12l[?25h[?25l[?7l ], [6, 4])[?7h[?12l[?25h[?25l[?7l-], [6, 4])[?7h[?12l[?25h[?25l[?7l1], [6, 4])[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l1]])[?7h[?12l[?25h[?25l[?7l,]])[?7h[?12l[?25h[?25l[?7l ]])[?7h[?12l[?25h[?25l[?7l0]])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: M = matrix(QQ, [[-1, -1], [1, 0]])

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM = matrix(QQ, [[-1, -1], [1, 0]])[?7h[?12l[?25h[?25l[?7l^3[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: M^3

[?7h[?12l[?25h[?2004l[?7h[1 0]
[0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM^3[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l = M - identity_matrix(R9, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l - identity_matrix(R9, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7lQ, 2)[?7h[?12l[?25h[?25l[?7lQ, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: M1 = M - identity_matrix(QQ, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM1 = M - identity_matrix(QQ, 2)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.rank()[?7h[?12l[?25h[?25l[?7lkernel()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: M1.kernel()

[?7h[?12l[?25h[?2004l[?7hVector space of degree 2 and dimension 0 over Rational Field
Basis matrix:
[]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l11/3-4[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llicznik[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l0 dx
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
f2 ((-x^6 - 1)/(x^2*y - y)) dx
((x^4 + x^2 + 1)/(x^6*y)) dx
[0]
[0]
t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
((x^10 - x^6 + 1)/(x^2*y - y)) dx
(x^7 + x, 0)
((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
((-x^6 - 1)/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cartier_matrix()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7las[?7h[?12l[?25h[?25l[?7las_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l1y)[?7h[?12l[?25h[?25l[?7l/y)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, superelliptic_function(C, 1/y))

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [6], in <cell line: 1>()
----> 1 AS = as_cover(C, superelliptic_function(C, Integer(1)/y))

NameError: name 'y' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, superelliptic_function(C, 1/y))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCy)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsuper)[?7h[?12l[?25h[?25l[?7lsupe)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7ly)[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y)^(-1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, (C.y)^(-1))

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

File <string>:6, in __init__(self, C, list_of_fcts, prec)

TypeError: object of type 'superelliptic_function' has no len()
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, (C.y)^(-1))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[(C.y)^(-1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [(C.y)^(-1)])

[?7h[?12l[?25h[?2004lno  0 -th root; divide by 1
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [8], in <cell line: 1>()
----> 1 AS = as_cover(C, [(C.y)**(-Integer(1))])

File <string>:44, in __init__(self, C, list_of_fcts, prec)

ValueError: not enough values to unpack (expected 4, got 2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x+1)^5 - x^5[?7h[?12l[?25h[?25l[?7lC.x/C.y).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly)^3/(C.)^4[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l(-1)[?7h[?12l[?25h[?25l[?7l(-1)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l0 dx
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
f2 ((-x^6 - 1)/(x^2*y - y)) dx
((x^4 + x^2 + 1)/(x^6*y)) dx
[0]
[0]
t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
((x^10 - x^6 + 1)/(x^2*y - y)) dx
(x^7 + x, 0)
((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
((-x^6 - 1)/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.p_rank()

[?7h[?12l[?25h[?2004lHyperelliptic Curve over Finite Field of size 3 defined by y^2 = x^3 + 2*x
[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR.<u,v> = QQ[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 1)))". Alternatively, "R.<u,v> = QQ[]; WeierstrassForm(v^2 - (u^4 - 1), transformation=True)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lTru[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: R.<u,v> = QQ[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 1)))

[?7h[?12l[?25h[?2004l[?7hElliptic Curve defined by y^2 = x^3 + 4*x over Multivariate Polynomial Ring in u, v over Rational Field
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR.<u,v> = QQ[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 1)))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]; ElipticCurve(WeierstrasForm(v^2 - (u^4 - 1)[?7h[?12l[?25h[?25l[?7l[]; ElipticCurve(WeierstrasForm(v^2 - (u^4 - 1)[?7h[?12l[?25h[?25l[?7lG[]; ElipticCurve(WeierstrasForm(v^2 - (u^4 - 1)[?7h[?12l[?25h[?25l[?7lF[]; ElipticCurve(WeierstrasForm(v^2 - (u^4 - 1)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[; ElipticCurve(WeierstrasForm(v^2 - (u^4 - 1)[?7h[?12l[?25h[?25l[?7l; ElipticCurve(WeierstrasForm(v^2 - (u^4 - 1)[?7h[?12l[?25h[?25l[?7l(; ElipticCurve(WeierstrasForm(v^2 - (u^4 - 1)[?7h[?12l[?25h[?25l[?7l3; ElipticCurve(WeierstrasForm(v^2 - (u^4 - 1)[?7h[?12l[?25h[?25l[?7l(); ElipticCurve(WeierstrasForm(v^2 - (u^4 - 1)[?7h[?12l[?25h[?25l[?7l()[; ElipticCurve(WeierstrasForm(v^2 - (u^4 - 1)[?7h[?12l[?25h[?25l[?7l[]; ElipticCurve(WeierstrasForm(v^2 - (u^4 - 1)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: R.<u,v> = GF(3)[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 1)))

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
Input In [13], in <cell line: 1>()
----> 1 R = GF(Integer(3))['u, v']; (u, v,) = R._first_ngens(2); EllipticCurve(WeierstrassForm(v**Integer(2) - (u**Integer(4) - Integer(1))))

File /ext/sage/9.7/src/sage/misc/lazy_import.pyx:391, in sage.misc.lazy_import.LazyImport.__call__()
    389         True
    390     """
--> 391     return self.get_object()(*args, **kwds)
    392 
    393 def __repr__(self):

File /ext/sage/9.7/src/sage/schemes/toric/weierstrass.py:499, in WeierstrassForm(polynomial, variables, transformation)
    497     return WeierstrassForm_P1xP1(polynomial, variables)
    498 if polygon is polar_P2_112_polytope():
--> 499     return WeierstrassForm_P2_112(polynomial, variables)
    500 raise ValueError('Newton polytope is not contained in a reflexive polygon')

File /ext/sage/9.7/src/sage/schemes/toric/weierstrass.py:1078, in WeierstrassForm_P2_112(polynomial, variables)
   1076 delta = _partial_discriminant(polynomial, y, t)
   1077 Q = invariant_theory.binary_quartic(delta, x, z)
-> 1078 g2 = Q.EisensteinD()
   1079 g3 = -Q.EisensteinE()
   1080 return (-g2/4, -g3/4)

File /ext/sage/9.7/src/sage/misc/cachefunc.pyx:2299, in sage.misc.cachefunc.CachedMethodCallerNoArgs.__call__()
   2297 if self.cache is None:
   2298     f = self.f
-> 2299     self.cache = f(self._instance)
   2300 return self.cache
   2301 

File /ext/sage/9.7/src/sage/rings/invariants/invariant_theory.py:1480, in BinaryQuartic.EisensteinD(self)
   1455 @cached_method
   1456 def EisensteinD(self):
   1457     r"""
   1458     One of the Eisenstein invariants of a binary quartic.
   1459 
   (...)
   1478         3*a2^2 - 4*a1*a3 + a0*a4
   1479     """
-> 1480     a = self.scaled_coeffs()
   1481     assert len(a) == 5
   1482     return a[0]*a[4]+3*a[2]**2-4*a[1]*a[3]

File /ext/sage/9.7/src/sage/rings/invariants/invariant_theory.py:1452, in BinaryQuartic.scaled_coeffs(self)
   1425 """
   1426 The coefficients of a binary quartic.
   1427 
   (...)
   1449     (a0, a1, a2, a3, a4)
   1450 """
   1451 coeff = self.coeffs()
-> 1452 return (coeff[0], coeff[1]/4, coeff[2]/6, coeff[3]/4, coeff[4])

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:1196, in sage.structure.coerce.CoercionModel.bin_op()
   1194         return (<Action>action)._act_(x, y)
   1195     else:
-> 1196         return (<Action>action)._act_(y, x)
   1197 
   1198 # Now coerce to a common parent and do the operation there

File /ext/sage/9.7/src/sage/categories/action.pyx:494, in sage.categories.action.PrecomposedAction._act_()
    492     if self.S_precomposition is not None:
    493         x = self.S_precomposition._call_(x)
--> 494     return self._action._act_(g, x)
    495 
    496 def domain(self):

File /ext/sage/9.7/src/sage/categories/action.pyx:494, in sage.categories.action.PrecomposedAction._act_()
    492     if self.S_precomposition is not None:
    493         x = self.S_precomposition._call_(x)
--> 494     return self._action._act_(g, x)
    495 
    496 def domain(self):

File /ext/sage/9.7/src/sage/categories/action.pyx:407, in sage.categories.action.InverseAction._act_()
    405     if self.S_precomposition is not None:
    406         x = self.S_precomposition(x)
--> 407     return self._action._act_(~g, x)
    408 
    409 def codomain(self):

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2821, in sage.rings.finite_rings.integer_mod.IntegerMod_int.__invert__()
   2819 x = self.__modulus.inverses[self.ivalue]
   2820 if x is None:
-> 2821     raise ZeroDivisionError(f"inverse of Mod({self}, {self.__modulus.sageInteger}) does not exist")
   2822 else:
   2823     return x

ZeroDivisionError: inverse of Mod(0, 3) does not exist
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR.<u,v> = GF(3)[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 1)))[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR.<u,v> = GF(3)[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 1)))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l 1)[?7h[?12l[?25h[?25l[?7l+ 1)[?7h[?12l[?25h[?25l[?7lsage: R.<u,v> = GF(3)[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 + 1)))

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
Input In [14], in <cell line: 1>()
----> 1 R = GF(Integer(3))['u, v']; (u, v,) = R._first_ngens(2); EllipticCurve(WeierstrassForm(v**Integer(2) - (u**Integer(4) + Integer(1))))

File /ext/sage/9.7/src/sage/misc/lazy_import.pyx:391, in sage.misc.lazy_import.LazyImport.__call__()
    389         True
    390     """
--> 391     return self.get_object()(*args, **kwds)
    392 
    393 def __repr__(self):

File /ext/sage/9.7/src/sage/schemes/toric/weierstrass.py:499, in WeierstrassForm(polynomial, variables, transformation)
    497     return WeierstrassForm_P1xP1(polynomial, variables)
    498 if polygon is polar_P2_112_polytope():
--> 499     return WeierstrassForm_P2_112(polynomial, variables)
    500 raise ValueError('Newton polytope is not contained in a reflexive polygon')

File /ext/sage/9.7/src/sage/schemes/toric/weierstrass.py:1078, in WeierstrassForm_P2_112(polynomial, variables)
   1076 delta = _partial_discriminant(polynomial, y, t)
   1077 Q = invariant_theory.binary_quartic(delta, x, z)
-> 1078 g2 = Q.EisensteinD()
   1079 g3 = -Q.EisensteinE()
   1080 return (-g2/4, -g3/4)

