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

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---------------------------------------------------------------------------
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')
[?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[?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
[?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[0
[?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
[?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
[?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[?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[?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[?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[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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
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[?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[?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[?7l[0;94
[?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[0
[?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[?7
[?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[[0;38;5;2
[?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[?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[[0
[?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
[?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
[?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[?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([0;38;5;16;4
[?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
[?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^[0
[?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[?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[[0;38;5;210;48
[?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), f
[?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[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]^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