File /ext/sage/9.7/src/sage/misc/cachefunc.pyx:2299, in sage.misc.cachefunc.CachedMethodCallerNoArgs.__call__()
   2297 if self.cache is None:
   2298     f = self.f
-> 2299     self.cache = f(self._instance)
   2300 return self.cache
   2301 

File /ext/sage/9.7/src/sage/rings/invariants/invariant_theory.py:1480, in BinaryQuartic.EisensteinD(self)
   1455 @cached_method
   1456 def EisensteinD(self):
   1457     r"""
   1458     One of the Eisenstein invariants of a binary quartic.
   1459 
   (...)
   1478         3*a2^2 - 4*a1*a3 + a0*a4
   1479     """
-> 1480     a = self.scaled_coeffs()
   1481     assert len(a) == 5
   1482     return a[0]*a[4]+3*a[2]**2-4*a[1]*a[3]

File /ext/sage/9.7/src/sage/rings/invariants/invariant_theory.py:1452, in BinaryQuartic.scaled_coeffs(self)
   1425 """
   1426 The coefficients of a binary quartic.
   1427 
   (...)
   1449     (a0, a1, a2, a3, a4)
   1450 """
   1451 coeff = self.coeffs()
-> 1452 return (coeff[0], coeff[1]/4, coeff[2]/6, coeff[3]/4, coeff[4])

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:1196, in sage.structure.coerce.CoercionModel.bin_op()
   1194         return (<Action>action)._act_(x, y)
   1195     else:
-> 1196         return (<Action>action)._act_(y, x)
   1197 
   1198 # Now coerce to a common parent and do the operation there

File /ext/sage/9.7/src/sage/categories/action.pyx:494, in sage.categories.action.PrecomposedAction._act_()
    492     if self.S_precomposition is not None:
    493         x = self.S_precomposition._call_(x)
--> 494     return self._action._act_(g, x)
    495 
    496 def domain(self):

File /ext/sage/9.7/src/sage/categories/action.pyx:494, in sage.categories.action.PrecomposedAction._act_()
    492     if self.S_precomposition is not None:
    493         x = self.S_precomposition._call_(x)
--> 494     return self._action._act_(g, x)
    495 
    496 def domain(self):

File /ext/sage/9.7/src/sage/categories/action.pyx:407, in sage.categories.action.InverseAction._act_()
    405     if self.S_precomposition is not None:
    406         x = self.S_precomposition(x)
--> 407     return self._action._act_(~g, x)
    408 
    409 def codomain(self):

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2821, in sage.rings.finite_rings.integer_mod.IntegerMod_int.__invert__()
   2819 x = self.__modulus.inverses[self.ivalue]
   2820 if x is None:
-> 2821     raise ZeroDivisionError(f"inverse of Mod({self}, {self.__modulus.sageInteger}) does not exist")
   2822 else:
   2823     return x

ZeroDivisionError: inverse of Mod(0, 3) does not exist
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR.<u,v> = GF(3)[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 + 1)))[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7lQQ[]; ElliptcCurve(WierstassForm(v^2 - (u^4 - 1)))[?7h[?12l[?25h[?25l[?7lsage: R.<u,v> = QQ[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 1)))

[?7h[?12l[?25h[?2004l[?7hElliptic Curve defined by y^2 = x^3 + 4*x over Multivariate Polynomial Ring in u, v over Rational Field
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR.<u,v> = QQ[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 1)))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l2))[?7h[?12l[?25h[?25l[?7lsage: R.<u,v> = QQ[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 2)))

[?7h[?12l[?25h[?2004l[?7hElliptic Curve defined by y^2 = x^3 + 8*x over Multivariate Polynomial Ring in u, v over Rational Field
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR.<u,v> = QQ[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 2)))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l1))[?7h[?12l[?25h[?25l[?7l/))[?7h[?12l[?25h[?25l[?7l2))[?7h[?12l[?25h[?25l[?7lsage: R.<u,v> = QQ[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 1/2)))

[?7h[?12l[?25h[?2004l[?7hElliptic Curve defined by y^2 = x^3 + 2*x over Multivariate Polynomial Ring in u, v over Rational Field
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR.<u,v> = QQ[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 1/2)))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l+))[?7h[?12l[?25h[?25l[?7l1))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l 1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: R.<u,v> = QQ[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 + 1)))

[?7h[?12l[?25h[?2004l[?7hElliptic Curve defined by y^2 = x^3 + (-4)*x over Multivariate Polynomial Ring in u, v over Rational Field
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR.<u,v> = QQ[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 + 1)))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]; ElipticCurve(WeierstrasForm(v^2 - (u^4 + 1)[?7h[?12l[?25h[?25l[?7l[]; ElipticCurve(WeierstrasForm(v^2 - (u^4 + 1)[?7h[?12l[?25h[?25l[?7lG[]; ElipticCurve(WeierstrasForm(v^2 - (u^4 + 1)[?7h[?12l[?25h[?25l[?7lF[]; ElipticCurve(WeierstrasForm(v^2 - (u^4 + 1)[?7h[?12l[?25h[?25l[?7l([]; ElipticCurve(WeierstrasForm(v^2 - (u^4 + 1)[?7h[?12l[?25h[?25l[?7l3[]; ElipticCurve(WeierstrasForm(v^2 - (u^4 + 1)[?7h[?12l[?25h[?25l[?7l)[]; ElipticCurve(WeierstrasForm(v^2 - (u^4 + 1)[?7h[?12l[?25h[?25l[?7lsage: R.<u,v> = GF(3)[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 + 1)))

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
Input In [19], in <cell line: 1>()
----> 1 R = GF(Integer(3))['u, v']; (u, v,) = R._first_ngens(2); EllipticCurve(WeierstrassForm(v**Integer(2) - (u**Integer(4) + Integer(1))))

File /ext/sage/9.7/src/sage/misc/lazy_import.pyx:391, in sage.misc.lazy_import.LazyImport.__call__()
    389         True
    390     """
--> 391     return self.get_object()(*args, **kwds)
    392 
    393 def __repr__(self):

File /ext/sage/9.7/src/sage/schemes/toric/weierstrass.py:499, in WeierstrassForm(polynomial, variables, transformation)
    497     return WeierstrassForm_P1xP1(polynomial, variables)
    498 if polygon is polar_P2_112_polytope():
--> 499     return WeierstrassForm_P2_112(polynomial, variables)
    500 raise ValueError('Newton polytope is not contained in a reflexive polygon')

File /ext/sage/9.7/src/sage/schemes/toric/weierstrass.py:1078, in WeierstrassForm_P2_112(polynomial, variables)
   1076 delta = _partial_discriminant(polynomial, y, t)
   1077 Q = invariant_theory.binary_quartic(delta, x, z)
-> 1078 g2 = Q.EisensteinD()
   1079 g3 = -Q.EisensteinE()
   1080 return (-g2/4, -g3/4)

File /ext/sage/9.7/src/sage/misc/cachefunc.pyx:2299, in sage.misc.cachefunc.CachedMethodCallerNoArgs.__call__()
   2297 if self.cache is None:
   2298     f = self.f
-> 2299     self.cache = f(self._instance)
   2300 return self.cache
   2301 

File /ext/sage/9.7/src/sage/rings/invariants/invariant_theory.py:1480, in BinaryQuartic.EisensteinD(self)
   1455 @cached_method
   1456 def EisensteinD(self):
   1457     r"""
   1458     One of the Eisenstein invariants of a binary quartic.
   1459 
   (...)
   1478         3*a2^2 - 4*a1*a3 + a0*a4
   1479     """
-> 1480     a = self.scaled_coeffs()
   1481     assert len(a) == 5
   1482     return a[0]*a[4]+3*a[2]**2-4*a[1]*a[3]

File /ext/sage/9.7/src/sage/rings/invariants/invariant_theory.py:1452, in BinaryQuartic.scaled_coeffs(self)
   1425 """
   1426 The coefficients of a binary quartic.
   1427 
   (...)
   1449     (a0, a1, a2, a3, a4)
   1450 """
   1451 coeff = self.coeffs()
-> 1452 return (coeff[0], coeff[1]/4, coeff[2]/6, coeff[3]/4, coeff[4])

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:1196, in sage.structure.coerce.CoercionModel.bin_op()
   1194         return (<Action>action)._act_(x, y)
   1195     else:
-> 1196         return (<Action>action)._act_(y, x)
   1197 
   1198 # Now coerce to a common parent and do the operation there

File /ext/sage/9.7/src/sage/categories/action.pyx:494, in sage.categories.action.PrecomposedAction._act_()
    492     if self.S_precomposition is not None:
    493         x = self.S_precomposition._call_(x)
--> 494     return self._action._act_(g, x)
    495 
    496 def domain(self):

File /ext/sage/9.7/src/sage/categories/action.pyx:494, in sage.categories.action.PrecomposedAction._act_()
    492     if self.S_precomposition is not None:
    493         x = self.S_precomposition._call_(x)
--> 494     return self._action._act_(g, x)
    495 
    496 def domain(self):

File /ext/sage/9.7/src/sage/categories/action.pyx:407, in sage.categories.action.InverseAction._act_()
    405     if self.S_precomposition is not None:
    406         x = self.S_precomposition(x)
--> 407     return self._action._act_(~g, x)
    408 
    409 def codomain(self):

File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2821, in sage.rings.finite_rings.integer_mod.IntegerMod_int.__invert__()
   2819 x = self.__modulus.inverses[self.ivalue]
   2820 if x is None:
-> 2821     raise ZeroDivisionError(f"inverse of Mod({self}, {self.__modulus.sageInteger}) does not exist")
   2822 else:
   2823     return x

ZeroDivisionError: inverse of Mod(0, 3) does not exist
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR.<u,v> = GF(3)[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 + 1)))[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l0 dx
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
f2 ((-x^6 - 1)/(x^2*y - y)) dx
((x^4 + x^2 + 1)/(x^6*y)) dx
[0]
[0]
t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
((x^10 - x^6 + 1)/(x^2*y - y)) dx
(x^7 + x, 0)
((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
((-x^6 - 1)/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.p_rank()[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l4, 2)[?7h[?12l[?25h[?25l[?7l , 2)[?7h[?12l[?25h[?25l[?7l-, 2)[?7h[?12l[?25h[?25l[?7l , 2)[?7h[?12l[?25h[?25l[?7lx, 2)[?7h[?12l[?25h[?25l[?7l^, 2)[?7h[?12l[?25h[?25l[?7l3, 2)[?7h[?12l[?25h[?25l[?7l , 2)[?7h[?12l[?25h[?25l[?7l+, 2)[?7h[?12l[?25h[?25l[?7l , 2)[?7h[?12l[?25h[?25l[?7lx, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^4 - x^3 + x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^4 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l.p_rank()[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l_rank()[?7h[?12l[?25h[?25l[?7lsage: C.p_rank()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [3], in <cell line: 1>()
----> 1 C.p_rank()

File <string>:176, in p_rank(self)

File /ext/sage/9.7/src/sage/schemes/hyperelliptic_curves/hyperelliptic_finite_field.py:1889, in HyperellipticCurve_finite_field.p_rank(self)
   1855 r"""
   1856 INPUT:
   1857 
   (...)
   1880     0
   1881 """
   1882 #We use caching here since Hasse Witt is needed to compute p_rank. So if the Hasse Witt
   1883 #is already computed it is stored in list A. If it was not cached (i.e. A is empty), we simply
   1884 #compute it. If it is cached then we need to make sure that we have the correct one. So check
   (...)
   1887 # However, it seems a waste of time to manually analyse the cache
   1888 # -- See Trac Ticket #11115
-> 1889 N, E = self._Hasse_Witt_cached()
   1890 if E != self:
   1891     self._Hasse_Witt_cached.clear_cache()

File /ext/sage/9.7/src/sage/misc/cachefunc.pyx:2299, in sage.misc.cachefunc.CachedMethodCallerNoArgs.__call__()
   2297 if self.cache is None:
   2298     f = self.f
-> 2299     self.cache = f(self._instance)
   2300 return self.cache
   2301 

File /ext/sage/9.7/src/sage/schemes/hyperelliptic_curves/hyperelliptic_finite_field.py:1727, in HyperellipticCurve_finite_field._Hasse_Witt_cached(self)
   1647 r"""
   1648 This is where Hasse_Witt is actually computed.
   1649 
   (...)
   1712     0
   1713 """
   1714 # If Cartier Matrix is already cached for this curve, use that or evaluate it to get M,
   1715 #Coeffs, genus, Fq=base field of self, p=char(Fq). This is so we have one less matrix to
   1716 #compute.
   (...)
   1725 #that don't  accept arguments. Anyway, the easiest is to call
   1726 #the cached method and simply see whether the data belong to self.
-> 1727 M, Coeffs, g, Fq, p, E = self._Cartier_matrix_cached()
   1728 if E != self:
   1729     self._Cartier_matrix_cached.clear_cache()

File /ext/sage/9.7/src/sage/misc/cachefunc.pyx:2299, in sage.misc.cachefunc.CachedMethodCallerNoArgs.__call__()
   2297 if self.cache is None:
   2298     f = self.f
-> 2299     self.cache = f(self._instance)
   2300 return self.cache
   2301 

File /ext/sage/9.7/src/sage/schemes/hyperelliptic_curves/hyperelliptic_finite_field.py:1523, in HyperellipticCurve_finite_field._Cartier_matrix_cached(self)
   1521 #this implementation is for odd degree only, even degree will be handled later.
   1522 if d%2 == 0:
-> 1523     raise ValueError("In this implementation the degree of f must be odd")
   1524 #Compute resultant to make sure no repeated roots
   1525 df=f.derivative()

ValueError: In this implementation the degree of f must be odd
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.p_rank()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcatier_matrix()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrtier_matrix()[?7h[?12l[?25h[?25l[?7lsage: C.cartier_matrix()

[?7h[?12l[?25h[?2004l[?7h[0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cartier_matrix()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cartier_matrix()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^4 + 2*x^3 + x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l0 dx
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
f2 ((-x^6 - 1)/(x^2*y - y)) dx
((x^4 + x^2 + 1)/(x^6*y)) dx
[0]
[0]
t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
((x^10 - x^6 + 1)/(x^2*y - y)) dx
(x^7 + x, 0)
((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
((-x^6 - 1)/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.cartier_matrix()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrtier_matrix()[?7h[?12l[?25h[?25l[?7lsage: C.cartier_matrix()

[?7h[?12l[?25h[?2004l[?7h[0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cartier_matrix()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.cartier_matrix()[?7h[?12l[?25h[?25l[?7lp_ank()[?7h[?12l[?25h[?25l[?7l = superelliptic(x^4 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^4 - x^3 + x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^4 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l.carti_matrix()[?7h[?12l[?25h[?25l[?7lde_rhambsis()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx), (((-x^2 - x)/y) dx, 2/x*y, (1/(x*y)) dx)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l0 dx
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
f2 ((-x^6 - 1)/(x^2*y - y)) dx
((x^4 + x^2 + 1)/(x^6*y)) dx
[0]
[0]
t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
((x^10 - x^6 + 1)/(x^2*y - y)) dx
(x^7 + x, 0)
((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
((-x^6 - 1)/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx.cartier()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.dx

[?7h[?12l[?25h[?2004l[?7h1 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7liC.dx[?7h[?12l[?25h[?25l[?7lsC.dx[?7h[?12l[?25h[?25l[?7liC.dx[?7h[?12l[?25h[?25l[?7lnC.dx[?7h[?12l[?25h[?25l[?7lsC.dx[?7h[?12l[?25h[?25l[?7ltC.dx[?7h[?12l[?25h[?25l[?7laC.dx[?7h[?12l[?25h[?25l[?7lnC.dx[?7h[?12l[?25h[?25l[?7lceC.dx[?7h[?12l[?25h[?25l[?7lisinstance(C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: isinstance(C.dx,superelliptic_form)

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l0 dx
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
f2 ((-x^6 - 1)/(x^2*y - y)) dx
((x^4 + x^2 + 1)/(x^6*y)) dx
[0]
[0]
t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
((x^10 - x^6 + 1)/(x^2*y - y)) dx
(x^7 + x, 0)
((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
((-x^6 - 1)/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprint((x^8).quo_rem(x^4 + x^2 + 1))[?7h[?12l[?25h[?25l[?7larent)[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: patch(C)

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

File <string>:5, in patch(C)

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

[?7h[?12l[?25h[?2004l0 dx
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
f2 ((-x^6 - 1)/(x^2*y - y)) dx
((x^4 + x^2 + 1)/(x^6*y)) dx
[0]
[0]
t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
((x^10 - x^6 + 1)/(x^2*y - y)) dx
(x^7 + x, 0)
((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
((-x^6 - 1)/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lpatch(C)[?7h[?12l[?25h[?25l[?7lsage: patch(C)

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = 2*x^3 + x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpatch(C)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: patch(C).genus()

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = superelliptic(x^4 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7luperelliptic(x^4 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^4 - x^3 + x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^4 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpatch(C).genus()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ltch(C).genus()[?7h[?12l[?25h[?25l[?7lsage: patch(C).genus()

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpatch(C).genus()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l().genus()[?7h[?12l[?25h[?25l[?7lsage: patch(C)

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x + 1 over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpatch(C)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lstr(E.local_data(2))[?7h[?12l[?25h[?25l[?7let*list2)[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x

....: [?7h[?12l[?25h[?25l[?7l(

)[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x

....: )

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [10], in <cell line: 1>()
----> 1 second_patch(C.x
      2 )

File <string>:19, in second_patch(argument)

NameError: name 'y' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x

....: )[?7h[?12l[?25h[?25l[?7l(

[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [11], in <cell line: 1>()
----> 1 second_patch(C.x)

File <string>:19, in second_patch(argument)

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

[?7h[?12l[?25h[?2004l0 dx
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
f2 ((-x^6 - 1)/(x^2*y - y)) dx
((x^4 + x^2 + 1)/(x^6*y)) dx
[0]
[0]
t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
((x^10 - x^6 + 1)/(x^2*y - y)) dx
(x^7 + x, 0)
((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
((-x^6 - 1)/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [13], in <cell line: 1>()
----> 1 second_patch(C.x)

File <string>:20, in second_patch(argument)

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2411, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
   2409 if type(exp) is not Integer:
   2410     try:
-> 2411         exp = Integer(exp)
   2412     except TypeError:
   2413         try:

File /ext/sage/9.7/src/sage/rings/integer.pyx:658, in sage.rings.integer.Integer.__init__()
    656 otmp = getattr(x, "_integer_", None)
    657 if otmp is not None:
--> 658     set_from_Integer(self, otmp(the_integer_ring))
    659     return
    660 

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/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:1692, in sage.categories.map.FormalCompositeMap._call_()
   1690 """
   1691 for f in self.__list:
-> 1692     x = f._call_(x)
   1693 return x
   1694 

File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1620, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
   1618     Section._update_slots(self, _slots)
   1619 
-> 1620 cpdef Element _call_(self, _x):
   1621     """
   1622     Applies the section.

File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1654, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
   1652         raise ValueError("not integral")
   1653     if nmod_poly_degree(x._numer) > 0:
-> 1654         raise ValueError("not constant")
   1655 ans = IntegerMod_int.__new__(IntegerMod_int)
   1656 ans._parent = self.codomain()

ValueError: not constant
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^4 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l.dx[?7h[?12l[?25h[?25l[?7lsage: C.

[?7h[?12l[?25h[?2004l  Input In [14]
    C.
      ^
SyntaxError: invalid syntax

[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty()[1][?7h[?12l[?25h[?25l[?7lsage: C.x

[?7h[?12l[?25h[?2004l[?7hx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x+1)^5 - x^5[?7h[?12l[?25h[?25l[?7lC.x/C.y).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()^(11)/(C.y)^3*C.dx[?7h[?12l[?25h[?25l[?7l().pth_root([?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(C.x).function[?7h[?12l[?25h[?25l[?7l (C.x).function[?7h[?12l[?25h[?25l[?7l=(C.x).function[?7h[?12l[?25h[?25l[?7l (C.x).function[?7h[?12l[?25h[?25l[?7lsage: g = (C.x).function

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = (C.x).function[?7h[?12l[?25h[?25l[?7l(x+1) - g[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g(x = x+1, y = y+1)

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

NameError: name 'y' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y = C.fct_field[?7h[?12l[?25h[?25l[?7lsage: Fxy, Rxy, x, y = C.fct_field

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y = C.fct_field[?7h[?12l[?25h[?25l[?7lg(x = +1, y=y+1)[?7h[?12l[?25h[?25l[?7lsage: g(x = x+1, y = y+1)

[?7h[?12l[?25h[?2004l[?7hx + 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l0 dx
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
f2 ((-x^6 - 1)/(x^2*y - y)) dx
((x^4 + x^2 + 1)/(x^6*y)) dx
[0]
[0]
t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
((x^10 - x^6 + 1)/(x^2*y - y)) dx
(x^7 + x, 0)
((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
((-x^6 - 1)/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg(x = x+1, y = y+1)[?7h[?12l[?25h[?25l[?7lFxy, Ry, x,y= C.fct_field[?7h[?12l[?25h[?25l[?7lg(x = +1, y=y+1)[?7h[?12l[?25h[?25l[?7l =(C.x).function[?7h[?12l[?25h[?25l[?7lsage: g = (C.x).function

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = (C.x).function[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = (C.x).function[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg(x = x+1, y = y+1)[?7h[?12l[?25h[?25l[?7lFxy, Ry, x,y= C.fct_field[?7h[?12l[?25h[?25l[?7lg(x = +1, y=y+1)[?7h[?12l[?25h[?25l[?7l =(C.x).function[?7h[?12l[?25h[?25l[?7lC.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lload('init.sage'[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2411, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
   2410 try:
-> 2411     exp = Integer(exp)
   2412 except TypeError:

File /ext/sage/9.7/src/sage/rings/integer.pyx:658, in sage.rings.integer.Integer.__init__()
    657 if otmp is not None:
--> 658     set_from_Integer(self, otmp(the_integer_ring))
    659     return

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:829, in sage.rings.fraction_field_element.FractionFieldElement._conversion()
    828 if self.__denominator.is_one():
--> 829     return R(self.__numerator)
    830 else:

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)
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2414, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
   2413 try:
-> 2414     n = Rational(exp)
   2415 except TypeError:

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

File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value()
    625 elif hasattr(x, "_rational_"):
--> 626     set_from_Rational(self, x._rational_())
    627 

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

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:829, in sage.rings.fraction_field_element.FractionFieldElement._conversion()
    828 if self.__denominator.is_one():
--> 829     return R(self.__numerator)
    830 else:

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:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    160     print(type(C._element_constructor), C._element_constructor)
--> 161 raise
    162 

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/rational.pyx:538, in sage.rings.rational.Rational.__init__()
    537 if x is not None:
--> 538     self.__set_value(x, base)
    539 

File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value()
    625 elif hasattr(x, "_rational_"):
--> 626     set_from_Rational(self, x._rational_())
    627 

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:175, in sage.rings.polynomial.multi_polynomial.MPolynomial._rational_()
    174 from sage.rings.rational_field import QQ
--> 175 return self._scalar_conversion(QQ)
    176 

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:105, in sage.rings.polynomial.multi_polynomial.MPolynomial._scalar_conversion()
    104     return R(self.constant_coefficient())
--> 105 raise TypeError(f"unable to convert non-constant polynomial {self} to {R}")
    106 

TypeError: unable to convert non-constant polynomial x + 1 to Rational Field

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
Input In [22], in <cell line: 1>()
----> 1 second_patch(C.x)

File <string>:20, in second_patch(argument)

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2416, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
   2414     n = Rational(exp)
   2415 except TypeError:
-> 2416     raise TypeError("{} is neither an integer nor a rational".format(exp))
   2417 num = n.numerator()
   2418 den = n.denominator()

TypeError: x + 1 is neither an integer nor a rational
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l0 dx
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
f2 ((-x^6 - 1)/(x^2*y - y)) dx
((x^4 + x^2 + 1)/(x^6*y)) dx
[0]
[0]
t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
((x^10 - x^6 + 1)/(x^2*y - y)) dx
(x^7 + x, 0)
((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
((-x^6 - 1)/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2411, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
   2410 try:
-> 2411     exp = Integer(exp)
   2412 except TypeError:

File /ext/sage/9.7/src/sage/rings/integer.pyx:658, in sage.rings.integer.Integer.__init__()
    657 if otmp is not None:
--> 658     set_from_Integer(self, otmp(the_integer_ring))
    659     return

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:105, in sage.rings.polynomial.multi_polynomial.MPolynomial._scalar_conversion()
    104     return R(self.constant_coefficient())
--> 105 raise TypeError(f"unable to convert non-constant polynomial {self} to {R}")
    106 

TypeError: unable to convert non-constant polynomial x + 1 to Integer Ring

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2414, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
   2413 try:
-> 2414     n = Rational(exp)
   2415 except TypeError:

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

File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value()
    625 elif hasattr(x, "_rational_"):
--> 626     set_from_Rational(self, x._rational_())
    627 

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:175, in sage.rings.polynomial.multi_polynomial.MPolynomial._rational_()
    174 from sage.rings.rational_field import QQ
--> 175 return self._scalar_conversion(QQ)
    176 

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:105, in sage.rings.polynomial.multi_polynomial.MPolynomial._scalar_conversion()
    104     return R(self.constant_coefficient())
--> 105 raise TypeError(f"unable to convert non-constant polynomial {self} to {R}")
    106 

TypeError: unable to convert non-constant polynomial x + 1 to Rational Field

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
Input In [24], in <cell line: 1>()
----> 1 second_patch(C.x)

File <string>:20, in second_patch(argument)

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2416, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
   2414     n = Rational(exp)
   2415 except TypeError:
-> 2416     raise TypeError("{} is neither an integer nor a rational".format(exp))
   2417 num = n.numerator()
   2418 den = n.denominator()

TypeError: x + 1 is neither an integer nor a rational
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: x+1

[?7h[?12l[?25h[?2004l[?7hx + 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()x[?7h[?12l[?25h[?25l[?7l(x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()^(11)/(C.y)^3*C.dx[?7h[?12l[?25h[?25l[?7l().pth_root([?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(C.x).function[?7h[?12l[?25h[?25l[?7l (C.x).function[?7h[?12l[?25h[?25l[?7l=(C.x).function[?7h[?12l[?25h[?25l[?7l (C.x).function[?7h[?12l[?25h[?25l[?7lsage: g = (C.x).function

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = (C.x).function[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g = Rxy(g)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = Rxy(g)[?7h[?12l[?25h[?25l[?7l(x= x+1, y = y+1)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+1) - g[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g(x+1, y+1)

[?7h[?12l[?25h[?2004l[?7hx + 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(x+1, y+1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lx+1, y+1)[?7h[?12l[?25h[?25l[?7l x+1, y+1)[?7h[?12l[?25h[?25l[?7l=x+1, y+1)[?7h[?12l[?25h[?25l[?7l x+1, y+1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly+1)[?7h[?12l[?25h[?25l[?7l y+1)[?7h[?12l[?25h[?25l[?7l=y+1)[?7h[?12l[?25h[?25l[?7l y+1)[?7h[?12l[?25h[?25l[?7lsage: g(x = x+1, y = y+1)

[?7h[?12l[?25h[?2004l[?7hx + 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l0 dx
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
f2 ((-x^6 - 1)/(x^2*y - y)) dx
((x^4 + x^2 + 1)/(x^6*y)) dx
[0]
[0]
t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
((x^10 - x^6 + 1)/(x^2*y - y)) dx
(x^7 + x, 0)
((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
((-x^6 - 1)/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg(x = x+1, y = y+1)[?7h[?12l[?25h[?25l[?7l+1, y+1)[?7h[?12l[?25h[?25l[?7l = Rxy(g)[?7h[?12l[?25h[?25l[?7l(C.x).function[?7h[?12l[?25h[?25l[?7lx+1[?7h[?12l[?25h[?25l[?7lg = (C.x).function[?7h[?12l[?25h[?25l[?7lx+1[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lload('init.sage'[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x)

[?7h[?12l[?25h[?2004lx <class 'sage.rings.polynomial.polynomial_ring.PolynomialRing_field_with_category.element_class'>
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [31], in <cell line: 1>()
----> 1 second_patch(C.x)

File <string>:21, in second_patch(argument)

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2411, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
   2409 if type(exp) is not Integer:
   2410     try:
-> 2411         exp = Integer(exp)
   2412     except TypeError:
   2413         try:

File /ext/sage/9.7/src/sage/rings/integer.pyx:658, in sage.rings.integer.Integer.__init__()
    656 otmp = getattr(x, "_integer_", None)
    657 if otmp is not None:
--> 658     set_from_Integer(self, otmp(the_integer_ring))
    659     return
    660 

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/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:1692, in sage.categories.map.FormalCompositeMap._call_()
   1690 """
   1691 for f in self.__list:
-> 1692     x = f._call_(x)
   1693 return x
   1694 

File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1620, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
   1618     Section._update_slots(self, _slots)
   1619 
-> 1620 cpdef Element _call_(self, _x):
   1621     """
   1622     Applies the section.

File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1654, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
   1652         raise ValueError("not integral")
   1653     if nmod_poly_degree(x._numer) > 0:
-> 1654         raise ValueError("not constant")
   1655 ans = IntegerMod_int.__new__(IntegerMod_int)
   1656 ans._parent = self.codomain()

ValueError: not constant
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l0 dx
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
f2 ((-x^6 - 1)/(x^2*y - y)) dx
((x^4 + x^2 + 1)/(x^6*y)) dx
[0]
[0]
t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
((x^10 - x^6 + 1)/(x^2*y - y)) dx
(x^7 + x, 0)
((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
((-x^6 - 1)/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x[?7h[?12l[?25h[?25l[?7lload('init.sage'[?7h[?12l[?25h[?25l[?7lg(x = x+1, y = y+1)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x)

[?7h[?12l[?25h[?2004lx Univariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 3 <class 'sage.rings.polynomial.polynomial_ring.PolynomialRing_field_with_category.element_class'>
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [33], in <cell line: 1>()
----> 1 second_patch(C.x)

File <string>:21, in second_patch(argument)

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2411, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
   2409 if type(exp) is not Integer:
   2410     try:
-> 2411         exp = Integer(exp)
   2412     except TypeError:
   2413         try:

File /ext/sage/9.7/src/sage/rings/integer.pyx:658, in sage.rings.integer.Integer.__init__()
    656 otmp = getattr(x, "_integer_", None)
    657 if otmp is not None:
--> 658     set_from_Integer(self, otmp(the_integer_ring))
    659     return
    660 

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/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:1692, in sage.categories.map.FormalCompositeMap._call_()
   1690 """
   1691 for f in self.__list:
-> 1692     x = f._call_(x)
   1693 return x
   1694 

File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1620, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
   1618     Section._update_slots(self, _slots)
   1619 
-> 1620 cpdef Element _call_(self, _x):
   1621     """
   1622     Applies the section.

File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1654, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
   1652         raise ValueError("not integral")
   1653     if nmod_poly_degree(x._numer) > 0:
-> 1654         raise ValueError("not constant")
   1655 ans = IntegerMod_int.__new__(IntegerMod_int)
   1656 ans._parent = self.codomain()

ValueError: not constant
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y = C.fct_field[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: Fxy

[?7h[?12l[?25h[?2004l[?7hFraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lload('init.sage'[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x[?7h[?12l[?25h[?25l[?7lload('init.sage'[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x[?7h[?12l[?25h[?25l[?7lFxy[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[1][?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgC.x.function[?7h[?12l[?25h[?25l[?7l=C.x.function[?7h[?12l[?25h[?25l[?7l C.x.function[?7h[?12l[?25h[?25l[?7lC.x.function[?7h[?12l[?25h[?25l[?7l=C.x.function[?7h[?12l[?25h[?25l[?7lC.x.function[?7h[?12l[?25h[?25l[?7lC.x.function[?7h[?12l[?25h[?25l[?7l C.x.function[?7h[?12l[?25h[?25l[?7l=C.x.function[?7h[?12l[?25h[?25l[?7l C.x.function[?7h[?12l[?25h[?25l[?7lFC.x.function[?7h[?12l[?25h[?25l[?7lxC.x.function[?7h[?12l[?25h[?25l[?7lyC.x.function[?7h[?12l[?25h[?25l[?7l(C.x.function[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g = Fxy(C.x.function)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = Fxy(C.x.function)[?7h[?12l[?25h[?25l[?7l(x= x+1, y = y+1)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+1, y+1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx = x+1, y = y+1)[?7h[?12l[?25h[?25l[?7l( = x+1, y = y+1)[?7h[?12l[?25h[?25l[?7lsage: g(x = x+1, y = y+1)

[?7h[?12l[?25h[?2004l[?7hx + 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(x = x+1, y = y+1)[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l{[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l{}[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7lsage: g.subs({x:x+1, y:y+1})

[?7h[?12l[?25h[?2004l[?7hx + 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l0 dx
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
f2 ((-x^6 - 1)/(x^2*y - y)) dx
((x^4 + x^2 + 1)/(x^6*y)) dx
[0]
[0]
t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
((x^10 - x^6 + 1)/(x^2*y - y)) dx
(x^7 + x, 0)
((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
((-x^6 - 1)/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcond_patch(C.x)[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2411, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
   2410 try:
-> 2411     exp = Integer(exp)
   2412 except TypeError:

File /ext/sage/9.7/src/sage/rings/integer.pyx:658, in sage.rings.integer.Integer.__init__()
    657 if otmp is not None:
--> 658     set_from_Integer(self, otmp(the_integer_ring))
    659     return

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:829, in sage.rings.fraction_field_element.FractionFieldElement._conversion()
    828 if self.__denominator.is_one():
--> 829     return R(self.__numerator)
    830 else:

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)
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2414, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
   2413 try:
-> 2414     n = Rational(exp)
   2415 except TypeError:

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

File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value()
    625 elif hasattr(x, "_rational_"):
--> 626     set_from_Rational(self, x._rational_())
    627 

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

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:829, in sage.rings.fraction_field_element.FractionFieldElement._conversion()
    828 if self.__denominator.is_one():
--> 829     return R(self.__numerator)
    830 else:

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:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    160     print(type(C._element_constructor), C._element_constructor)
--> 161 raise
    162 

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/rational.pyx:538, in sage.rings.rational.Rational.__init__()
    537 if x is not None:
--> 538     self.__set_value(x, base)
    539 

File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value()
    625 elif hasattr(x, "_rational_"):
--> 626     set_from_Rational(self, x._rational_())
    627 

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:175, in sage.rings.polynomial.multi_polynomial.MPolynomial._rational_()
    174 from sage.rings.rational_field import QQ
--> 175 return self._scalar_conversion(QQ)
    176 

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:105, in sage.rings.polynomial.multi_polynomial.MPolynomial._scalar_conversion()
    104     return R(self.constant_coefficient())
--> 105 raise TypeError(f"unable to convert non-constant polynomial {self} to {R}")
    106 

TypeError: unable to convert non-constant polynomial x + 1 to Rational Field

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
Input In [39], in <cell line: 1>()
----> 1 second_patch(C.x)

File <string>:20, in second_patch(argument)

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2416, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
   2414     n = Rational(exp)
   2415 except TypeError:
-> 2416     raise TypeError("{} is neither an integer nor a rational".format(exp))
   2417 num = n.numerator()
   2418 den = n.denominator()

TypeError: x + 1 is neither an integer nor a rational
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l0 dx
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
f2 ((-x^6 - 1)/(x^2*y - y)) dx
((x^4 + x^2 + 1)/(x^6*y)) dx
[0]
[0]
t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
((x^10 - x^6 + 1)/(x^2*y - y)) dx
(x^7 + x, 0)
((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
((-x^6 - 1)/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2411, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
   2410 try:
-> 2411     exp = Integer(exp)
   2412 except TypeError:

File /ext/sage/9.7/src/sage/rings/integer.pyx:658, in sage.rings.integer.Integer.__init__()
    657 if otmp is not None:
--> 658     set_from_Integer(self, otmp(the_integer_ring))
    659     return

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:829, in sage.rings.fraction_field_element.FractionFieldElement._conversion()
    828 if self.__denominator.is_one():
--> 829     return R(self.__numerator)
    830 else:

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)
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2414, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
   2413 try:
-> 2414     n = Rational(exp)
   2415 except TypeError:

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

File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value()
    625 elif hasattr(x, "_rational_"):
--> 626     set_from_Rational(self, x._rational_())
    627 

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

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:829, in sage.rings.fraction_field_element.FractionFieldElement._conversion()
    828 if self.__denominator.is_one():
--> 829     return R(self.__numerator)
    830 else:

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:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    160     print(type(C._element_constructor), C._element_constructor)
--> 161 raise
    162 

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/rational.pyx:538, in sage.rings.rational.Rational.__init__()
    537 if x is not None:
--> 538     self.__set_value(x, base)
    539 

File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value()
    625 elif hasattr(x, "_rational_"):
--> 626     set_from_Rational(self, x._rational_())
    627 

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:175, in sage.rings.polynomial.multi_polynomial.MPolynomial._rational_()
    174 from sage.rings.rational_field import QQ
--> 175 return self._scalar_conversion(QQ)
    176 

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:105, in sage.rings.polynomial.multi_polynomial.MPolynomial._scalar_conversion()
    104     return R(self.constant_coefficient())
--> 105 raise TypeError(f"unable to convert non-constant polynomial {self} to {R}")
    106 

TypeError: unable to convert non-constant polynomial x + 1 to Rational Field

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
Input In [41], in <cell line: 1>()
----> 1 second_patch(C.x)

File <string>:20, in second_patch(argument)

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2416, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
   2414     n = Rational(exp)
   2415 except TypeError:
-> 2416     raise TypeError("{} is neither an integer nor a rational".format(exp))
   2417 num = n.numerator()
   2418 den = n.denominator()

TypeError: x + 1 is neither an integer nor a rational
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(z[0])[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7ltype[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: type(x+1)

[?7h[?12l[?25h[?2004l[?7h<class 'sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint'>
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(x+1)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2411, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
   2410 try:
-> 2411     exp = Integer(exp)
   2412 except TypeError:

File /ext/sage/9.7/src/sage/rings/integer.pyx:658, in sage.rings.integer.Integer.__init__()
    657 if otmp is not None:
--> 658     set_from_Integer(self, otmp(the_integer_ring))
    659     return

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:829, in sage.rings.fraction_field_element.FractionFieldElement._conversion()
    828 if self.__denominator.is_one():
--> 829     return R(self.__numerator)
    830 else:

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)
File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2414, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
   2413 try:
-> 2414     n = Rational(exp)
   2415 except TypeError:

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

File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value()
    625 elif hasattr(x, "_rational_"):
--> 626     set_from_Rational(self, x._rational_())
    627 

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

File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:829, in sage.rings.fraction_field_element.FractionFieldElement._conversion()
    828 if self.__denominator.is_one():
--> 829     return R(self.__numerator)
    830 else:

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:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
    160     print(type(C._element_constructor), C._element_constructor)
--> 161 raise
    162 

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/rational.pyx:538, in sage.rings.rational.Rational.__init__()
    537 if x is not None:
--> 538     self.__set_value(x, base)
    539 

File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value()
    625 elif hasattr(x, "_rational_"):
--> 626     set_from_Rational(self, x._rational_())
    627 

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:175, in sage.rings.polynomial.multi_polynomial.MPolynomial._rational_()
    174 from sage.rings.rational_field import QQ
--> 175 return self._scalar_conversion(QQ)
    176 

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:105, in sage.rings.polynomial.multi_polynomial.MPolynomial._scalar_conversion()
    104     return R(self.constant_coefficient())
--> 105 raise TypeError(f"unable to convert non-constant polynomial {self} to {R}")
    106 

TypeError: unable to convert non-constant polynomial x + 1 to Rational Field

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
Input In [43], in <cell line: 1>()
----> 1 second_patch(C.x)

File <string>:20, in second_patch(argument)

File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2416, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
   2414     n = Rational(exp)
   2415 except TypeError:
-> 2416     raise TypeError("{} is neither an integer nor a rational".format(exp))
   2417 num = n.numerator()
   2418 den = n.denominator()

TypeError: x + 1 is neither an integer nor a rational
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpatch(C)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: patch(C)

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = 2*x^3 + x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpatch(C)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: patch(patch(C))

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpatch(patch(C))[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l0 dx
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
f2 ((-x^6 - 1)/(x^2*y - y)) dx
((x^4 + x^2 + 1)/(x^6*y)) dx
[0]
[0]
t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
((x^10 - x^6 + 1)/(x^2*y - y)) dx
(x^7 + x, 0)
((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
((-x^6 - 1)/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lpatch(patch(C))[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x)

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lload('init.sage'[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l0 dx
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
f2 ((-x^6 - 1)/(x^2*y - y)) dx
((x^4 + x^2 + 1)/(x^6*y)) dx
[0]
[0]
t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
((x^10 - x^6 + 1)/(x^2*y - y)) dx
(x^7 + x, 0)
((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
((-x^6 - 1)/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x)

[?7h[?12l[?25h[?2004l[?7h1/x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lesecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lcsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7losecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lnsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7ldsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7l_second_patch(C.x)[?7h[?12l[?25h[?25l[?7lpsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lasecond_patch(C.x)[?7h[?12l[?25h[?25l[?7ltsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lcsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lhsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7l(second_patch(C.x)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: second_patch(second_patch(C.x))

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

[?7h[?12l[?25h[?2004l0 dx
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
f2 ((-x^6 - 1)/(x^2*y - y)) dx
((x^4 + x^2 + 1)/(x^6*y)) dx
[0]
[0]
t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
((x^10 - x^6 + 1)/(x^2*y - y)) dx
(x^7 + x, 0)
((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
((-x^6 - 1)/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsecond_patch(second_patch(C.x))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7ldx)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: second_patch(second_patch(C.dx))

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
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()

AttributeError: 'superelliptic_function' object has no attribute 'numerator'

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
Input In [53], in <cell line: 1>()
----> 1 second_patch(second_patch(C.dx))

File <string>:26, in second_patch(argument)

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: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 2/x^2/1 to an element of Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l0 dx
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
f2 ((-x^6 - 1)/(x^2*y - y)) dx
((x^4 + x^2 + 1)/(x^6*y)) dx
[0]
[0]
t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
((x^10 - x^6 + 1)/(x^2*y - y)) dx
(x^7 + x, 0)
((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
((-x^6 - 1)/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsecond_patch(second_patch(C.dx))[?7h[?12l[?25h[?25l[?7lsage: second_patch(second_patch(C.dx))

[?7h[?12l[?25h[?2004l[?7h1 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(second_patch(C.dx))[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.dx)

[?7h[?12l[?25h[?2004l[?7h((-1)/x^2) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l = superelliptic(x^4 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x^4 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^4 - x^3 + x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^4 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l.x[?7h[?12l[?25h[?25l[?7lheight[?7h[?12l[?25h[?25l[?7lolomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[(1/y) dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l = supeelliptc(x^4 - x^3 + x, 2[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l1 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l1 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^11 - x^3 + x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^11 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l.holomophic_dfferentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[(1/y) dx, (x/y) dx, (x^2/y) dx, (x^3/y) dx, (x^4/y) dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ldrafty/draft5.sage')[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l(afty/draft5.sage')[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7lr.sage')[?7h[?12l[?25h[?25l[?7le.sage')[?7h[?12l[?25h[?25l[?7lg.sage')[?7h[?12l[?25h[?25l[?7lu.sage')[?7h[?12l[?25h[?25l[?7ll.sage')[?7h[?12l[?25h[?25l[?7la.sage')[?7h[?12l[?25h[?25l[?7lr.sage')[?7h[?12l[?25h[?25l[?7l .sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l_.sage')[?7h[?12l[?25h[?25l[?7lo.sage')[?7h[?12l[?25h[?25l[?7ln.sage')[?7h[?12l[?25h[?25l[?7l_.sage')[?7h[?12l[?25h[?25l[?7lU.sage')[?7h[?12l[?25h[?25l[?7l0.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: load('drafty/regular_on_U0.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: regula

 regular_form

 regulator   





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

 regular_form



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





[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: regular_form((C.y)^(-1)*C.dx)

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







 [?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7lsage: ((C.y)^(-1)*C.dx).form

[?7h[?12l[?25h[?2004l[?7h1/y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 



 [?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbn((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7lo((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7le((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7ln((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7lo((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7lm((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7li((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7ln((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7la((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7lt((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7lo((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7lr((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7l(((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: denominator(((C.y)^(-1)*C.dx).form) == y

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldenominator(((C.y)^(-1)*C.dx).form) == y[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/regular_on_U0.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7ldenominator(((C.y)^(-1)*C.dx).form) == y[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lsage: regular_form((C.y)^(-1)*C.dx)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [66], in <cell line: 1>()
----> 1 regular_form((C.y)**(-Integer(1))*C.dx)

File <string>:8, in regular_form(omega)

ValueError: too many values to unpack (expected 2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/regular_on_U0.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lsage: regular_form((C.y)^(-1)*C.dx)

[?7h[?12l[?25h[?2004l1
[?7h((x^9 + x^7 - x^5 + x^3 - x)/y, (x^10 + x^8 - x^6 + x^4 + x^2 + 1)/y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/regular_on_U0.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lsage: regular_form((C.y)^(-1)*C.dx)

[?7h[?12l[?25h[?2004l1
[?7h(x^9 + x^7 - x^5 + x^3 - x, x^10 + x^8 - x^6 + x^4 + x^2 + 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l = supeelliptc(x^11 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x^11 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx^3 + x, 2)[?7h[?12l[?25h[?25l[?7lx^3 + x, 2)[?7h[?12l[?25h[?25l[?7lx^3 + x, 2)[?7h[?12l[?25h[?25l[?7lx^3 + x, 2)[?7h[?12l[?25h[?25l[?7lx^3 + x, 2)[?7h[?12l[?25h[?25l[?7lx^3 + x, 2)[?7h[?12l[?25h[?25l[?7l^3 + x, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l x, 2)[?7h[?12l[?25h[?25l[?7l- x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 - x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7lsage: regular_form((C.y)^(-1)*C.dx)

[?7h[?12l[?25h[?2004l1
[?7h(0, -1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/regular_on_U0.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lsage: regular_form((C.y)^(-1)*C.dx)

[?7h[?12l[?25h[?2004l1 0 2
[?7h(0, -1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/regular_on_U0.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lsage: regular_form((C.y)^(-1)*C.dx)

[?7h[?12l[?25h[?2004l1 0 2
[?7h(0, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/regular_on_U0.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lsage: regular_form((C.y)^(-1)*C.dx)

[?7h[?12l[?25h[?2004l[?7h(0, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/regular_on_U0.sage')

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lsage: regular_form((C.y)^(-1)*C.dx)

[?7h[?12l[?25h[?2004l[?7h(0, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in range(3):[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.subs({x:x+1, y:y+1})[?7h[?12l[?25h[?25l[?7l = Fxy(C..function)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx^4 +x^2 + 1[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: g = x^3 + 2

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = x^3 + 2[?7h[?12l[?25h[?25l[?7l.subs({x:x+1, y:y+1})[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.lift()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [82], in <cell line: 1>()
----> 1 g.lift()

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 'lift'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.lift()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.lift()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(x+1)[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7ltype[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: type(g)

[?7h[?12l[?25h[?2004l[?7h<class 'sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint'>
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(g)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltyp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpatch(patch(C))[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrent(x)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: parent(g)

[?7h[?12l[?25h[?2004l[?7hUnivariate Polynomial Ring in x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.lift()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.lift()

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [85], in <cell line: 1>()
----> 1 g.lift()

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 'lift'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.lift()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lZ[?7h[?12l[?25h[?25l[?7lZ[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.change_ring(ZZ)

[?7h[?12l[?25h[?2004l[?7hx^3 + 2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.change_ring(ZZ)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: g.change_ring(ZZ) + 3

[?7h[?12l[?25h[?2004l[?7hx^3 + 5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.change_ring(ZZ) + 3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l) + 3[?7h[?12l[?25h[?25l[?7l) + 3[?7h[?12l[?25h[?25l[?7lI) + 3[?7h[?12l[?25h[?25l[?7ln) + 3[?7h[?12l[?25h[?25l[?7lt) + 3[?7h[?12l[?25h[?25l[?7le) + 3[?7h[?12l[?25h[?25l[?7lg) + 3[?7h[?12l[?25h[?25l[?7le) + 3[?7h[?12l[?25h[?25l[?7lr) + 3[?7h[?12l[?25h[?25l[?7ls) + 3[?7h[?12l[?25h[?25l[?7l(() + 3[?7h[?12l[?25h[?25l[?7l9) + 3[?7h[?12l[?25h[?25l[?7l(()) + 3[?7h[?12l[?25h[?25l[?7lsage: g.change_ring(Integers(9)) + 3

[?7h[?12l[?25h[?2004l[?7hx^3 + 5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.change_ring(Integers(9)) + 3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7lsage: g.change_ring(Integers(9)) + 9

[?7h[?12l[?25h[?2004l[?7hx^3 + 2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.change_ring(Integers(9)) + 9[?7h[?12l[?25h[?25l[?7l = x^3 + 2[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: g = x + 2*y

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = x + 2*y[?7h[?12l[?25h[?25l[?7l.change_ring(Integers(9)) + 9[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lZZ) + 3[?7h[?12l[?25h[?25l[?7lZ[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.change_ring(ZZ)

[?7h[?12l[?25h[?2004l[?7hx + 2*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.change_ring(ZZ)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lI)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lg)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l9))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l) + 9[?7h[?12l[?25h[?25l[?7l() + 9[?7h[?12l[?25h[?25l[?7lsage: g.change_ring(Integers(9)) + 9

[?7h[?12l[?25h[?2004l[?7hx + 2*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.change_ring(Integers(9)) + 9[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.change_ring(Integers(9))

[?7h[?12l[?25h[?2004l[?7hx + 2*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.change_ring(Integers(9))[?7h[?12l[?25h[?25l[?7l = x + 2*y[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx + 2*y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x + 2*y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*x+1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g = (x + 2*y)/(-8*x+1)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = (x + 2*y)/(-8*x+1)[?7h[?12l[?25h[?25l[?7l.change_ring(Integers(9))[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lge_ring(Integers(9))[?7h[?12l[?25h[?25l[?7lsage: g.change_ring(Integers(9))

[?7h[?12l[?25h[?2004lsage/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'
  """
---------------------------------------------------------------------------
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/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:

TypeError                                 Traceback (most recent call last)
Input In [95], in <cell line: 1>()
----> 1 g.change_ring(Integers(Integer(9)))

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:3377, in sage.rings.polynomial.polynomial_element.Polynomial.change_ring()
   3375         return self.map_coefficients(R)
   3376     else:
-> 3377         return self._parent.change_ring(R)(self.list(copy=False))
   3378 
   3379 cpdef dict _mpoly_dict_recursive(self, tuple variables=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: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: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 /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zmod_flint.pyx:106, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint.__init__()
    104 k = parent._base
    105 if check:
--> 106     lst = [k(i) for i in x]
    107 else:
    108     lst = x

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: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: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/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):

TypeError: unable to convert x/(x + 1) to a rational
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.change_ring(Integers(9))[?7h[?12l[?25h[?25l[?7lsage: g.change_ring(Integers(9))

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
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/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:

TypeError                                 Traceback (most recent call last)
Input In [96], in <cell line: 1>()
----> 1 g.change_ring(Integers(Integer(9)))

File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:3377, in sage.rings.polynomial.polynomial_element.Polynomial.change_ring()
   3375         return self.map_coefficients(R)
   3376     else:
-> 3377         return self._parent.change_ring(R)(self.list(copy=False))
   3378 
   3379 cpdef dict _mpoly_dict_recursive(self, tuple variables=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: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: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 /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zmod_flint.pyx:106, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint.__init__()
    104 k = parent._base
    105 if check:
--> 106     lst = [k(i) for i in x]
    107 else:
    108     lst = x

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: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: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/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):

TypeError: unable to convert x/(x + 1) to a rational
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7linit.sag')[?7h[?12l[?25h[?25l[?7l(nit.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l0 dx
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
f2 ((-x^6 - 1)/(x^2*y - y)) dx
((x^4 + x^2 + 1)/(x^6*y)) dx
[0]
[0]
t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
((x^10 - x^6 + 1)/(x^2*y - y)) dx
(x^7 + x, 0)
((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
((-x^6 - 1)/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ldrafty/rgular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l(afty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7ld.sage')[?7h[?12l[?25h[?25l[?7lr.sage')[?7h[?12l[?25h[?25l[?7la.sage')[?7h[?12l[?25h[?25l[?7lf.sage')[?7h[?12l[?25h[?25l[?7lt.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft.sage')

[?7h[?12l[?25h[?2004l(y, -x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('drafty/draft.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft.sage')

[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
(y, -x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.holomophic_dfferentials_basis()[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis()

[?7h[?12l[?25h[?2004l[?7h[(1/y) dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsC.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7leC.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7lcC.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7loC.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7lnC.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7ldC.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7l_C.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7lpC.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7laC.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7ltC.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7lcC.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7lhC.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7l(C.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.holomorphic_differentials_basis()[0])

[?7h[?12l[?25h[?2004l[?7h((-1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(g)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ltch(patch(C))[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: patch(C)

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l?identity_matrix[?7h[?12l[?25h[?25l[?7lsuperelliptic[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuperelliptic[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lsage: ?second_patch

[?7h[?12l[?25h[?2004lSignature:      second_patch(argument)
Init docstring: Initialize self.  See help(type(self)) for accurate signature.
File:           Dynamically generated function. No source code available.
Type:           function
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ld_patch[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: help(second_patch)

[?7h[?12l[?25h[?2004l[?1049h[?1h=
Help on function second_patch in module __main__:

second_patch(argument)
(END)

(END)
 ::qq
[?1l>[?1049l
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l?second_patch[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lsage: ?regula

 regular_form

 regulator   





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

 regular_form



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





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

[?7h[?12l[?25h[?2004lSignature:      regular_form(omega)
Docstring:     
Given a form omega regular on U0, present it as P(x, y) dx + Q(x, y)
dy for some polynomial P, Q.
   The output is A(x)*y, B(x), where omega = A(x) y dx + B(x) dy
Init docstring: Initialize self.  See help(type(self)) for accurate signature.
File:           Dynamically generated function. No source code available.
Type:           function
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7l(nit.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l0 dx
3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
f2 ((-x^6 - 1)/(x^2*y - y)) dx
((x^4 + x^2 + 1)/(x^6*y)) dx
[0]
[0]
t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
((x^10 - x^6 + 1)/(x^2*y - y)) dx
(x^7 + x, 0)
((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
((-x^6 - 1)/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l?regular_form[?7h[?12l[?25h[?25l[?7lhelp(second_patch)[?7h[?12l[?25h[?25l[?7l?second_patch[?7h[?12l[?25h[?25l[?7lpath(C)[?7h[?12l[?25h[?25l[?7l?seond_patch[?7h[?12l[?25h[?25l[?7lhelp(second_patch)[?7h[?12l[?25h[?25l[?7l?regular_form[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

I-search:[?7h[?12l[?25h[?25l[?7lload('init.sage')

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

;[?7h[?12l[?25h[?25l[?7lload('init.sage')

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

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

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

[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
False
(y, -x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
((2*x^3 + 1)/y) dx (1/y) dx
(y, -x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
((2*x^3 + 1)/y) dx (1/y) dx
3*x^3 + 1 1
(y, -x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 1 over Finite Field of size 5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
((2*x^3 + 1)/y) dx (1/y) dx
1 1
(y, -x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
((-2*x^3 + 1)/y) dx (1/y) dx
1 1
(y, -x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
(1/y) dx (1/y) dx
1 1
(y, x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
False
(y, x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7ldx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: C.dx == C.dx

[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx == C.dx[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
(1/y) dx (1/y) dx
(y, x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx == C.dx[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C == C

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

[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
(1/y) dx (1/y) dx
(y, x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7licznik[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lega[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: omega = C.de

 C.de_rham_basis                     C.degrees_de_rham1                 

 C.degrees_de_rham0                  C.degrees_holomorphic_differentials





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

 C.de_rham_basis                    



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





[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega = C.de_rham_basis()

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







 [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7licznik[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt

 lift            

 lift_form_to_drw

 lift_to_sl2z    

 

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

 lift            





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

 lift            

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







[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: lift_form_to_drw(omega)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [24], in <cell line: 1>()
----> 1 lift_form_to_drw(omega)

File <string>:29, in lift_form_to_drw(omega)

File <string>:5, in regular_form(omega)

AttributeError: 'list' object has no attribute 'curve'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift_form_to_drw(omega)[?7h[?12l[?25h[?25l[?7lomega = C.derham_basis()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: omega = C.de_rham_basis()[0]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7llift_form_todrw(omega)[?7h[?12l[?25h[?25l[?7lsage: lift_form_to_drw(omega)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [26], in <cell line: 1>()
----> 1 lift_form_to_drw(omega)

File <string>:29, in lift_form_to_drw(omega)

File <string>:10, in regular_form(omega)

AttributeError: 'superelliptic_cech' object has no attribute 'form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift_form_to_drw(omega)[?7h[?12l[?25h[?25l[?7lomega = C.derham_basis()[0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: omega = C.holomorphic_differentials_basis()[0]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega = C.holomorphic_differentials_basis()[0][?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega = C.holomorphic_differentials_basis()[0][?7h[?12l[?25h[?25l[?7llift_form_t_drw(omega)[?7h[?12l[?25h[?25l[?7lsage: lift_form_to_drw(omega)

[?7h[?12l[?25h[?2004l(1/y) dx (1/y) dx
y dx + x dy
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR.<u,v> = GF(3)[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 + 1)))[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: R = Integers(25)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR = Integers(25)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: R(2^5)

[?7h[?12l[?25h[?2004l[?7h7
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR(2^5)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l%[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: R(7^5)

[?7h[?12l[?25h[?2004l[?7h7
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR(7^5)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: R(2^25)

[?7h[?12l[?25h[?2004l[?7h7
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in range(3):[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lin range(3):[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l):[?7h[?12l[?25h[?25l[?7l2):[?7h[?12l[?25h[?25l[?7l5):[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: for a in range(25):

....: [?7h[?12l[?25h[?25l[?7lif m%p != 0:[?7h[?12l[?25h[?25l[?7lif[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la not in lista2:[?7h[?12l[?25h[?25l[?7l%[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7land[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l....:     if a%5 == 2 and a^5 == 1:

....: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lan[?7h[?12l[?25h[?25l[?7land[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l%[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l

....: [?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l....:         print(a)

....: [?7h[?12l[?25h[?25l[?7lsage: for a in range(25):

....:     if a%5 == 2 and a^5%25 == 1:

....:         print(a)

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for a in range(25):

....:     if a%5 == 2 and a^5%25 == 1:

....:         print(a)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a^5%25 = 1:[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()%25 = 1:[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

....: 

....:         print(a)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l        print(a)

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

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

....: [?7h[?12l[?25h[?25l[?7lsage: for a in range(25):

....:     if a%5 == 2 and (a^5)%25 == 1:

....:         print(a)

....: 

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for a in range(25):

....:     if a%5 == 2 and (a^5)%25 == 1:

....:         print(a)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7la:[?7h[?12l[?25h[?25l[?7l

()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:         print(a)

....: [?7h[?12l[?25h[?25l[?7lsage: for a in range(25):

....:     if a%5 == 2 and (a^5)%25 == a:

....:         print(a)

....: 

[?7h[?12l[?25h[?2004l7
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR(2^25)[?7h[?12l[?25h[?25l[?7l(2^25)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laR(2)[?7h[?12l[?25h[?25l[?7l R(2)[?7h[?12l[?25h[?25l[?7l=R(2)[?7h[?12l[?25h[?25l[?7l R(2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: a = R(2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = R(2)[?7h[?12l[?25h[?25l[?7lsage: a

[?7h[?12l[?25h[?2004l[?7h2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a.lift()

[?7h[?12l[?25h[?2004l[?7h2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift_form_to_drw(omega)[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
(1/y) dx (1/y) dx
(y, x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(g)[?7h[?12l[?25h[?25l[?7lextE.local_data(2))[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: teichmuller(C.x + 2*C.y)

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

File <string>:22, in teichmuller(fct)

UnboundLocalError: local variable 'fct1' referenced before assignment
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
(1/y) dx (1/y) dx
(y, x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lsage: teichmuller(C.x + 2*C.y)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [42], in <cell line: 1>()
----> 1 teichmuller(C.x + Integer(2)*C.y)

File <string>:22, in teichmuller(fct)

TypeError: unsupported operand type(s) for -: 'PolynomialRing_field_with_category.element_class' and 'superelliptic_function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
(1/y) dx (1/y) dx
(y, x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lsage: teichmuller(C.x + 2*C.y)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [44], in <cell line: 1>()
----> 1 teichmuller(C.x + Integer(2)*C.y)

File <string>:24, in teichmuller(fct)

File <string>:24, in teichmuller(fct)

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.fraction_field_FpT.FpTElement' object has no attribute 'lift'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
(1/y) dx (1/y) dx
(y, x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lsage: teichmuller(C.x + 2*C.y)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [46], in <cell line: 1>()
----> 1 teichmuller(C.x + Integer(2)*C.y)

File <string>:18, in teichmuller(fct)

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

[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
(1/y) dx (1/y) dx
(y, x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lsage: teichmuller(C.x + 2*C.y)

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

File <string>:23, in teichmuller(fct)

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

[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
(1/y) dx (1/y) dx
(y, x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lsage: teichmuller(C.x + 2*C.y)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [50], in <cell line: 1>()
----> 1 teichmuller(C.x + Integer(2)*C.y)

File <string>:26, in teichmuller(fct)

File <string>:26, in teichmuller(fct)

File /ext/sage/9.7/src/sage/rings/integer.pyx:1769, in sage.rings.integer.Integer.__add__()
   1767         return y
   1768 
-> 1769     return coercion_model.bin_op(left, right, operator.add)
   1770 
   1771 cpdef _add_(self, right):

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 +: 'Integer Ring' and '<class '__main__.superelliptic_witt'>'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
(1/y) dx (1/y) dx
(y, x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lsage: teichmuller(C.x + 2*C.y)

[?7h[?12l[?25h[?2004l[?7h<repr(<__main__.superelliptic_witt at 0x7f3375d368c0>) failed: NameError: name 'f0' is not defined>
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
(1/y) dx (1/y) dx
(y, x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lsage: teichmuller(C.x + 2*C.y)

[?7h[?12l[?25h[?2004l[?7hx + 32*y + V(2*x^2*y + 4*x^4 + 4*x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC == C[?7h[?12l[?25h[?25l[?7lsage: C

[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 1 over Finite Field of size 5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
(1/y) dx (1/y) dx
(y, x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lsage: teichmuller(C.x + 2*C.y)

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [57], in <cell line: 1>()
----> 1 teichmuller(C.x + Integer(2)*C.y)

File <string>:43, in teichmuller(fct)

File <string>:43, in teichmuller(fct)

File <string>:38, in teichmuller(fct)

File <string>:6, in __init__(self, C, f0, f1)

File <string>:23, in reduce_rational_fct(fct, 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.integer.Integer' object has no attribute 'monomials'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
(1/y) dx (1/y) dx
(y, x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lsage: teichmuller(C.x + 2*C.y)

[?7h[?12l[?25h[?2004l[?7hx + 7*y + V(2*x^2*y + 4*x^4 + 4*x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
(1/y) dx (1/y) dx
(y, x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l == C[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR(2^25)[?7h[?12l[?25h[?25l[?7lx.<x> = PolynomialRing(GF(3))[?7h[?12l[?25h[?25l[?7l.<x> = PolynomialRing(GF(3))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l4))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: Rx.<x> = PolynomialRing(GF(4))

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l == C[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lrelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 3)[?7h[?12l[?25h[?25l[?7l, 3)[?7h[?12l[?25h[?25l[?7l, 3)[?7h[?12l[?25h[?25l[?7l+, 3)[?7h[?12l[?25h[?25l[?7l , 3)[?7h[?12l[?25h[?25l[?7l1, 3)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 + 1, 3)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 + 1, 3)[?7h[?12l[?25h[?25l[?7l.dx == C.dx[?7h[?12l[?25h[?25l[?7lis_smooth()[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lsmooth()[?7h[?12l[?25h[?25l[?7lsage: C.is_smooth()

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.is_smooth()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lp_rank()[?7h[?12l[?25h[?25l[?7lsage: C.p_rank()

 C.p_rank    

 C.polynomial





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



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

  C.a_number                               C.basis_of_cohomology                    C.degrees_de_rham0                        

  C.base_ring                              C.cartier_matrix                         C.degrees_de_rham1                        

  C.basis_de_rham_degrees                  C.characteristic                         C.degrees_holomorphic_differentials      >

  C.basis_holomorphic_differentials_degree C.de_rham_basis                          C.dr_frobenius_matrix                     [?7h[?12l[?25h[?25l[?7lgenus()







[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.genus()

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7lis_smooth()[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 + 1, 3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + 1, 2)[?7h[?12l[?25h[?25l[?7l4 + 1, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^4 + 1, 2)

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



 [?7h[?12l[?25h[?25l[?7lC = superelliptic(x^4 + 1, 2)[?7h[?12l[?25h[?25l[?7l.gens()[?7h[?12l[?25h[?25l[?7lis_smooth()[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_smooth()[?7h[?12l[?25h[?25l[?7lsage: C.is_smooth()

[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.is_smooth()[?7h[?12l[?25h[?25l[?7l = superelliptic(x^4 + 1, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7lx, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^4 + x, 2)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^4 + x, 2)[?7h[?12l[?25h[?25l[?7l.is_smooth()[?7h[?12l[?25h[?25l[?7lsage: C.is_smooth()

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.is_smooth()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.genus()

[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[x^5 + x^4 + z0*z1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [(C.y)^(-1)])[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.cartier_matrix()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in range(25):[?7h[?12l[?25h[?25l[?7l =x^3 - x[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: f = AS.magical_element()[0]

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = AS.magical_element()[0][?7h[?12l[?25h[?25l[?7lsage: f

[?7h[?12l[?25h[?2004l[?7hx^5 + x^4 + z0*z1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f.valuation()

[?7h[?12l[?25h[?2004l[?7h-13
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [(C.y)^(-1)])[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.cartier_matrix()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: AS.exponent_of_different

 AS.exponent_of_different     

 AS.exponent_of_different_prim





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

 AS.exponent_of_different     



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

 AS.exponent_of_different     

 AS.exponent_of_different_prim[?7h[?12l[?25h[?25l[?7l





[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.exponent_of_different_prim()

[?7h[?12l[?25h[?2004l[?7h13
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 





 [?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lf.valuation()[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.valuation()[?7h[?12l[?25h[?25l[?7l = AS.magical_element()[0][?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf + z0^2[?7h[?12l[?25h[?25l[?7l1f + z0^2[?7h[?12l[?25h[?25l[?7l f + z0^2[?7h[?12l[?25h[?25l[?7l=f + z0^2[?7h[?12l[?25h[?25l[?7l f + z0^2[?7h[?12l[?25h[?25l[?7lsage: f1 = f + z0^2

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [6], in <cell line: 1>()
----> 1 f1 = f + z0**Integer(2)

NameError: name 'z0' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = f + z0^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = f + z0^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz0^2[?7h[?12l[?25h[?25l[?7lSz0^2[?7h[?12l[?25h[?25l[?7l.z0^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: f1 = f + AS.z[0]^2

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = f + AS.z[0]^2[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f1.valuation()

[?7h[?12l[?25h[?2004l[?7h-20
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[x^4 + z0*z1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lsage: AS.exponent_of_different_prim()

[?7h[?12l[?25h[?2004l[?7h13
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004l[x^5 + x^4 + z0*z1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]*[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfAS.z[0]*AS.z[1][?7h[?12l[?25h[?25l[?7l1AS.z[0]*AS.z[1][?7h[?12l[?25h[?25l[?7l AS.z[0]*AS.z[1][?7h[?12l[?25h[?25l[?7l=AS.z[0]*AS.z[1][?7h[?12l[?25h[?25l[?7l AS.z[0]*AS.z[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]+[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[1]+x^4[?7h[?12l[?25h[?25l[?7lAS.z[1]+x^4[?7h[?12l[?25h[?25l[?7lSAS.z[1]+x^4[?7h[?12l[?25h[?25l[?7l.AS.z[1]+x^4[?7h[?12l[?25h[?25l[?7lzAS.z[1]+x^4[?7h[?12l[?25h[?25l[?7l[AS.z[1]+x^4[?7h[?12l[?25h[?25l[?7l0AS.z[1]+x^4[?7h[?12l[?25h[?25l[?7l[]AS.z[1]+x^4[?7h[?12l[?25h[?25l[?7l[] AS.z[1]+x^4[?7h[?12l[?25h[?25l[?7l+AS.z[1]+x^4[?7h[?12l[?25h[?25l[?7l AS.z[1]+x^4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])+x^4[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: f1 = AS.z[0]*(AS.z[0] + AS.z[1])+x^4

[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Input In [12], in <cell line: 1>()
----> 1 f1 = AS.z[Integer(0)]*(AS.z[Integer(0)] + AS.z[Integer(1)])+x**Integer(4)

File <string>:23, 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.polynomial_gf2x.Polynomial_GF2X' object has no attribute 'function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = AS.z[0]*(AS.z[0] + AS.z[1])+x^4[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: f1

[?7h[?12l[?25h[?2004l[?7hx^5 + x^4 + z0^2 + z0*z1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1[?7h[?12l[?25h[?25l[?7l = AS.z[0]*(AS.z[0] + AS.z[1])+x^4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAx^4[?7h[?12l[?25h[?25l[?7lSx^4[?7h[?12l[?25h[?25l[?7l.x^4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: f1 = AS.z[0]*(AS.z[0] + AS.z[1])+AS.x^4

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = AS.z[0]*(AS.z[0] + AS.z[1])+AS.x^4[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lluation()[?7h[?12l[?25h[?25l[?7lsage: f1.valuation()

[?7h[?12l[?25h[?2004l[?7h-13
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/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.                       │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx.<x> = PolynomialRing(GF(4))[?7h[?12l[?25h[?25l[?7l.<u,v> = GF(3)[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 + 1)))[?7h[?12l[?25h[?25l[?7l<[?7h[?12l[?25h[?25l[?7l>[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx>[?7h[?12l[?25h[?25l[?7l = PolynomialRing(GF(3))[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l PolynomialRing(GF(3))[?7h[?12l[?25h[?25l[?7lsage: R.<x> = PolynomialRing(GF(3))

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1.valuation()[?7h[?12l[?25h[?25l[?7l = AS.magical_element()[0][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx^3 - x[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: f = x^3 + 2*x - 1

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(C.holomorphic_differentials_basis()[0])[?7h[?12l[?25h[?25l[?7ltr(E.local_data(2))[?7h[?12l[?25h[?25l[?7lstr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l"[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l"[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l"[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]"[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: str(f).replace("x", "[x]")

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

[?7h[?12l[?25h[?2004l[x^5 + x^4 + z0*z1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lsage: teichmuller(C.x + 2*C.y)

[?7h[?12l[?25h[?2004l[?7h[x] + V(0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

[?7h[?12l[?25h[?2004lTraceback (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 [6] 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>:26 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>:14
    return "[" + str(t) "] + " + str(f0).replace("x", "[x]").replace("y", "[y]") + " + V(" + str(f1) + ")"
                        ^
SyntaxError: invalid syntax

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

[?7h[?12l[?25h[?2004l[x^5 + x^4 + z0*z1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.lift()[?7h[?12l[?25h[?25l[?7l = R(2[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lw[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a = superelliptic_witt(C, C.x, 0, C.y)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = superelliptic_witt(C, C.x, 0, C.y)[?7h[?12l[?25h[?25l[?7lsage: a

[?7h[?12l[?25h[?2004l[?7h[x] + 0 + V(x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = superelliptic_witt(C, C.x, 0, C.y)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x, 0, C.y)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(), 0, C.y)[?7h[?12l[?25h[?25l[?7l()^, 0, C.y)[?7h[?12l[?25h[?25l[?7l2, 0, C.y)[?7h[?12l[?25h[?25l[?7l , 0, C.y)[?7h[?12l[?25h[?25l[?7l+, 0, C.y)[?7h[?12l[?25h[?25l[?7l , 0, C.y)[?7h[?12l[?25h[?25l[?7lC, 0, C.y)[?7h[?12l[?25h[?25l[?7l., 0, C.y)[?7h[?12l[?25h[?25l[?7ly, 0, C.y)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: a = superelliptic_witt(C, (C.x)^2 + C.y, 0, C.y)

[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = superelliptic_witt(C, (C.x)^2 + C.y, 0, C.y)[?7h[?12l[?25h[?25l[?7lsage: a

[?7h[?12l[?25h[?2004l[?7h[x^2 + x] + 0 + V(x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd ..
]0;~/Research/2021 De Rham/DeRhamComputation~/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/as_covers/as_cover_class.sage
	modified:   sage/as_covers/as_form_class.sage
	modified:   sage/drafty/draft.sage
	modified:   sage/drafty/draft2.sage
	modified:   sage/init.sage
	modified:   sage/superelliptic/superelliptic_class.sage
	modified:   sage/superelliptic/superelliptic_form_class.sage
	modified:   sage/superelliptic/superelliptic_function_class.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/as_cartier.sage
	sage/drafty/better_trace.sage
	sage/drafty/cartier_image_representation.sage
	sage/drafty/draft4.sage
	sage/drafty/draft5.sage
	sage/drafty/draft6.sage
	sage/drafty/draft7.sage
	sage/drafty/lift_to_de_rham.sage
	sage/drafty/pole_numbers.sage
	sage/drafty/regular_on_U0.sage
	sage/drafty/second_patch.sage
	sage/drafty/superelliptic_drw.sage
	sage/superelliptic/decomposition_into_g0_g8.sage
	sage/superelliptic/frobenius_kernel.sage
	sage/superelliptic/tests/
	superelliptic_arbitrary_field.ipynb

no changes added to commit (use "git add" and/or "git commit -a")
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ add sage/drafty/addgit add sage/drafty/superelliptic_drw.sage sage/drafty/superelliptic/decomposition_into_g0_g8.sage 
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ g