jgarnek/DeRhamComputation
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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[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.x)^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2)/(AS.x)^3
[?7h[?12l[?25h[?2004l[?7h(x^2*z1 - z0*z1^2)/x^3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2)/(AS.x)^3[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2)/(AS.x)^3)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2)/(AS.x)^3).valuation()
[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR.<x1,x2,y1,y2> = QQ[][?7h[?12l[?25h[?25l[?7lxy[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: Rxy
[?7h[?12l[?25h[?2004l[?7hMultivariate Polynomial Ring in x, y over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l = Rxy(x^2 + y^3)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lRxy(x^2 + y^3)[?7h[?12l[?25h[?25l[?7lsage: f = Rxy(x^2 + y^3)
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = AS.genus()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7lx6[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g = Rxy(x^5 + x*y)
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = Rxy(x^5 + x*y)[?7h[?12l[?25h[?25l[?7l.parent()[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.quo_rem(f)
[?7h[?12l[?25h[?2004l[?7h(0, x^5 + x*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx^2*z1 - z0*z1^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1 - z0*z1^2[?7h[?12l[?25h[?25l[?7l[] - z0*z1^2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0*z1^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]*z1^2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: x^2*z[1] - z[0]*z[1]^2
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [18], in <cell line: 1>()
----> 1 x**Integer(2)*z[Integer(1)] - z[Integer(0)]*z[Integer(1)]**Integer(2)
NameError: name 'z' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxy[?7h[?12l[?25h[?25l[?7l.<x1,x2,y1,y2> = QQ[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxy[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lzQ, Rxyz, x, y, z = AS.fct_field[?7h[?12l[?25h[?25l[?7l.<>[?7h[?12l[?25h[?25l[?7lx>[?7h[?12l[?25h[?25l[?7l,>[?7h[?12l[?25h[?25l[?7l >[?7h[?12l[?25h[?25l[?7ly>[?7h[?12l[?25h[?25l[?7l,>[?7h[?12l[?25h[?25l[?7l >[?7h[?12l[?25h[?25l[?7lz>[?7h[?12l[?25h[?25l[?7l0>[?7h[?12l[?25h[?25l[?7l,>[?7h[?12l[?25h[?25l[?7l >[?7h[?12l[?25h[?25l[?7lz>[?7h[?12l[?25h[?25l[?7l1>[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lP[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(),[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: Rxyz.<x, y, z0, z1> = PolynomialRing(GF(3), 4)
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx^2*z[1] - z[0]*z[1]^2[?7h[?12l[?25h[?25l[?7l, y = Rxyz.gens()[:2][?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l.g[?7h[?12l[?25h[?25l[?7lens[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: x, y, z0, z1 = Rxyz.gens()
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y, z0, z1 = Rxyz.gens()[?7h[?12l[?25h[?25l[?7lRxyz.<x, y, z0, z1> = PolynomialRing(GF(3), 4)[?7h[?12l[?25h[?25l[?7lx^2*z[1]- z[0]*[1]^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[^2[?7h[?12l[?25h[?25l[?7l^2[?7h[?12l[?25h[?25l[?7l^2[?7h[?12l[?25h[?25l[?7l1^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[*z1^2[?7h[?12l[?25h[?25l[?7l*z1^2[?7h[?12l[?25h[?25l[?7l*z1^2[?7h[?12l[?25h[?25l[?7l0*z1^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[ - z0*z1^2[?7h[?12l[?25h[?25l[?7l - z0*z1^2[?7h[?12l[?25h[?25l[?7l - z0*z1^2[?7h[?12l[?25h[?25l[?7l1 - z0*z1^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^2*z1 - z0*z1^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (x^2*z1 - z0*z1^2).quo_rem(x^2)
[?7h[?12l[?25h[?2004l[?7h(z1, -z0*z1^2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^2*z1 - z0*z1^2).quo_rem(x^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
(x^2*z1 - z0*z1^2 + z1^2)/x^3
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [22], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:75, in coordinates(self, threshold, basis)
File <string>:84, in coordinates(self, basis)
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
 895 if mor is not None:
 896 if no_extra_args:
--> 897 return mor._call_(x)
 898 else:
 899 return mor._call_with_args(x, args, kwds)
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
 786 return self._call_with_args(x, args, kwds)
 787
--> 788 cpdef Element _call_(self, x):
 789 """
 790 Call method with a single argument, not implemented in the base class.
File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
 1249 return num
 1250 if check and not den.is_unit():
 1251 # This should probably be a ValueError.
 1252 # However, too much existing code is expecting this to throw a
 1253 # TypeError, so we decided to keep it for the time being.
-> 1254 raise TypeError("fraction must have unit denominator")
 1255 return num * den.inverse_of_unit()
TypeError: fraction must have unit denominator
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^2*z1 - z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((x^2*z1 - z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lAx^2*z1 - z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7lSx^2*z1 - z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l.x^2*z1 - z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz1 - z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7lSz1 - z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l.z1 - z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1 - z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7lp1 - z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l1 - z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[] - z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7lSz0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l.z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7lSz1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l.z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz1^2)/x^3[?7h[?12l[?25h[?25l[?7lSz1^2)/x^3[?7h[?12l[?25h[?25l[?7l.z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2)/x^3[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lAx^3[?7h[?12l[?25h[?25l[?7lSx^3[?7h[?12l[?25h[?25l[?7l.x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2 + AS.z[1]^2)/AS.x^3).valuation()
[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2 + AS.z[1]^2)/AS.x^3).valuation()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
0
0 0
0
0 0
0
0 0
0
0 0
0
0 0
0
0 0
0
0 0
0
0 0
0
0 0
0
0 0
0
0 0
0
0 0
0
0 0
0
0 0
0
0 0
0
0 0
0
0 0
0
0 0
0
0 0
(x^2*z1 - z0*z1^2 + z1^2)/x^3
0 0
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [24], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:76, in coordinates(self, threshold, basis)
File <string>:84, in coordinates(self, basis)
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
 895 if mor is not None:
 896 if no_extra_args:
--> 897 return mor._call_(x)
 898 else:
 899 return mor._call_with_args(x, args, kwds)
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
 786 return self._call_with_args(x, args, kwds)
 787
--> 788 cpdef Element _call_(self, x):
 789 """
 790 Call method with a single argument, not implemented in the base class.
File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
 1249 return num
 1250 if check and not den.is_unit():
 1251 # This should probably be a ValueError.
 1252 # However, too much existing code is expecting this to throw a
 1253 # TypeError, so we decided to keep it for the time being.
-> 1254 raise TypeError("fraction must have unit denominator")
 1255 return num * den.inverse_of_unit()
TypeError: fraction must have unit denominator
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
0
! 0 0
0
! 0 0
0
! 0 0
0
! 0 0
0
! 0 0
0
! 0 0
0
! 0 0
0
! 0 0
0
! 0 0
0
! 0 0
0
! 0 0
0
! 0 0
0
! 0 0
0
! 0 0
0
! 0 0
0
! 0 0
0
! 0 0
0
! 0 0
0
! 0 0
(x^2*z1 - z0*z1^2 + z1^2)/x^3
! 0 0
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [25], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:76, in coordinates(self, threshold, basis)
File <string>:84, in coordinates(self, basis)
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
 895 if mor is not None:
 896 if no_extra_args:
--> 897 return mor._call_(x)
 898 else:
 899 return mor._call_with_args(x, args, kwds)
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
 786 return self._call_with_args(x, args, kwds)
 787
--> 788 cpdef Element _call_(self, x):
 789 """
 790 Call method with a single argument, not implemented in the base class.
File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
 1249 return num
 1250 if check and not den.is_unit():
 1251 # This should probably be a ValueError.
 1252 # However, too much existing code is expecting this to throw a
 1253 # TypeError, so we decided to keep it for the time being.
-> 1254 raise TypeError("fraction must have unit denominator")
 1255 return num * den.inverse_of_unit()
TypeError: fraction must have unit denominator
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
? 0
! 0 0
? 0
! 0 0
? 0
! 0 0
? 0
! 0 0
? 0
! 0 0
? 0
! 0 0
? 0
! 0 0
? 0
! 0 0
? 0
! 0 0
? 0
! 0 0
? 0
! 0 0
? 0
! 0 0
? 0
! 0 0
? 0
! 0 0
? 0
! 0 0
? 0
! 0 0
? 0
! 0 0
? 0
! 0 0
? 0
! 0 0
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
! 0 0
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [26], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:76, in coordinates(self, threshold, basis)
File <string>:84, in coordinates(self, basis)
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
 895 if mor is not None:
 896 if no_extra_args:
--> 897 return mor._call_(x)
 898 else:
 899 return mor._call_with_args(x, args, kwds)
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
 786 return self._call_with_args(x, args, kwds)
 787
--> 788 cpdef Element _call_(self, x):
 789 """
 790 Call method with a single argument, not implemented in the base class.
File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
 1249 return num
 1250 if check and not den.is_unit():
 1251 # This should probably be a ValueError.
 1252 # However, too much existing code is expecting this to throw a
 1253 # TypeError, so we decided to keep it for the time being.
-> 1254 raise TypeError("fraction must have unit denominator")
 1255 return num * den.inverse_of_unit()
TypeError: fraction must have unit denominator
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004lTraceback (most recent call last):
File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
exec(code_obj, self.user_global_ns, self.user_ns)
Input In [27] in <cell line: 1>
load('init.sage')
File sage/misc/persist.pyx:175 in sage.misc.persist.load
sage.repl.load.load(filename, globals())
File /ext/sage/9.7/src/sage/repl/load.py:272 in load
exec(preparse_file(f.read()) + "\n", globals)
File <string>:8 in <module>
File sage/misc/persist.pyx:175 in sage.misc.persist.load
sage.repl.load.load(filename, globals())
 File /ext/sage/9.7/src/sage/repl/load.py:272 in load
 exec(preparse_file(f.read()) + "\n", globals)
 File <string>:72
 print('!', self.f.function - rem/f_den, '!!:' quo)
 ^
SyntaxError: invalid syntax. Perhaps you forgot a comma?
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? 0
! 0 !!: 0
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
! 0 !!: 0
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [28], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:76, in coordinates(self, threshold, basis)
File <string>:84, in coordinates(self, basis)
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
 895 if mor is not None:
 896 if no_extra_args:
--> 897 return mor._call_(x)
 898 else:
 899 return mor._call_with_args(x, args, kwds)
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
 786 return self._call_with_args(x, args, kwds)
 787
--> 788 cpdef Element _call_(self, x):
 789 """
 790 Call method with a single argument, not implemented in the base class.
File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
 1249 return num
 1250 if check and not den.is_unit():
 1251 # This should probably be a ValueError.
 1252 # However, too much existing code is expecting this to throw a
 1253 # TypeError, so we decided to keep it for the time being.
-> 1254 raise TypeError("fraction must have unit denominator")
 1255 return num * den.inverse_of_unit()
TypeError: fraction must have unit denominator
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l((AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2 + AS.z[1]^2)/AS.x^3).valuation()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l((AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2 + AS.z[1]^2)/AS.x^3).valuation()[?7h[?12l[?25h[?25l[?7l()l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2 + AS.z[1]^2)/AS.x^3).valuation()
[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? 0
q r: 0 0
! 0 !!: 0
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
q r: 0 x^2*z1 - z0*z1^2 + z1^2
! 0 !!: 0
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [30], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:77, in coordinates(self, threshold, basis)
File <string>:84, in coordinates(self, basis)
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
 895 if mor is not None:
 896 if no_extra_args:
--> 897 return mor._call_(x)
 898 else:
 899 return mor._call_with_args(x, args, kwds)
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
 786 return self._call_with_args(x, args, kwds)
 787
--> 788 cpdef Element _call_(self, x):
 789 """
 790 Call method with a single argument, not implemented in the base class.
File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
 1249 return num
 1250 if check and not den.is_unit():
 1251 # This should probably be a ValueError.
 1252 # However, too much existing code is expecting this to throw a
 1253 # TypeError, so we decided to keep it for the time being.
-> 1254 raise TypeError("fraction must have unit denominator")
 1255 return num * den.inverse_of_unit()
TypeError: fraction must have unit denominator
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [31], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:77, in coordinates(self, threshold, basis)
File <string>:77, in coordinates(self, basis)
File <string>:137, in holomorphic_differentials_basis(self, threshold)
File <string>:399, in holomorphic_combinations(S)
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
KeyboardInterrupt:
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l((AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2 + AS.z[1]^2)/AS.x^3).valuation()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? 0
0 q r: 0 0
! 0 !!: 0
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
! 0 !!: 0
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [32], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:77, in coordinates(self, threshold, basis)
File <string>:84, in coordinates(self, basis)
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
 895 if mor is not None:
 896 if no_extra_args:
--> 897 return mor._call_(x)
 898 else:
 899 return mor._call_with_args(x, args, kwds)
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
 786 return self._call_with_args(x, args, kwds)
 787
--> 788 cpdef Element _call_(self, x):
 789 """
 790 Call method with a single argument, not implemented in the base class.
File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
 1249 return num
 1250 if check and not den.is_unit():
 1251 # This should probably be a ValueError.
 1252 # However, too much existing code is expecting this to throw a
 1253 # TypeError, so we decided to keep it for the time being.
-> 1254 raise TypeError("fraction must have unit denominator")
 1255 return num * den.inverse_of_unit()
TypeError: fraction must have unit denominator
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
! 0 !!: 0
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [33], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:78, in coordinates(self, threshold, basis)
File <string>:84, in coordinates(self, basis)
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
 895 if mor is not None:
 896 if no_extra_args:
--> 897 return mor._call_(x)
 898 else:
 899 return mor._call_with_args(x, args, kwds)
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
 786 return self._call_with_args(x, args, kwds)
 787
--> 788 cpdef Element _call_(self, x):
 789 """
 790 Call method with a single argument, not implemented in the base class.
File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
 1249 return num
 1250 if check and not den.is_unit():
 1251 # This should probably be a ValueError.
 1252 # However, too much existing code is expecting this to throw a
 1253 # TypeError, so we decided to keep it for the time being.
-> 1254 raise TypeError("fraction must have unit denominator")
 1255 return num * den.inverse_of_unit()
TypeError: fraction must have unit denominator
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 
[?7h[?12l[?25h[?2004l[?7h[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
! 0 !!: 0
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [34], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:79, in coordinates(self, threshold, basis)
File <string>:84, in coordinates(self, basis)
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
 895 if mor is not None:
 896 if no_extra_args:
--> 897 return mor._call_(x)
 898 else:
 899 return mor._call_with_args(x, args, kwds)
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
 786 return self._call_with_args(x, args, kwds)
 787
--> 788 cpdef Element _call_(self, x):
 789 """
 790 Call method with a single argument, not implemented in the base class.
File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
 1249 return num
 1250 if check and not den.is_unit():
 1251 # This should probably be a ValueError.
 1252 # However, too much existing code is expecting this to throw a
 1253 # TypeError, so we decided to keep it for the time being.
-> 1254 raise TypeError("fraction must have unit denominator")
 1255 return num * den.inverse_of_unit()
TypeError: fraction must have unit denominator
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 
[?7h[?12l[?25h[?2004l[?7h[?7h[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
! 0 !!: 0
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [35], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:79, in coordinates(self, threshold, basis)
File <string>:84, in coordinates(self, basis)
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
 895 if mor is not None:
 896 if no_extra_args:
--> 897 return mor._call_(x)
 898 else:
 899 return mor._call_with_args(x, args, kwds)
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
 786 return self._call_with_args(x, args, kwds)
 787
--> 788 cpdef Element _call_(self, x):
 789 """
 790 Call method with a single argument, not implemented in the base class.
File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
 1249 return num
 1250 if check and not den.is_unit():
 1251 # This should probably be a ValueError.
 1252 # However, too much existing code is expecting this to throw a
 1253 # TypeError, so we decided to keep it for the time being.
-> 1254 raise TypeError("fraction must have unit denominator")
 1255 return num * den.inverse_of_unit()
TypeError: fraction must have unit denominator
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
^C^C
KeyboardInterrupt
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
! 0 !!: 0
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [37], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:79, in coordinates(self, threshold, basis)
File <string>:84, in coordinates(self, basis)
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
 895 if mor is not None:
 896 if no_extra_args:
--> 897 return mor._call_(x)
 898 else:
 899 return mor._call_with_args(x, args, kwds)
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
 786 return self._call_with_args(x, args, kwds)
 787
--> 788 cpdef Element _call_(self, x):
 789 """
 790 Call method with a single argument, not implemented in the base class.
File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
 1249 return num
 1250 if check and not den.is_unit():
 1251 # This should probably be a ValueError.
 1252 # However, too much existing code is expecting this to throw a
 1253 # TypeError, so we decided to keep it for the time being.
-> 1254 raise TypeError("fraction must have unit denominator")
 1255 return num * den.inverse_of_unit()
TypeError: fraction must have unit denominator
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
! 0 !!: 0
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [38], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:79, in coordinates(self, threshold, basis)
File <string>:84, in coordinates(self, basis)
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
 895 if mor is not None:
 896 if no_extra_args:
--> 897 return mor._call_(x)
 898 else:
 899 return mor._call_with_args(x, args, kwds)
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
 786 return self._call_with_args(x, args, kwds)
 787
--> 788 cpdef Element _call_(self, x):
 789 """
 790 Call method with a single argument, not implemented in the base class.
File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
 1249 return num
 1250 if check and not den.is_unit():
 1251 # This should probably be a ValueError.
 1252 # However, too much existing code is expecting this to throw a
 1253 # TypeError, so we decided to keep it for the time being.
-> 1254 raise TypeError("fraction must have unit denominator")
 1255 return num * den.inverse_of_unit()
TypeError: fraction must have unit denominator
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [39], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:56, in coordinates(self, threshold, basis)
File /ext/sage/9.7/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds)
 583 return expression.sum(*args, **kwds)
 584 elif max(len(args),len(kwds)) <= 1:
--> 585 return sum(expression, *args, **kwds)
 586 else:
 587 from sage.symbolic.ring import SR
File <string>:56, in <genexpr>(.0)
File <string>:47, in __mul__(self, other)
File <string>:3, in __init__(self, C, g)
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
KeyboardInterrupt:
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()
[?7h[?12l[?25h[?2004l
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
! 0 !!: 0
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [1], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:79, in coordinates(self, threshold, basis)
File <string>:84, in coordinates(self, basis)
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
 895 if mor is not None:
 896 if no_extra_args:
--> 897 return mor._call_(x)
 898 else:
 899 return mor._call_with_args(x, args, kwds)
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
 786 return self._call_with_args(x, args, kwds)
 787
--> 788 cpdef Element _call_(self, x):
 789 """
 790 Call method with a single argument, not implemented in the base class.
File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
 1249 return num
 1250 if check and not den.is_unit():
 1251 # This should probably be a ValueError.
 1252 # However, too much existing code is expecting this to throw a
 1253 # TypeError, so we decided to keep it for the time being.
-> 1254 raise TypeError("fraction must have unit denominator")
 1255 return num * den.inverse_of_unit()
TypeError: fraction must have unit denominator
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
! 0 !!: 0
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [2], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:79, in coordinates(self, threshold, basis)
File <string>:84, in coordinates(self, basis)
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
 895 if mor is not None:
 896 if no_extra_args:
--> 897 return mor._call_(x)
 898 else:
 899 return mor._call_with_args(x, args, kwds)
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
 786 return self._call_with_args(x, args, kwds)
 787
--> 788 cpdef Element _call_(self, x):
 789 """
 790 Call method with a single argument, not implemented in the base class.
File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
 1249 return num
 1250 if check and not den.is_unit():
 1251 # This should probably be a ValueError.
 1252 # However, too much existing code is expecting this to throw a
 1253 # TypeError, so we decided to keep it for the time being.
-> 1254 raise TypeError("fraction must have unit denominator")
 1255 return num * den.inverse_of_unit()
TypeError: fraction must have unit denominator
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
! 0 !!: 0
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [3], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:79, in coordinates(self, threshold, basis)
File <string>:84, in coordinates(self, basis)
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
 895 if mor is not None:
 896 if no_extra_args:
--> 897 return mor._call_(x)
 898 else:
 899 return mor._call_with_args(x, args, kwds)
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
 786 return self._call_with_args(x, args, kwds)
 787
--> 788 cpdef Element _call_(self, x):
 789 """
 790 Call method with a single argument, not implemented in the base class.
File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
 1249 return num
 1250 if check and not den.is_unit():
 1251 # This should probably be a ValueError.
 1252 # However, too much existing code is expecting this to throw a
 1253 # TypeError, so we decided to keep it for the time being.
-> 1254 raise TypeError("fraction must have unit denominator")
 1255 return num * den.inverse_of_unit()
TypeError: fraction must have unit denominator
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004lWARNING: your terminal doesn't support cursor position requests (CPR).
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
nowe!!!! ( (1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( (z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( (z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( (z0*z1 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( (x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( (x*z0 + x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( (x^2) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( ((-x^4 - z1)/x^2) * dx, z1/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( ((-z1^2)/x^2) * dx, z1^2/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( ((x^2*z1 - z0*z1 - z1)/x^2) * dx, (z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( ((x^4*z0 + x^2*z0^2*z1 + x^4 - x^2*z0*z1 + x^2*z1^2 + x^2*z1 - z0*z1^2 - z1^2)/x^2) * dx, (z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( ((-x^2*z0*z1 - x^2*z1 - z0^2*z1 + z0*z1 - z1)/x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( ((-z0^2*z1^2 + z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( ((-x^4*z0^2 + x^4*z0 + x^4*z1 - x^4 + z1^2)/x^3) * dx, z1^2/x^2 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( ((x^2*z1^2 + z0*z1^2 + z1^2)/x^3) * dx, (z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( ((x^4*z0^2 - x^4*z0 - x^2*z0*z1^2 + x^4 - x^2*z1^2 + z0^2*z1^2 - z0*z1^2 + z1^2)/x^3) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
nowe!!!! ( ((-z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
! 0 !!: 0
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [1], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:79, in coordinates(self, threshold, basis)
File <string>:84, in coordinates(self, basis)
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
 895 if mor is not None:
 896 if no_extra_args:
--> 897 return mor._call_(x)
 898 else:
 899 return mor._call_with_args(x, args, kwds)
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
 786 return self._call_with_args(x, args, kwds)
 787
--> 788 cpdef Element _call_(self, x):
 789 """
 790 Call method with a single argument, not implemented in the base class.
File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
 1249 return num
 1250 if check and not den.is_unit():
 1251 # This should probably be a ValueError.
 1252 # However, too much existing code is expecting this to throw a
 1253 # TypeError, so we decided to keep it for the time being.
-> 1254 raise TypeError("fraction must have unit denominator")
 1255 return num * den.inverse_of_unit()
TypeError: fraction must have unit denominator
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
nowe!!!! ( (1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (1) * dx, 0 )
nowe!!!! ( (z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (z1) * dx, 0 )
nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
nowe!!!! ( (z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (z0 + 1) * dx, 0 )
nowe!!!! ( (z0*z1 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (z0*z1 + z1) * dx, 0 )
nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (z0^2 - z0 + 1) * dx, 0 )
nowe!!!! ( (x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x) * dx, 0 )
nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
nowe!!!! ( (x*z0 + x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x*z0 + x) * dx, 0 )
nowe!!!! ( (x^2) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2) * dx, 0 )
nowe!!!! ( ((-x^4 - z1)/x^2) * dx, z1/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (0) * dx, 0 )
nowe!!!! ( ((-z1^2)/x^2) * dx, z1^2/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (0) * dx, 0 )
nowe!!!! ( ((x^2*z1 - z0*z1 - z1)/x^2) * dx, (z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2) * dx, 0 )
nowe!!!! ( ((x^4*z0 + x^2*z0^2*z1 + x^4 - x^2*z0*z1 + x^2*z1^2 + x^2*z1 - z0*z1^2 - z1^2)/x^2) * dx, (z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2 - z0*z1 + z1) * dx, 0 )
nowe!!!! ( ((-x^2*z0*z1 - x^2*z1 - z0^2*z1 + z0*z1 - z1)/x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2) * dx, 0 )
nowe!!!! ( ((-z0^2*z1^2 + z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 )
nowe!!!! ( ((-x^4*z0^2 + x^4*z0 + x^4*z1 - x^4 + z1^2)/x^3) * dx, z1^2/x^2 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x*z0 - x) * dx, 0 )
nowe!!!! ( ((x^2*z1^2 + z0*z1^2 + z1^2)/x^3) * dx, (z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x*z0^2 - x*z1) * dx, 0 )
nowe!!!! ( ((x^4*z0^2 - x^4*z0 - x^2*z0*z1^2 + x^4 - x^2*z1^2 + z0^2*z1^2 - z0*z1^2 + z1^2)/x^3) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x*z0^2 - x*z0 - x*z1 + x) * dx, 0 )
nowe!!!! ( ((-z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
! 0 !!: 0
selfik ( ((-x^4 - z1^2 - z1)/x^2) * dx, 0 )
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [2], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:80, in coordinates(self, threshold, basis)
File <string>:84, in coordinates(self, basis)
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
 895 if mor is not None:
 896 if no_extra_args:
--> 897 return mor._call_(x)
 898 else:
 899 return mor._call_with_args(x, args, kwds)
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
 786 return self._call_with_args(x, args, kwds)
 787
--> 788 cpdef Element _call_(self, x):
 789 """
 790 Call method with a single argument, not implemented in the base class.
File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
 1249 return num
 1250 if check and not den.is_unit():
 1251 # This should probably be a ValueError.
 1252 # However, too much existing code is expecting this to throw a
 1253 # TypeError, so we decided to keep it for the time being.
-> 1254 raise TypeError("fraction must have unit denominator")
 1255 return num * den.inverse_of_unit()
TypeError: fraction must have unit denominator
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
nowe!!!! ( (1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (1) * dx, 0 )
nowe!!!! ( (z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (z1) * dx, 0 )
nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
nowe!!!! ( (z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (z0 + 1) * dx, 0 )
nowe!!!! ( (z0*z1 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (z0*z1 + z1) * dx, 0 )
nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (z0^2 - z0 + 1) * dx, 0 )
nowe!!!! ( (x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x) * dx, 0 )
nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
nowe!!!! ( (x*z0 + x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x*z0 + x) * dx, 0 )
nowe!!!! ( (x^2) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2) * dx, 0 )
nowe!!!! ( ((-x^4 - z1)/x^2) * dx, z1/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (0) * dx, 0 )
nowe!!!! ( ((-z1^2)/x^2) * dx, z1^2/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (0) * dx, 0 )
nowe!!!! ( ((x^2*z1 - z0*z1 - z1)/x^2) * dx, (z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2) * dx, 0 )
nowe!!!! ( ((x^4*z0 + x^2*z0^2*z1 + x^4 - x^2*z0*z1 + x^2*z1^2 + x^2*z1 - z0*z1^2 - z1^2)/x^2) * dx, (z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2 - z0*z1 + z1) * dx, 0 )
nowe!!!! ( ((-x^2*z0*z1 - x^2*z1 - z0^2*z1 + z0*z1 - z1)/x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2) * dx, 0 )
nowe!!!! ( ((-z0^2*z1^2 + z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 )
nowe!!!! ( ((-x^4*z0^2 + x^4*z0 + x^4*z1 - x^4 + z1^2)/x^3) * dx, z1^2/x^2 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x*z0 - x) * dx, 0 )
nowe!!!! ( ((x^2*z1^2 + z0*z1^2 + z1^2)/x^3) * dx, (z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x*z0^2 - x*z1) * dx, 0 )
nowe!!!! ( ((x^4*z0^2 - x^4*z0 - x^2*z0*z1^2 + x^4 - x^2*z1^2 + z0^2*z1^2 - z0*z1^2 + z1^2)/x^3) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x*z0^2 - x*z0 - x*z1 + x) * dx, 0 )
nowe!!!! ( ((-z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
! 0 !!: 0
selfik ( ((-x^4 - z1^2 - z1)/x^2) * dx, 0 )
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [3], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:80, in coordinates(self, threshold, basis)
File <string>:84, in coordinates(self, basis)
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
 895 if mor is not None:
 896 if no_extra_args:
--> 897 return mor._call_(x)
 898 else:
 899 return mor._call_with_args(x, args, kwds)
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
 786 return self._call_with_args(x, args, kwds)
 787
--> 788 cpdef Element _call_(self, x):
 789 """
 790 Call method with a single argument, not implemented in the base class.
File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
 1249 return num
 1250 if check and not den.is_unit():
 1251 # This should probably be a ValueError.
 1252 # However, too much existing code is expecting this to throw a
 1253 # TypeError, so we decided to keep it for the time being.
-> 1254 raise TypeError("fraction must have unit denominator")
 1255 return num * den.inverse_of_unit()
TypeError: fraction must have unit denominator
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
nowe!!!! ( (1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (1) * dx, 0 )
nowe!!!! ( (z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (z1) * dx, 0 )
nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
nowe!!!! ( (z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (z0 + 1) * dx, 0 )
nowe!!!! ( (z0*z1 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (z0*z1 + z1) * dx, 0 )
nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (z0^2 - z0 + 1) * dx, 0 )
nowe!!!! ( (x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x) * dx, 0 )
nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
nowe!!!! ( (x*z0 + x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x*z0 + x) * dx, 0 )
nowe!!!! ( (x^2) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2) * dx, 0 )
nowe!!!! ( ((-x^4 - z1)/x^2) * dx, z1/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (0) * dx, 0 )
nowe!!!! ( ((-z1^2)/x^2) * dx, z1^2/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (0) * dx, 0 )
nowe!!!! ( ((x^2*z1 - z0*z1 - z1)/x^2) * dx, (z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2) * dx, 0 )
nowe!!!! ( ((x^4*z0 + x^2*z0^2*z1 + x^4 - x^2*z0*z1 + x^2*z1^2 + x^2*z1 - z0*z1^2 - z1^2)/x^2) * dx, (z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2 - z0*z1 + z1) * dx, 0 )
nowe!!!! ( ((-x^2*z0*z1 - x^2*z1 - z0^2*z1 + z0*z1 - z1)/x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2) * dx, 0 )
nowe!!!! ( ((-z0^2*z1^2 + z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 )
nowe!!!! ( ((-x^4*z0^2 + x^4*z0 + x^4*z1 - x^4 + z1^2)/x^3) * dx, z1^2/x^2 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x*z0 - x) * dx, 0 )
nowe!!!! ( ((x^2*z1^2 + z0*z1^2 + z1^2)/x^3) * dx, (z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x*z0^2 - x*z1) * dx, 0 )
nowe!!!! ( ((x^4*z0^2 - x^4*z0 - x^2*z0*z1^2 + x^4 - x^2*z1^2 + z0^2*z1^2 - z0*z1^2 + z1^2)/x^3) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x*z0^2 - x*z0 - x*z1 + x) * dx, 0 )
nowe!!!! ( ((-z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
! 0 !!: 0
selfik ( ((-x^4 - z1^2 - z1)/x^2) * dx, 0 )
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [4], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:80, in coordinates(self, threshold, basis)
File <string>:84, in coordinates(self, basis)
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
 895 if mor is not None:
 896 if no_extra_args:
--> 897 return mor._call_(x)
 898 else:
 899 return mor._call_with_args(x, args, kwds)
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
 786 return self._call_with_args(x, args, kwds)
 787
--> 788 cpdef Element _call_(self, x):
 789 """
 790 Call method with a single argument, not implemented in the base class.
File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
 1249 return num
 1250 if check and not den.is_unit():
 1251 # This should probably be a ValueError.
 1252 # However, too much existing code is expecting this to throw a
 1253 # TypeError, so we decided to keep it for the time being.
-> 1254 raise TypeError("fraction must have unit denominator")
 1255 return num * den.inverse_of_unit()
TypeError: fraction must have unit denominator
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
nowe!!!! ( (1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (1) * dx, 0 )
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (z1) * dx, 0 )
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (z0 + 1) * dx, 0 )
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0*z1 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (z0*z1 + z1) * dx, 0 )
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (z0^2 - z0 + 1) * dx, 0 )
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x) * dx, 0 )
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x*z0 + x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x*z0 + x) * dx, 0 )
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^4 - z1)/x^2) * dx, z1/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (0) * dx, 0 )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z1^2)/x^2) * dx, z1^2/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (0) * dx, 0 )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^2*z1 - z0*z1 - z1)/x^2) * dx, (z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^4*z0 + x^2*z0^2*z1 + x^4 - x^2*z0*z1 + x^2*z1^2 + x^2*z1 - z0*z1^2 - z1^2)/x^2) * dx, (z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2 - z0*z1 + z1) * dx, 0 )
(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^2*z0*z1 - x^2*z1 - z0^2*z1 + z0*z1 - z1)/x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z0^2*z1^2 + z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 )
(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^4*z0^2 + x^4*z0 + x^4*z1 - x^4 + z1^2)/x^3) * dx, z1^2/x^2 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x*z0 - x) * dx, 0 )
(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^2*z1^2 + z0*z1^2 + z1^2)/x^3) * dx, (z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x*z0^2 - x*z1) * dx, 0 )
(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^4*z0^2 - x^4*z0 - x^2*z0*z1^2 + x^4 - x^2*z1^2 + z0^2*z1^2 - z0*z1^2 + z1^2)/x^3) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
! 0 !!: 0
selfik ( (x*z0^2 - x*z0 - x*z1 + x) * dx, 0 )
(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
! 0 !!: 0
selfik ( ((-x^4 - z1^2 - z1)/x^2) * dx, 0 )
((-x^4 - z1^2 - z1)/x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [5], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:80, in coordinates(self, threshold, basis)
File <string>:85, in coordinates(self, basis)
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
 895 if mor is not None:
 896 if no_extra_args:
--> 897 return mor._call_(x)
 898 else:
 899 return mor._call_with_args(x, args, kwds)
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
 786 return self._call_with_args(x, args, kwds)
 787
--> 788 cpdef Element _call_(self, x):
 789 """
 790 Call method with a single argument, not implemented in the base class.
File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
 1249 return num
 1250 if check and not den.is_unit():
 1251 # This should probably be a ValueError.
 1252 # However, too much existing code is expecting this to throw a
 1253 # TypeError, so we decided to keep it for the time being.
-> 1254 raise TypeError("fraction must have unit denominator")
 1255 return num * den.inverse_of_unit()
TypeError: fraction must have unit denominator
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
nowe!!!! ( (1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (1) * dx, 0 )
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [6], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:77, in coordinates(self, threshold, basis)
File <string>:133, in diffn(self)
File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
 493 """
--> 494 return self.getattr_from_category(name)
 495
 496 cdef getattr_from_category(self, name):
File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
 505 else:
 506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
 508
 509 def __dir__(self):
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
 359 dummy_error_message.cls = type(self)
 360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
 362 attribute = <object>attr
 363 # Check for a descriptor (__get__ in Python)
AttributeError: 'sage.rings.integer.Integer' object has no attribute 'derivative'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
nowe!!!! ( (1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (1) * dx, 0 )
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (z1) * dx, 0 )
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (z0 + 1) * dx, 0 )
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0*z1 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (z0*z1 + z1) * dx, 0 )
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (z0^2 - z0 + 1) * dx, 0 )
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (x) * dx, 0 )
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x*z0 + x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (x*z0 + x) * dx, 0 )
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^4 - z1)/x^2) * dx, z1/x )
? 0
0 q r: 0 0
if 0 True
selfik ( (0) * dx, 0 )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z1^2)/x^2) * dx, z1^2/x )
? 0
0 q r: 0 0
if 0 True
selfik ( (0) * dx, 0 )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^2*z1 - z0*z1 - z1)/x^2) * dx, (z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
selfik ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^4*z0 + x^2*z0^2*z1 + x^4 - x^2*z0*z1 + x^2*z1^2 + x^2*z1 - z0*z1^2 - z1^2)/x^2) * dx, (z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
selfik ( (x^2 - z0*z1 + z1) * dx, 0 )
(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^2*z0*z1 - x^2*z1 - z0^2*z1 + z0*z1 - z1)/x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
selfik ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z0^2*z1^2 + z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
selfik ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 )
(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^4*z0^2 + x^4*z0 + x^4*z1 - x^4 + z1^2)/x^3) * dx, z1^2/x^2 )
? 0
0 q r: 0 0
if 0 True
selfik ( (x*z0 - x) * dx, 0 )
(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^2*z1^2 + z0*z1^2 + z1^2)/x^3) * dx, (z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
selfik ( (x*z0^2 - x*z1) * dx, 0 )
(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^4*z0^2 - x^4*z0 - x^2*z0*z1^2 + x^4 - x^2*z1^2 + z0^2*z1^2 - z0*z1^2 + z1^2)/x^3) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
selfik ( (x*z0^2 - x*z0 - x*z1 + x) * dx, 0 )
(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
selfik ( ((-x^4 - z1^2 - z1)/x^2) * dx, 0 )
((-x^4 - z1^2 - z1)/x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [7], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:80, in coordinates(self, threshold, basis)
File <string>:85, in coordinates(self, basis)
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
 895 if mor is not None:
 896 if no_extra_args:
--> 897 return mor._call_(x)
 898 else:
 899 return mor._call_with_args(x, args, kwds)
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
 786 return self._call_with_args(x, args, kwds)
 787
--> 788 cpdef Element _call_(self, x):
 789 """
 790 Call method with a single argument, not implemented in the base class.
File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
 1249 return num
 1250 if check and not den.is_unit():
 1251 # This should probably be a ValueError.
 1252 # However, too much existing code is expecting this to throw a
 1253 # TypeError, so we decided to keep it for the time being.
-> 1254 raise TypeError("fraction must have unit denominator")
 1255 return num * den.inverse_of_unit()
TypeError: fraction must have unit denominator
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
nowe!!!! ( (1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (1) * dx, 0 )
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [8], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:78, in coordinates(self, threshold, basis)
File <string>:133, in diffn(self)
AttributeError: 'as_function' object has no attribute 'derivative'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l((AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2 + AS.z[1]^2)/AS.x^3).valuation()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
nowe!!!! ( (1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (1) * dx, 0 )
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (z1) * dx, 0 )
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (z0 + 1) * dx, 0 )
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0*z1 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (z0*z1 + z1) * dx, 0 )
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (z0^2 - z0 + 1) * dx, 0 )
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (x) * dx, 0 )
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x*z0 + x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (x*z0 + x) * dx, 0 )
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
selfik ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^4 - z1)/x^2) * dx, z1/x )
? 0
0 q r: 0 0
if 0 True
selfik ( (0) * dx, 0 )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z1^2)/x^2) * dx, z1^2/x )
? 0
0 q r: 0 0
if 0 True
selfik ( (0) * dx, 0 )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^2*z1 - z0*z1 - z1)/x^2) * dx, (z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
selfik ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^4*z0 + x^2*z0^2*z1 + x^4 - x^2*z0*z1 + x^2*z1^2 + x^2*z1 - z0*z1^2 - z1^2)/x^2) * dx, (z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
selfik ( (x^2 - z0*z1 + z1) * dx, 0 )
(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^2*z0*z1 - x^2*z1 - z0^2*z1 + z0*z1 - z1)/x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
selfik ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z0^2*z1^2 + z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
selfik ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 )
(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^4*z0^2 + x^4*z0 + x^4*z1 - x^4 + z1^2)/x^3) * dx, z1^2/x^2 )
? 0
0 q r: 0 0
if 0 True
selfik ( (x*z0 - x) * dx, 0 )
(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^2*z1^2 + z0*z1^2 + z1^2)/x^3) * dx, (z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
selfik ( (x*z0^2 - x*z1) * dx, 0 )
(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^4*z0^2 - x^4*z0 - x^2*z0*z1^2 + x^4 - x^2*z1^2 + z0^2*z1^2 - z0*z1^2 + z1^2)/x^3) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
selfik ( (x*z0^2 - x*z0 - x*z1 + x) * dx, 0 )
(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
selfik ( ((-x^4 - z1^2 - z1)/x^2) * dx, 0 )
((-x^4 - z1^2 - z1)/x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [9], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:80, in coordinates(self, threshold, basis)
File <string>:85, in coordinates(self, basis)
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
 895 if mor is not None:
 896 if no_extra_args:
--> 897 return mor._call_(x)
 898 else:
 899 return mor._call_with_args(x, args, kwds)
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
 786 return self._call_with_args(x, args, kwds)
 787
--> 788 cpdef Element _call_(self, x):
 789 """
 790 Call method with a single argument, not implemented in the base class.
File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
 1249 return num
 1250 if check and not den.is_unit():
 1251 # This should probably be a ValueError.
 1252 # However, too much existing code is expecting this to throw a
 1253 # TypeError, so we decided to keep it for the time being.
-> 1254 raise TypeError("fraction must have unit denominator")
 1255 return num * den.inverse_of_unit()
TypeError: fraction must have unit denominator
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[?7h[?12l[?25h[?2004l[?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
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0
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0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for f in AS.cohomology_of_structure_sheaf_basis():
....:  for omega in AS.holomorphic_differentials_basis():
....:  print(om.serre_duality_pairing(f))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lif in AS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7li,f in AS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7l f in AS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leAS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7lnAS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7luAS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7lmAS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7leAS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7lrAS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7laAS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7ltAS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7leAS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7lenumerate(AS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l
[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()):[?7h[?12l[?25h[?25l[?7l()
[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ljomega in AS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7l,omega in AS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7l omega in AS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leAS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7lnAS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7luAS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7lmAS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7leAS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7lrAS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7laAS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7ltAS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7leAS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7lenumerate(AS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l
()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()):[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l
()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lprin(om.sere_duality_pairing(f))[?7h[?12l[?25h[?25l[?7l(om.sere_duality_pairing(f))[?7h[?12l[?25h[?25l[?7l(om.sere_duality_pairing(f))[?7h[?12l[?25h[?25l[?7l(om.sere_duality_pairing(f))[?7h[?12l[?25h[?25l[?7l(om.sere_duality_pairing(f))[?7h[?12l[?25h[?25l[?7li(om.sere_duality_pairing(f))[?7h[?12l[?25h[?25l[?7lif(om.sere_duality_pairing(f))[?7h[?12l[?25h[?25l[?7l (om.sere_duality_pairing(f))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l![?7h[?12l[?25h[?25l[?7l!=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lL[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l....:  if (om.serre_duality_pairing(f)) != 0:
....: [?7h[?12l[?25h[?25l[?7lprint("Collision")[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lj[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l....:  print(i, j)
....: [?7h[?12l[?25h[?25l[?7lsage: for i, f in enumerate(AS.cohomology_of_structure_sheaf_basis()):
....:  for j, omega in enumerate(AS.holomorphic_differentials_basis()):
....:  if (om.serre_duality_pairing(f)) != 0:
....:  print(i, j)
....: 
[?7h[?12l[?25h[?2004l4 0
4 1
4 2
4 3
4 4
4 5
4 6
4 7
4 8
4 9
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
(0, 0, 2, 0, 0, 0, 0, 0, 0, 0)
(0, 0, 0, 0, 0, 2, 0, 0, 0, 0)
(0, 0, 0, 0, 2, 0, 0, 0, 0, 0)
(0, 0, 0, 2, 0, 0, 0, 0, 0, 0)
(0, 2, 2, 0, 0, 0, 0, 0, 0, 0)
(2, 0, 2, 0, 0, 2, 0, 0, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 1, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 0, 2, 0)
(0, 0, 0, 0, 0, 0, 2, 1, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 0, 0, 2)
(0, 0, 2, 0, 0, 0, 0, 0, 0, 0)
(0, 0, 0, 0, 0, 2, 0, 0, 0, 0)
(0, 0, 0, 0, 2, 0, 0, 0, 0, 0)
(0, 0, 0, 2, 0, 0, 0, 0, 0, 0)
(0, 2, 2, 0, 0, 0, 0, 0, 0, 0)
(2, 0, 2, 0, 0, 2, 0, 0, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 1, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 0, 2, 0)
(0, 0, 0, 0, 0, 0, 2, 1, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 0, 0, 2)
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
nowe!!!! ( (1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (z1) * dx
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (z0 + 1) * dx
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0*z1 + z1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (z0*z1 + z1) * dx
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x*z0 + x) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0 + x) * dx
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2) * dx, 0 )
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^4 - z1)/x^2) * dx, z1/x )
? 0
0 q r: 0 0
if 0 True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z1^2)/x^2) * dx, z1^2/x )
? 0
0 q r: 0 0
if 0 True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^2*z1 - z0*z1 - z1)/x^2) * dx, (z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^4*z0 + x^2*z0^2*z1 + x^4 - x^2*z0*z1 + x^2*z1^2 + x^2*z1 - z0*z1^2 - z1^2)/x^2) * dx, (z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
hol_form (x^2 - z0*z1 + z1) * dx
(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^2*z0*z1 - x^2*z1 - z0^2*z1 + z0*z1 - z1)/x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z0^2*z1^2 + z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
? 0
0 q r: 0 0
if 0 True
hol_form (x^2*z0 + z0^2*z1 + z1^2) * dx
(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^4*z0^2 + x^4*z0 + x^4*z1 - x^4 + z1^2)/x^3) * dx, z1^2/x^2 )
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0 - x) * dx
(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^2*z1^2 + z0*z1^2 + z1^2)/x^3) * dx, (z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0^2 - x*z1) * dx
(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^4*z0^2 - x^4*z0 - x^2*z0*z1^2 + x^4 - x^2*z1^2 + z0^2*z1^2 - z0*z1^2 + z1^2)/x^3) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0^2 - x*z0 - x*z1 + x) * dx
(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
hol_form ((-x^4 - z1^2 - z1)/x^2) * dx
((-x^4 - z1^2 - z1)/x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [12], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:80, in coordinates(self, threshold, basis)
File <string>:85, in coordinates(self, basis)
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
 895 if mor is not None:
 896 if no_extra_args:
--> 897 return mor._call_(x)
 898 else:
 899 return mor._call_with_args(x, args, kwds)
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
 786 return self._call_with_args(x, args, kwds)
 787
--> 788 cpdef Element _call_(self, x):
 789 """
 790 Call method with a single argument, not implemented in the base class.
File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
 1249 return num
 1250 if check and not den.is_unit():
 1251 # This should probably be a ValueError.
 1252 # However, too much existing code is expecting this to throw a
 1253 # TypeError, so we decided to keep it for the time being.
-> 1254 raise TypeError("fraction must have unit denominator")
 1255 return num * den.inverse_of_unit()
TypeError: fraction must have unit denominator
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: for i, f in enumerate(AS.cohomology_of_structure_sheaf_basis()):
....:  for j, omega in enumerate(AS.holomorphic_differentials_basis()):
....:  if (om.serre_duality_pairing(f)) != 0:
....:  print(i, j)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l
()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l
[?7h[?12l[?25h[?25l[?7l
()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  print(i, j)
....: [?7h[?12l[?25h[?25l[?7lsage: for i, f in enumerate(AS.cohomology_of_structure_sheaf_basis()):
....:  for j, omega in enumerate(AS.holomorphic_differentials_basis()):
....:  if (om.serre_duality_pairing(f)) != 0:
....:  print(i, j)
....: 
[?7h[?12l[?25h[?2004l(0, 0, 2, 0, 0, 0, 0, 0, 0, 0)
(0, 0, 0, 0, 0, 2, 0, 0, 0, 0)
(0, 0, 0, 0, 2, 0, 0, 0, 0, 0)
(0, 0, 0, 2, 0, 0, 0, 0, 0, 0)
(0, 2, 2, 0, 0, 0, 0, 0, 0, 0)
(2, 0, 2, 0, 0, 2, 0, 0, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 1, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 0, 2, 0)
(0, 0, 0, 0, 0, 0, 2, 1, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 0, 0, 2)
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [13], in <cell line: 1>()
 1 for i, f in enumerate(AS.cohomology_of_structure_sheaf_basis()):
 2 for j, omega in enumerate(AS.holomorphic_differentials_basis()):
----> 3 if (om.serre_duality_pairing(f)) != Integer(0):
 4 print(i, j)
File <string>:117, in serre_duality_pairing(self, fct)
File /ext/sage/9.7/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds)
 583 return expression.sum(*args, **kwds)
 584 elif max(len(args),len(kwds)) <= 1:
--> 585 return sum(expression, *args, **kwds)
 586 else:
 587 from sage.symbolic.ring import SR
File <string>:117, in <genexpr>(.0)
AttributeError: 'NoneType' object has no attribute 'residue'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lcohlogy_of_structure_hef_basis()[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.cohomology_of_structure_sheaf_basis()
[?7h[?12l[?25h[?2004l(0, 0, 2, 0, 0, 0, 0, 0, 0, 0)
(0, 0, 0, 0, 0, 2, 0, 0, 0, 0)
(0, 0, 0, 0, 2, 0, 0, 0, 0, 0)
(0, 0, 0, 2, 0, 0, 0, 0, 0, 0)
(0, 2, 2, 0, 0, 0, 0, 0, 0, 0)
(2, 0, 2, 0, 0, 2, 0, 0, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 1, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 0, 2, 0)
(0, 0, 0, 0, 0, 0, 2, 1, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 0, 0, 2)
[?7h[z1/x,
z1^2/x,
z0*z1/x,
z0*z1^2/x,
z0^2*z1/x,
z0^2*z1^2/x,
z1^2/x^2,
z0*z1^2/x^2,
z0^2*z1^2/x^2,
z0^2*z1^2/x^3]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: AS.cohomology_of_structure_sheaf_basis()[1]
[?7h[?12l[?25h[?2004l(0, 0, 2, 0, 0, 0, 0, 0, 0, 0)
(0, 0, 0, 0, 0, 2, 0, 0, 0, 0)
(0, 0, 0, 0, 2, 0, 0, 0, 0, 0)
(0, 0, 0, 2, 0, 0, 0, 0, 0, 0)
(0, 2, 2, 0, 0, 0, 0, 0, 0, 0)
(2, 0, 2, 0, 0, 2, 0, 0, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 1, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 0, 2, 0)
(0, 0, 0, 0, 0, 0, 2, 1, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 0, 0, 2)
[?7hz1^2/x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l AS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l=AS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l AS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A = AS.cohomology_of_structure_sheaf_basis()[1]
[?7h[?12l[?25h[?2004l(0, 0, 2, 0, 0, 0, 0, 0, 0, 0)
(0, 0, 0, 0, 0, 2, 0, 0, 0, 0)
(0, 0, 0, 0, 2, 0, 0, 0, 0, 0)
(0, 0, 0, 2, 0, 0, 0, 0, 0, 0)
(0, 2, 2, 0, 0, 0, 0, 0, 0, 0)
(2, 0, 2, 0, 0, 2, 0, 0, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 1, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 0, 2, 0)
(0, 0, 0, 0, 0, 0, 2, 1, 0, 0)
(0, 0, 0, 0, 0, 0, 0, 0, 0, 2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.serre_duality_pairing(f)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = AS.holomorphic_dfferentials_basis()[1][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[1][?7h[?12l[?25h[?25l[?7lsage: om = AS.holomorphic_differentials_basis()[1]
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentials_basis()[1][?7h[?12l[?25h[?25l[?7lm.serre_duality_pairng(f)[?7h[?12l[?25h[?25l[?7lserre_duality_pairing(f)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lA)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: om.serre_duality_pairing(A)
[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.serre_duality_pairing(A)[?7h[?12l[?25h[?25l[?7l = AS.holomorphic_dfferentials_basis()[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l2][?7h[?12l[?25h[?25l[?7lsage: om = AS.holomorphic_differentials_basis()[2]
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentials_basis()[2][?7h[?12l[?25h[?25l[?7l.serre_duality_pairng(A)[?7h[?12l[?25h[?25l[?7lsage: om.serre_duality_pairing(A)
[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.serre_duality_pairing(A)[?7h[?12l[?25h[?25l[?7l = AS.holomorphic_dfferentials_basis()[2][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l3][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7lsage: om = AS.holomorphic_differentials_basis()[3]
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentials_basis()[3][?7h[?12l[?25h[?25l[?7l.serre_duality_pairng(A)[?7h[?12l[?25h[?25l[?7lsage: om.serre_duality_pairing(A)
[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.serre_duality_pairing(A)[?7h[?12l[?25h[?25l[?7l = AS.holomorphic_dfferentials_basis()[3][?7h[?12l[?25h[?25l[?7l[];[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lduality_pairing[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om = AS.holomorphic_differentials_basis()[3]; om.serre_duality_pairing(A)
[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentials_basis()[3]; om.serre_duality_pairing(A)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l]; om.sere_duality_pairing(A)[?7h[?12l[?25h[?25l[?7l4]; om.sere_duality_pairing(A)[?7h[?12l[?25h[?25l[?7lsage: om = AS.holomorphic_differentials_basis()[4]; om.serre_duality_pairing(A)
[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = AS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7lS.cohomlgy_f_strucure_shaf_bsis()[1][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lhlrphic_differential_bsis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis()
[?7h[?12l[?25h[?2004l[?7h[(1) * dx,
(z1) * dx,
(x^2*z0 + z0^2*z1 + z1^2) * dx,
(z0) * dx,
(z0*z1) * dx,
(z0^2) * dx,
(x) * dx,
(-x*z0^2 + x*z1) * dx,
(x*z0) * dx,
(x^2) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentils_basis()[4]; om.serre_duality_pairing(A)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]; om.sere_duality_pairing(A)[?7h[?12l[?25h[?25l[?7l5]; om.sere_duality_pairing(A)[?7h[?12l[?25h[?25l[?7lsage: om = AS.holomorphic_differentials_basis()[5]; om.serre_duality_pairing(A)
[?7h[?12l[?25h[?2004l[?7h2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentials_basis()[5]; om.serre_duality_pairing(A)[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_bsis()[?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentils_basis()[4]; om.serre_duality_pairing(A)[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l.serre_duality_pairng(A)[?7h[?12l[?25h[?25l[?7l = AS.holomorphic_dfferentials_basis()[3][?7h[?12l[?25h[?25l[?7l.serre_duality_pairng(A)[?7h[?12l[?25h[?25l[?7l = AS.holomorphic_dfferentials_basis()[2][?7h[?12l[?25h[?25l[?7l.serre_duality_pairng(A)[?7h[?12l[?25h[?25l[?7l = AS.holomorphic_dfferentials_basis()[1][?7h[?12l[?25h[?25l[?7lA = AS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7lS.cohomlgy_f_strucure_shaf_bsis()[1][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: for i, f in enumerate(AS.cohomology_of_structure_sheaf_basis()):
....:  for j, omega in enumerate(AS.holomorphic_differentials_basis()):
....:  if (om.serre_duality_pairing(f)) != 0:
....:  print(i, j)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')
 
 
 [?7h[?12l[?25h[?25l[?7lfor i, f in enumerate(AS.cohomology_of_structure_sheaf_basis()):
....:  for j, omega in enumerate(AS.holomorphic_differentials_basis()):
....:  if (om.serre_duality_pairing(f)) != 0:
....:  print(i, j)[?7h[?12l[?25h[?25l[?7lload('init.sage')
 
 
 [?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004lTraceback (most recent call last):
File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
exec(code_obj, self.user_global_ns, self.user_ns)
Input In [27] in <cell line: 1>
load('init.sage')
File sage/misc/persist.pyx:175 in sage.misc.persist.load
sage.repl.load.load(filename, globals())
File /ext/sage/9.7/src/sage/repl/load.py:272 in load
exec(preparse_file(f.read()) + "\n", globals)
File <string>:8 in <module>
File sage/misc/persist.pyx:175 in sage.misc.persist.load
sage.repl.load.load(filename, globals())
 File /ext/sage/9.7/src/sage/repl/load.py:272 in load
 exec(preparse_file(f.read()) + "\n", globals)
 File <string>:68
 print('products:' [omega.serre_duality_pairing(self.f) for omega in AS.holomorphic_differentials_basis()])
 ^
SyntaxError: invalid syntax. Perhaps you forgot a comma?
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
nowe!!!! ( (1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z1) * dx
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z0 + 1) * dx
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0*z1 + z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z0*z1 + z1) * dx
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x*z0 + x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0 + x) * dx
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^4 - z1)/x^2) * dx, z1/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z1^2)/x^2) * dx, z1^2/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^2*z1 - z0*z1 - z1)/x^2) * dx, (z0*z1 + z1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^4*z0 + x^2*z0^2*z1 + x^4 - x^2*z0*z1 + x^2*z1^2 + x^2*z1 - z0*z1^2 - z1^2)/x^2) * dx, (z0*z1^2 + z1^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2 - z0*z1 + z1) * dx
(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^2*z0*z1 - x^2*z1 - z0^2*z1 + z0*z1 - z1)/x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z0^2*z1^2 + z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2*z0 + z0^2*z1 + z1^2) * dx
(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-x^4*z0^2 + x^4*z0 + x^4*z1 - x^4 + z1^2)/x^3) * dx, z1^2/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0 - x) * dx
(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^2*z1^2 + z0*z1^2 + z1^2)/x^3) * dx, (z0*z1^2 + z1^2)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0^2 - x*z1) * dx
(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((x^4*z0^2 - x^4*z0 - x^2*z0*z1^2 + x^4 - x^2*z1^2 + z0^2*z1^2 - z0*z1^2 + z1^2)/x^3) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0^2 - x*z0 - x*z1 + x) * dx
(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( ((-z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
hol_form ((-x^4 - z1^2 - z1)/x^2) * dx
((-x^4 - z1^2 - z1)/x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [28], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:81, in coordinates(self, threshold, basis)
File <string>:85, in coordinates(self, basis)
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
 895 if mor is not None:
 896 if no_extra_args:
--> 897 return mor._call_(x)
 898 else:
 899 return mor._call_with_args(x, args, kwds)
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
 786 return self._call_with_args(x, args, kwds)
 787
--> 788 cpdef Element _call_(self, x):
 789 """
 790 Call method with a single argument, not implemented in the base class.
File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
 1249 return num
 1250 if check and not den.is_unit():
 1251 # This should probably be a ValueError.
 1252 # However, too much existing code is expecting this to throw a
 1253 # TypeError, so we decided to keep it for the time being.
-> 1254 raise TypeError("fraction must have unit denominator")
 1255 return num * den.inverse_of_unit()
TypeError: fraction must have unit denominator
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldR = AS.de_rham_basis(threshold = 20)[?7h[?12l[?25h[?25l[?7le_rham_coodinate(AS, dR[0])[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lbasis(AS)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lis(AS)[?7h[?12l[?25h[?25l[?7lsage: de_rham_basis(AS)
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [29], in <cell line: 1>()
----> 1 de_rham_basis(AS)
NameError: name 'de_rham_basis' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_basis(AS)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAde_rham_basis()[?7h[?12l[?25h[?25l[?7lSde_rham_basis()[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis()
[?7h[?12l[?25h[?2004lz1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[?7h[( (1) * dx, 0 ),
( (z1) * dx, 0 ),
( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ),
( (z0) * dx, 0 ),
( (z0*z1) * dx, 0 ),
( (z0^2) * dx, 0 ),
( (x) * dx, 0 ),
( (-x*z0^2 + x*z1) * dx, 0 ),
( (x*z0) * dx, 0 ),
( (x^2) * dx, 0 ),
( ((-x^4 - z1)/x^2) * dx, z1/x ),
( ((-z1^2)/x^2) * dx, z1^2/x ),
( ((x^2*z1 - z0*z1)/x^2) * dx, z0*z1/x ),
( ((x^4*z0 + x^2*z0^2*z1 + x^2*z1^2 - z0*z1^2)/x^2) * dx, z0*z1^2/x ),
( ((-x^2*z0*z1 - z0^2*z1)/x^2) * dx, z0^2*z1/x ),
( ((-z0^2*z1^2)/x^2) * dx, z0^2*z1^2/x ),
( ((-x^4*z0^2 + x^4*z1 + z1^2)/x^3) * dx, z1^2/x^2 ),
( ((x^2*z1^2 + z0*z1^2)/x^3) * dx, z0*z1^2/x^2 ),
( ((x^4*z0^2 - x^2*z0*z1^2 + z0^2*z1^2)/x^3) * dx, z0^2*z1^2/x^2 ),
( ((-z0*z1^2)/x^2) * dx, z0^2*z1^2/x^3 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lgnus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus()
[?7h[?12l[?25h[?2004l[?7h10
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
nowe!!!! ( (1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z1) * dx
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z0 + 1) * dx
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0*z1 + z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z0*z1 + z1) * dx
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x*z0 + x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0 + x) * dx
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (0) * dx, z1/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z1) * dx, z1^2/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + x^2) * dx, (z0*z1 + z1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0*z1 + x^2*z0 - x^2*z1 + z0^2*z1 + x^2 - z0*z1 + z1) * dx, (z0*z1^2 + z1^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2 - z0*z1 + z1) * dx
(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0^2 - x^2*z0 + x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0^2*z1 + x^2*z0*z1 - x^2*z1 + z0*z1^2 + z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2*z0 + z0^2*z1 + z1^2) * dx
(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z0 - x) * dx, z1^2/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0 - x) * dx
(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0*z1 - x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0^2 - x*z1) * dx
(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2*z1 + x*z0^2 + x*z0*z1 - x*z0 - x*z1 + x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0^2 - x*z0 - x*z1 + x) * dx
(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-z0^2*z1 + z0*z1 - z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
hol_form (z0*z1 - z1) * dx
(z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z1 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z1 + 1) * dx
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z0) * dx
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0*z1 + z0) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z0*z1 + z0) * dx
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0^2) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z0^2) * dx
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z1 + x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (-x*z0^2 + x*z1 + x) * dx
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x*z0) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0) * dx
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (0) * dx, (z1 + 1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 1/x
1/x q r: 0 1
if 1/x True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z1 - x^2) * dx, (z1^2 - z1 + 1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 1/x
1/x q r: 0 1
if 1/x True
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0) * dx, (z0*z1 + z0)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? z0/x
z0/x q r: 0 z0
if z0/x True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0*z1 + z0^2*z1 + z0^2) * dx, (z0*z1^2 - z0*z1 + z0)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? z0/x
z0/x q r: 0 z0
if z0/x True
hol_form (z0^2) * dx
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0^2) * dx, (z0^2*z1 + z0^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (z0^2 - z1)/x
(z0^2 - z1)/x q r: 0 z0^2 - z1
if (z0^2 - z1)/x True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0^2*z1 - x^2*z0^2 + z0*z1^2 - z0*z1 + z0) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (z0^2 - z1)/x
(z0^2 - z1)/x q r: 0 z0^2 - z1
if (z0^2 - z1)/x True
hol_form (-z0*z1 + z0) * dx
(-z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2) * dx, (z1^2 - z1 + 1)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (-z1 + 1)/x^2
(-z1 + 1)/x^2 q r: 0 -z1 + 1
if (-z1 + 1)/x^2 True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0*z1 - x*z0) * dx, (z0*z1^2 - z0*z1 + z0)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (-z0*z1 + z0)/x^2
(-z0*z1 + z0)/x^2 q r: 0 -z0*z1 + z0
if (-z0*z1 + z0)/x^2 True
hol_form (-x*z0) * dx
(-x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2*z1) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (-z0^2*z1 + z0^2 - z1^2)/x^2
(-z0^2*z1 + z0^2 - z1^2)/x^2 q r: 0 -z0^2*z1 + z0^2 - z1^2
if (-z0^2*z1 + z0^2 - z1^2)/x^2 False
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [32], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:82, in coordinates(self, threshold, basis)
ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
nowe!!!! ( (1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z1) * dx
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z0 + 1) * dx
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0*z1 + z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z0*z1 + z1) * dx
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x*z0 + x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0 + x) * dx
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (0) * dx, z1/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z1) * dx, z1^2/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + x^2) * dx, (z0*z1 + z1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0*z1 + x^2*z0 - x^2*z1 + z0^2*z1 + x^2 - z0*z1 + z1) * dx, (z0*z1^2 + z1^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2 - z0*z1 + z1) * dx
(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0^2 - x^2*z0 + x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0^2*z1 + x^2*z0*z1 - x^2*z1 + z0*z1^2 + z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2*z0 + z0^2*z1 + z1^2) * dx
(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z0 - x) * dx, z1^2/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0 - x) * dx
(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0*z1 - x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0^2 - x*z1) * dx
(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2*z1 + x*z0^2 + x*z0*z1 - x*z0 - x*z1 + x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0^2 - x*z0 - x*z1 + x) * dx
(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-z0^2*z1 + z0*z1 - z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
hol_form (z0*z1 - z1) * dx
(z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z1 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z1 + 1) * dx
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z0) * dx
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0*z1 + z0) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z0*z1 + z0) * dx
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0^2) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (z0^2) * dx
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z1 + x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (-x*z0^2 + x*z1 + x) * dx
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x*z0) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x*z0) * dx
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (0) * dx, (z1 + 1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 1/x
1/x q r: 0 1
if 1/x True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z1 - x^2) * dx, (z1^2 - z1 + 1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 1/x
1/x q r: 0 1
if 1/x True
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0) * dx, (z0*z1 + z0)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? z0/x
z0/x q r: 0 z0
if z0/x True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0*z1 + z0^2*z1 + z0^2) * dx, (z0*z1^2 - z0*z1 + z0)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? z0/x
z0/x q r: 0 z0
if z0/x True
hol_form (z0^2) * dx
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0^2) * dx, (z0^2*z1 + z0^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (z0^2 - z1)/x
(z0^2 - z1)/x q r: 0 z0^2 - z1
if (z0^2 - z1)/x True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0^2*z1 - x^2*z0^2 + z0*z1^2 - z0*z1 + z0) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (z0^2 - z1)/x
(z0^2 - z1)/x q r: 0 z0^2 - z1
if (z0^2 - z1)/x True
hol_form (-z0*z1 + z0) * dx
(-z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2) * dx, (z1^2 - z1 + 1)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (-z1 + 1)/x^2
(-z1 + 1)/x^2 q r: 0 -z1 + 1
if (-z1 + 1)/x^2 True
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0*z1 - x*z0) * dx, (z0*z1^2 - z0*z1 + z0)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (-z0*z1 + z0)/x^2
(-z0*z1 + z0)/x^2 q r: 0 -z0*z1 + z0
if (-z0*z1 + z0)/x^2 True
hol_form (-x*z0) * dx
(-x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2*z1) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (-z0^2*z1 + z0^2 - z1^2)/x^2
(-z0^2*z1 + z0^2 - z1^2)/x^2 q r: 0 -z0^2*z1 + z0^2 - z1^2
if (-z0^2*z1 + z0^2 - z1^2)/x^2 False
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [33], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:82, in coordinates(self, threshold, basis)
ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lon[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l].group_action[?7h[?12l[?25h[?25l[?7l1].group_action[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[)[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l1])[?7h[?12l[?25h[?25l[?7l,])[?7h[?12l[?25h[?25l[?7l ])[?7h[?12l[?25h[?25l[?7l0])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis()[1].group_action([1, 0])
[?7h[?12l[?25h[?2004l[?7h(z1) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[1].group_action([1, 0])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l0])[?7h[?12l[?25h[?25l[?7l,])[?7h[?12l[?25h[?25l[?7l ])[?7h[?12l[?25h[?25l[?7l1])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis()[1].group_action([0, 1])
[?7h[?12l[?25h[?2004l[?7h(z1 + 1) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[1].group_action([0, 1])[?7h[?12l[?25h[?25l[?7l10[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
nowe!!!! ( (1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (1) * dx
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z1) * dx
hol_form (z1) * dx
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0 + 1) * dx
hol_form (z0 + 1) * dx
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0*z1 + z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0*z1 + z1) * dx
hol_form (z0*z1 + z1) * dx
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0^2 - z0 + 1) * dx
hol_form (z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x) * dx
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (-x*z0^2 + x*z0 + x*z1 - x) * dx
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x*z0 + x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x*z0 + x) * dx
hol_form (x*z0 + x) * dx
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2) * dx
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (0) * dx, z1/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (0) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z1) * dx, z1^2/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (0) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + x^2) * dx, (z0*z1 + z1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2) * dx
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0*z1 + x^2*z0 - x^2*z1 + z0^2*z1 + x^2 - z0*z1 + z1) * dx, (z0*z1^2 + z1^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2 - z0*z1 + z1) * dx
hol_form (x^2 - z0*z1 + z1) * dx
(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0^2 - x^2*z0 + x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2) * dx
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0^2*z1 + x^2*z0*z1 - x^2*z1 + z0*z1^2 + z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2*z0 + z0^2*z1 + z1^2) * dx
hol_form (x^2*z0 + z0^2*z1 + z1^2) * dx
(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z0 - x) * dx, z1^2/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x*z0 - x) * dx
hol_form (x*z0 - x) * dx
(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0*z1 - x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x*z0^2 - x*z1) * dx
hol_form (x*z0^2 - x*z1) * dx
(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2*z1 + x*z0^2 + x*z0*z1 - x*z0 - x*z1 + x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x*z0^2 - x*z0 - x*z1 + x) * dx
hol_form (x*z0^2 - x*z0 - x*z1 + x) * dx
(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-z0^2*z1 + z0*z1 - z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
omega - df ((x^4 - x^2*z0*z1 + x^2*z1 + z1^2 + z1)/x^2) * dx
hol_form (z0*z1 - z1) * dx
(z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (1) * dx
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z1 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z1 + 1) * dx
hol_form (z1 + 1) * dx
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx
hol_form (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0) * dx
hol_form (z0) * dx
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0*z1 + z0) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0*z1 + z0) * dx
hol_form (z0*z1 + z0) * dx
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0^2) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0^2) * dx
hol_form (z0^2) * dx
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x) * dx
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z1 + x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (-x*z0^2 + x*z1 + x) * dx
hol_form (-x*z0^2 + x*z1 + x) * dx
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x*z0) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x*z0) * dx
hol_form (x*z0) * dx
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2) * dx
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (0) * dx, (z1 + 1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 1/x
1/x q r: 0 1
if 1/x True
omega - df (1/x^2) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z1 - x^2) * dx, (z1^2 - z1 + 1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 1/x
1/x q r: 0 1
if 1/x True
omega - df ((-x^4 + 1)/x^2) * dx
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0) * dx, (z0*z1 + z0)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? z0/x
z0/x q r: 0 z0
if z0/x True
omega - df ((-x^2 + z0)/x^2) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0*z1 + z0^2*z1 + z0^2) * dx, (z0*z1^2 - z0*z1 + z0)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? z0/x
z0/x q r: 0 z0
if z0/x True
omega - df ((x^2*z0^2 - x^2 + z0)/x^2) * dx
hol_form (z0^2) * dx
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0^2) * dx, (z0^2*z1 + z0^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (z0^2 - z1)/x
(z0^2 - z1)/x q r: 0 z0^2 - z1
if (z0^2 - z1)/x True
omega - df ((-x^4 + x^2*z0 + z0^2 - z1)/x^2) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0^2*z1 - x^2*z0^2 + z0*z1^2 - z0*z1 + z0) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (z0^2 - z1)/x
(z0^2 - z1)/x q r: 0 z0^2 - z1
if (z0^2 - z1)/x True
omega - df ((-x^4 - x^2*z0*z1 - x^2*z0 + z0^2 - z1)/x^2) * dx
hol_form (-z0*z1 + z0) * dx
(-z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2) * dx, (z1^2 - z1 + 1)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (-z1 + 1)/x^2
(-z1 + 1)/x^2 q r: 0 -z1 + 1
if (-z1 + 1)/x^2 True
omega - df ((-x^4 + z1 - 1)/x^3) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0*z1 - x*z0) * dx, (z0*z1^2 - z0*z1 + z0)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (-z0*z1 + z0)/x^2
(-z0*z1 + z0)/x^2 q r: 0 -z0*z1 + z0
if (-z0*z1 + z0)/x^2 True
omega - df ((x^4*z0 + x^2*z1 - x^2 + z0*z1 - z0)/x^3) * dx
hol_form (-x*z0) * dx
(-x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2*z1) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (-z0^2*z1 + z0^2 - z1^2)/x^2
(-z0^2*z1 + z0^2 - z1^2)/x^2 q r: 0 -z0^2*z1 + z0^2 - z1^2
if (-z0^2*z1 + z0^2 - z1^2)/x^2 False
omega - df ((-x^4*z0^2 + x^4*z1 - x^2*z0*z1 + x^2*z0 + z0^2*z1 - z0^2 + z1^2)/x^3) * dx
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [36], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:83, in coordinates(self, threshold, basis)
ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[1].group_action([0, 1])[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis()
[?7h[?12l[?25h[?2004lz1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[?7h[( (1) * dx, 0 ),
( (z1) * dx, 0 ),
( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ),
( (z0) * dx, 0 ),
( (z0*z1) * dx, 0 ),
( (z0^2) * dx, 0 ),
( (x) * dx, 0 ),
( (-x*z0^2 + x*z1) * dx, 0 ),
( (x*z0) * dx, 0 ),
( (x^2) * dx, 0 ),
( (0) * dx, z1/x ),
( (-x^2*z1) * dx, z1^2/x ),
( (x^2*z0) * dx, z0*z1/x ),
( (-x^2*z0*z1 + x^2*z0 + z0^2*z1) * dx, z0*z1^2/x ),
( (x^2*z0^2) * dx, z0^2*z1/x ),
( (-x^2*z0^2*z1 + z0*z1^2) * dx, z0^2*z1^2/x ),
( (-x*z0^2) * dx, z1^2/x^2 ),
( (-x*z0*z1) * dx, z0*z1^2/x^2 ),
( (-x*z0^2*z1 + x*z0^2) * dx, z0^2*z1^2/x^2 ),
( (-z0^2*z1) * dx, z0^2*z1^2/x^3 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomAS.de_rham_bais()[?7h[?12l[?25h[?25l[?7l,AS.de_rham_basis()[?7h[?12l[?25h[?25l[?7l AS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lfAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7l AS.de_rham_basis()[?7h[?12l[?25h[?25l[?7l=AS.de_rham_basis()[?7h[?12l[?25h[?25l[?7l AS.de_rham_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l16[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: om, f = AS.de_rham_basis()[16]
[?7h[?12l[?25h[?2004lz1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [38], in <cell line: 1>()
----> 1 om, f = AS.de_rham_basis()[Integer(16)]
TypeError: cannot unpack non-iterable as_cech object
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom, f = AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l= AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7l= AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7l= AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7l= AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7l= AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7l= AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc= AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7lc= AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7l = AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: cc = AS.de_rham_basis()[16]
[?7h[?12l[?25h[?2004lz1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcc = AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[0][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7liffn[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: cc[0] - cc[1].diffn()
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [40], in <cell line: 1>()
----> 1 cc[Integer(0)] - cc[Integer(1)].diffn()
TypeError: 'as_cech' object is not subscriptable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcc[0] - cc[1].diffn()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lsage: cc
[?7h[?12l[?25h[?2004l[?7h( (-x*z0^2) * dx, z1^2/x^2 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0] - cc[1].diffn()[?7h[?12l[?25h[?25l[?7l = AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7l[0] - cc[1].diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[ - c[1].difn()[?7h[?12l[?25h[?25l[?7l - c[1].difn()[?7h[?12l[?25h[?25l[?7l - c[1].difn()[?7h[?12l[?25h[?25l[?7l. - c[1].difn()[?7h[?12l[?25h[?25l[?7lom- cc[1].diffn()[?7h[?12l[?25h[?25l[?7le - c[1].difn()[?7h[?12l[?25h[?25l[?7lg - c[1].difn()[?7h[?12l[?25h[?25l[?7la - c[1].difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[1.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7lf.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: cc.omega - cc.f.diffn()
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [42], in <cell line: 1>()
----> 1 cc.omega - cc.f.diffn()
AttributeError: 'as_cech' object has no attribute 'omega'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcc.omega - cc.f.diffn()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lsage: cc
[?7h[?12l[?25h[?2004l[?7h( (-x*z0^2) * dx, z1^2/x^2 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcc[?7h[?12l[?25h[?25l[?7l.omega - cc.f.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0 - c.f.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: cc.omega0 - cc.f.diffn()
[?7h[?12l[?25h[?2004l[?7h((-x^4*z0^2 - x^4*z1 - z1^2)/x^3) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcc.omega0 - cc.f.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(c.omega0 - c.f.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (cc.omega0 - cc.f.diffn()).expansion_at_infty()
[?7h[?12l[?25h[?2004l[?7h2*t^-3 + t + 2*t^9 + t^13 + t^21 + 2*t^25 + t^29 + 2*t^45 + t^49 + 2*t^61 + 2*t^65 + 2*t^69 + t^73 + t^85 + 2*t^93 + t^97 + t^113 + t^121 + t^129 + 2*t^133 + t^137 + t^141 + 2*t^153 + t^157 + 2*t^169 + 2*t^173 + 2*t^177 + t^189 + t^193 + 2*t^201 + 2*t^205 + t^217 + 2*t^221 + 2*t^225 + 2*t^229 + t^237 + t^241 + 2*t^249 + t^265 + 2*t^273 + t^277 + t^289 + 2*t^297 + t^301 + 2*t^309 + t^313 + t^325 + 2*t^333 + t^345 + t^349 + 2*t^353 + t^357 + t^361 + t^365 + t^373 + 2*t^385 + 2*t^389 + t^397 + t^421 + 2*t^433 + t^437 + t^441 + t^445 + t^453 + t^457 + t^461 + t^465 + 2*t^477 + t^481 + 2*t^489 + 2*t^493 + 2*t^501 + 2*t^505 + t^513 + t^517 + 2*t^525 + 2*t^537 + t^541 + 2*t^545 + 2*t^549 + 2*t^561 + t^565 + t^569 + 2*t^573 + t^577 + t^585 + t^589 + 2*t^597 + 2*t^601 + t^609 + t^613 + 2*t^621 + t^625 + 2*t^633 + t^637 + 2*t^645 + 2*t^649 + t^657 + t^661 + 2*t^669 + t^685 + 2*t^689 + 2*t^693 + 2*t^697 + t^705 + t^709 + 2*t^717 + 2*t^721 + t^729 + t^733 + 2*t^741 + 2*t^745 + t^757 + 2*t^765 + 2*t^777 + t^781 + t^785 + 2*t^789 + 2*t^793 + t^805 + 2*t^813 + t^817 + t^829 + 2*t^837 + t^853 + 2*t^861 + t^877 + 2*t^885 + 2*t^897 + t^901 + 2*t^909 + t^913 + t^921 + t^925 + t^929 + 2*t^933 + 2*t^945 + t^949 + 2*t^957 + 2*t^961 + O(t^969)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls.coefficient_matrix()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
omega val 0
z1^2/x
omega val 12
z0*z1/x
omega val 6
z0*z1^2/x
omega val 2
z0^2*z1/x
omega val 0
z0^2*z1^2/x
omega val 0
z1^2/x^2
omega val 1
z0*z1^2/x^2
omega val 3
z0^2*z1^2/x^2
omega val 1
z0^2*z1^2/x^3
omega val 6
nowe!!!! ( (1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (1) * dx
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z1) * dx
hol_form (z1) * dx
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0 + 1) * dx
hol_form (z0 + 1) * dx
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0*z1 + z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0*z1 + z1) * dx
hol_form (z0*z1 + z1) * dx
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0^2 - z0 + 1) * dx
hol_form (z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x) * dx
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (-x*z0^2 + x*z0 + x*z1 - x) * dx
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x*z0 + x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x*z0 + x) * dx
hol_form (x*z0 + x) * dx
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2) * dx
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (0) * dx, z1/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (0) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z1) * dx, z1^2/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (0) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + x^2) * dx, (z0*z1 + z1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2) * dx
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0*z1 + x^2*z0 - x^2*z1 + z0^2*z1 + x^2 - z0*z1 + z1) * dx, (z0*z1^2 + z1^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2 - z0*z1 + z1) * dx
hol_form (x^2 - z0*z1 + z1) * dx
(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0^2 - x^2*z0 + x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2) * dx
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0^2*z1 + x^2*z0*z1 - x^2*z1 + z0*z1^2 + z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2*z0 + z0^2*z1 + z1^2) * dx
hol_form (x^2*z0 + z0^2*z1 + z1^2) * dx
(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z0 - x) * dx, z1^2/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x*z0 - x) * dx
hol_form (x*z0 - x) * dx
(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0*z1 - x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x*z0^2 - x*z1) * dx
hol_form (x*z0^2 - x*z1) * dx
(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2*z1 + x*z0^2 + x*z0*z1 - x*z0 - x*z1 + x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x*z0^2 - x*z0 - x*z1 + x) * dx
hol_form (x*z0^2 - x*z0 - x*z1 + x) * dx
(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-z0^2*z1 + z0*z1 - z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
omega - df ((x^4 - x^2*z0*z1 + x^2*z1 + z1^2 + z1)/x^2) * dx
hol_form (z0*z1 - z1) * dx
(z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (1) * dx
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z1 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z1 + 1) * dx
hol_form (z1 + 1) * dx
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx
hol_form (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0) * dx
hol_form (z0) * dx
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0*z1 + z0) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0*z1 + z0) * dx
hol_form (z0*z1 + z0) * dx
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0^2) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0^2) * dx
hol_form (z0^2) * dx
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x) * dx
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z1 + x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (-x*z0^2 + x*z1 + x) * dx
hol_form (-x*z0^2 + x*z1 + x) * dx
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x*z0) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x*z0) * dx
hol_form (x*z0) * dx
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2) * dx
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (0) * dx, (z1 + 1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 1/x
1/x q r: 0 1
if 1/x True
omega - df (1/x^2) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z1 - x^2) * dx, (z1^2 - z1 + 1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 1/x
1/x q r: 0 1
if 1/x True
omega - df ((-x^4 + 1)/x^2) * dx
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0) * dx, (z0*z1 + z0)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? z0/x
z0/x q r: 0 z0
if z0/x True
omega - df ((-x^2 + z0)/x^2) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0*z1 + z0^2*z1 + z0^2) * dx, (z0*z1^2 - z0*z1 + z0)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? z0/x
z0/x q r: 0 z0
if z0/x True
omega - df ((x^2*z0^2 - x^2 + z0)/x^2) * dx
hol_form (z0^2) * dx
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0^2) * dx, (z0^2*z1 + z0^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (z0^2 - z1)/x
(z0^2 - z1)/x q r: 0 z0^2 - z1
if (z0^2 - z1)/x True
omega - df ((-x^4 + x^2*z0 + z0^2 - z1)/x^2) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0^2*z1 - x^2*z0^2 + z0*z1^2 - z0*z1 + z0) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (z0^2 - z1)/x
(z0^2 - z1)/x q r: 0 z0^2 - z1
if (z0^2 - z1)/x True
omega - df ((-x^4 - x^2*z0*z1 - x^2*z0 + z0^2 - z1)/x^2) * dx
hol_form (-z0*z1 + z0) * dx
(-z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2) * dx, (z1^2 - z1 + 1)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (-z1 + 1)/x^2
(-z1 + 1)/x^2 q r: 0 -z1 + 1
if (-z1 + 1)/x^2 True
omega - df ((-x^4 + z1 - 1)/x^3) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0*z1 - x*z0) * dx, (z0*z1^2 - z0*z1 + z0)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (-z0*z1 + z0)/x^2
(-z0*z1 + z0)/x^2 q r: 0 -z0*z1 + z0
if (-z0*z1 + z0)/x^2 True
omega - df ((x^4*z0 + x^2*z1 - x^2 + z0*z1 - z0)/x^3) * dx
hol_form (-x*z0) * dx
(-x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2*z1) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (-z0^2*z1 + z0^2 - z1^2)/x^2
(-z0^2*z1 + z0^2 - z1^2)/x^2 q r: 0 -z0^2*z1 + z0^2 - z1^2
if (-z0^2*z1 + z0^2 - z1^2)/x^2 False
omega - df ((-x^4*z0^2 + x^4*z1 - x^2*z0*z1 + x^2*z0 + z0^2*z1 - z0^2 + z1^2)/x^3) * dx
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [46], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:84, in coordinates(self, threshold, basis)
ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus()
[?7h[?12l[?25h[?2004l[?7h10
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(cc.omega0 - cc.f.diffn()).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
11 10
omega val 0
z1^2/x
11 10
omega val 12
z0*z1/x
11 10
omega val 6
z0*z1^2/x
11 10
omega val 2
z0^2*z1/x
11 10
omega val 0
z0^2*z1^2/x
11 10
omega val 0
z1^2/x^2
11 10
omega val 1
z0*z1^2/x^2
11 10
omega val 3
z0^2*z1^2/x^2
11 10
omega val 1
z0^2*z1^2/x^3
11 10
omega val 6
nowe!!!! ( (1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (1) * dx
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z1) * dx
hol_form (z1) * dx
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0 + 1) * dx
hol_form (z0 + 1) * dx
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0*z1 + z1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0*z1 + z1) * dx
hol_form (z0*z1 + z1) * dx
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0^2 - z0 + 1) * dx
hol_form (z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x) * dx
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (-x*z0^2 + x*z0 + x*z1 - x) * dx
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x*z0 + x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x*z0 + x) * dx
hol_form (x*z0 + x) * dx
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2) * dx
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (0) * dx, z1/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (0) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z1) * dx, z1^2/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (0) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + x^2) * dx, (z0*z1 + z1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2) * dx
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0*z1 + x^2*z0 - x^2*z1 + z0^2*z1 + x^2 - z0*z1 + z1) * dx, (z0*z1^2 + z1^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2 - z0*z1 + z1) * dx
hol_form (x^2 - z0*z1 + z1) * dx
(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0^2 - x^2*z0 + x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2) * dx
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0^2*z1 + x^2*z0*z1 - x^2*z1 + z0*z1^2 + z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2*z0 + z0^2*z1 + z1^2) * dx
hol_form (x^2*z0 + z0^2*z1 + z1^2) * dx
(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z0 - x) * dx, z1^2/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x*z0 - x) * dx
hol_form (x*z0 - x) * dx
(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0*z1 - x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x*z0^2 - x*z1) * dx
hol_form (x*z0^2 - x*z1) * dx
(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2*z1 + x*z0^2 + x*z0*z1 - x*z0 - x*z1 + x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x*z0^2 - x*z0 - x*z1 + x) * dx
hol_form (x*z0^2 - x*z0 - x*z1 + x) * dx
(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-z0^2*z1 + z0*z1 - z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (x^2*z1 - z0*z1^2 + z1^2)/x^3
(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2
if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True
omega - df ((x^4 - x^2*z0*z1 + x^2*z1 + z1^2 + z1)/x^2) * dx
hol_form (z0*z1 - z1) * dx
(z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (1) * dx
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z1 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z1 + 1) * dx
hol_form (z1 + 1) * dx
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx
hol_form (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0) * dx
hol_form (z0) * dx
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0*z1 + z0) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0*z1 + z0) * dx
hol_form (z0*z1 + z0) * dx
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (z0^2) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (z0^2) * dx
hol_form (z0^2) * dx
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x) * dx
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2 + x*z1 + x) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (-x*z0^2 + x*z1 + x) * dx
hol_form (-x*z0^2 + x*z1 + x) * dx
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x*z0) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x*z0) * dx
hol_form (x*z0) * dx
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2) * dx, 0 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 0
0 q r: 0 0
if 0 True
omega - df (x^2) * dx
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (0) * dx, (z1 + 1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 1/x
1/x q r: 0 1
if 1/x True
omega - df (1/x^2) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z1 - x^2) * dx, (z1^2 - z1 + 1)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? 1/x
1/x q r: 0 1
if 1/x True
omega - df ((-x^4 + 1)/x^2) * dx
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0) * dx, (z0*z1 + z0)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? z0/x
z0/x q r: 0 z0
if z0/x True
omega - df ((-x^2 + z0)/x^2) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0*z1 + z0^2*z1 + z0^2) * dx, (z0*z1^2 - z0*z1 + z0)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? z0/x
z0/x q r: 0 z0
if z0/x True
omega - df ((x^2*z0^2 - x^2 + z0)/x^2) * dx
hol_form (z0^2) * dx
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (x^2*z0^2) * dx, (z0^2*z1 + z0^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (z0^2 - z1)/x
(z0^2 - z1)/x q r: 0 z0^2 - z1
if (z0^2 - z1)/x True
omega - df ((-x^4 + x^2*z0 + z0^2 - z1)/x^2) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x^2*z0^2*z1 - x^2*z0^2 + z0*z1^2 - z0*z1 + z0) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (z0^2 - z1)/x
(z0^2 - z1)/x q r: 0 z0^2 - z1
if (z0^2 - z1)/x True
omega - df ((-x^4 - x^2*z0*z1 - x^2*z0 + z0^2 - z1)/x^2) * dx
hol_form (-z0*z1 + z0) * dx
(-z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2) * dx, (z1^2 - z1 + 1)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (-z1 + 1)/x^2
(-z1 + 1)/x^2 q r: 0 -z1 + 1
if (-z1 + 1)/x^2 True
omega - df ((-x^4 + z1 - 1)/x^3) * dx
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0*z1 - x*z0) * dx, (z0*z1^2 - z0*z1 + z0)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (-z0*z1 + z0)/x^2
(-z0*z1 + z0)/x^2 q r: 0 -z0*z1 + z0
if (-z0*z1 + z0)/x^2 True
omega - df ((x^4*z0 + x^2*z1 - x^2 + z0*z1 - z0)/x^3) * dx
hol_form (-x*z0) * dx
(-x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
nowe!!!! ( (-x*z0^2*z1) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^2 )
products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
? (-z0^2*z1 + z0^2 - z1^2)/x^2
(-z0^2*z1 + z0^2 - z1^2)/x^2 q r: 0 -z0^2*z1 + z0^2 - z1^2
if (-z0^2*z1 + z0^2 - z1^2)/x^2 False
omega - df ((-x^4*z0^2 + x^4*z1 - x^2*z0*z1 + x^2*z0 + z0^2*z1 - z0^2 + z1^2)/x^3) * dx
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [48], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:84, in coordinates(self, threshold, basis)
ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
omega val 0
z1^2/x
omega val 12
z0*z1/x
omega val 6
z0*z1^2/x
omega val 2
z0^2*z1/x
omega val 0
z0^2*z1^2/x
omega val 0
z1^2/x^2
omega val 1
z0*z1^2/x^2
omega val 3
z0^2*z1^2/x^2
omega val 1
z0^2*z1^2/x^3
omega val 6
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [49], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:77, in coordinates(self, threshold, basis)
ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lhomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7lsage: AS.cohomology_of_structure_sheaf_basis()[1]
[?7h[?12l[?25h[?2004l[?7hz1^2/x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i, f in enumerate(AS.cohomology_of_structure_sheaf_basis()):[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: for eta in AS.de_rham_basis():
....: [?7h[?12l[?25h[?25l[?7lprint(om.serre_duality_pairing(f))[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:  print(eta.omega0, eta.omega8.valuation())
....: [?7h[?12l[?25h[?25l[?7lsage: for eta in AS.de_rham_basis():
....:  print(eta.omega0, eta.omega8.valuation())
....: 
[?7h[?12l[?25h[?2004lz1/x
omega val 0
z1^2/x
omega val 12
z0*z1/x
omega val 6
z0*z1^2/x
omega val 2
z0^2*z1/x
omega val 0
z0^2*z1^2/x
omega val 0
z1^2/x^2
omega val 1
z0*z1^2/x^2
omega val 3
z0^2*z1^2/x^2
omega val 1
z0^2*z1^2/x^3
omega val 6
(1) * dx 18
(z1) * dx 6
(x^2*z0 + z0^2*z1 + z1^2) * dx 2
(z0) * dx 12
(z0*z1) * dx 0
(z0^2) * dx 6
(x) * dx 9
(-x*z0^2 + x*z1) * dx 1
(x*z0) * dx 3
(x^2) * dx 0
(0) * dx 0
(x^2*z1) * dx 12
(-x^2*z0) * dx 6
(x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx 2
(-x^2*z0^2) * dx 0
(x^2*z0^2*z1 - z0*z1^2) * dx 0
(x*z0^2) * dx 1
(x*z0*z1) * dx 3
(x*z0^2*z1 - x*z0^2) * dx 1
(z0^2*z1) * dx 6
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for eta in AS.de_rham_basis():
....:  print(eta.omega0, eta.omega8.valuation())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lAS.cohomology_ofstructure_sheaf_basis()[1]
 [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (z1) * dx
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (z0 + 1) * dx
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (z0*z1 + z1) * dx
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (x*z0 + x) * dx
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (-x^2 + z0*z1 - z1) * dx
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (-x^2*z0 - z0^2*z1 - z1^2) * dx
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (-x*z0 + x) * dx
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (-x*z0^2 + x*z1) * dx
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (-z0*z1 + z1) * dx
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (z1 + 1) * dx
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (z0) * dx
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (z0*z1 + z0) * dx
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (z0^2) * dx
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (-x*z0^2 + x*z1 + x) * dx
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (x*z0) * dx
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (-z0^2) * dx
(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (z0*z1 - z0) * dx
(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
hol_form (x*z0) * dx
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [52], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:78, in coordinates(self, threshold, basis)
ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lhlrphic_differential_bsis()[1].group_action([0, 1])[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lomorphic_differentials_basis()[1].group_action([0, 1])[?7h[?12l[?25h[?25l[?7l([][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls()[1].group_action([0, 1])[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis()
[?7h[?12l[?25h[?2004l[?7h[(1) * dx,
(z1) * dx,
(x^2*z0 + z0^2*z1 + z1^2) * dx,
(z0) * dx,
(z0*z1) * dx,
(z0^2) * dx,
(x) * dx,
(-x*z0^2 + x*z1) * dx,
(x*z0) * dx,
(x^2) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
( (1) * dx, 0 )
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (z1) * dx, 0 )
hol_form (z1) * dx
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (z0 + 1) * dx, 0 )
hol_form (z0 + 1) * dx
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (z0*z1 + z1) * dx, 0 )
hol_form (z0*z1 + z1) * dx
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (z0^2 - z0 + 1) * dx, 0 )
hol_form (z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (x) * dx, 0 )
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (x*z0 + x) * dx, 0 )
hol_form (x*z0 + x) * dx
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (x^2) * dx, 0 )
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (0) * dx, 0 )
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (0) * dx, 0 )
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (-x^2) * dx, 0 )
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (-x^2 + z0*z1 - z1) * dx, 0 )
hol_form (-x^2 + z0*z1 - z1) * dx
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (-x^2) * dx, 0 )
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (-x^2*z0 - z0^2*z1 - z1^2) * dx, 0 )
hol_form (-x^2*z0 - z0^2*z1 - z1^2) * dx
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (-x*z0 + x) * dx, 0 )
hol_form (-x*z0 + x) * dx
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (-x*z0^2 + x*z1) * dx, 0 )
hol_form (-x*z0^2 + x*z1) * dx
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (-z0*z1 + z1) * dx, (x^2*z1 - z0*z1^2 + z1^2)/x^3 )
hol_form (-z0*z1 + z1) * dx
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (1) * dx, 0 )
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (z1 + 1) * dx, 0 )
hol_form (z1 + 1) * dx
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 )
hol_form (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (z0) * dx, 0 )
hol_form (z0) * dx
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (z0*z1 + z0) * dx, 0 )
hol_form (z0*z1 + z0) * dx
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (z0^2) * dx, 0 )
hol_form (z0^2) * dx
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (x) * dx, 0 )
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (-x*z0^2 + x*z1 + x) * dx, 0 )
hol_form (-x*z0^2 + x*z1 + x) * dx
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (x*z0) * dx, 0 )
hol_form (x*z0) * dx
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (x^2) * dx, 0 )
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (0) * dx, 1/x )
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (x^2) * dx, 1/x )
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (0) * dx, z0/x )
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (-z0^2) * dx, z0/x )
hol_form (-z0^2) * dx
(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (0) * dx, (z0^2 - z1)/x )
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (z0*z1 - z0) * dx, (z0^2 - z1)/x )
hol_form (z0*z1 - z0) * dx
(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (0) * dx, (-z1 + 1)/x^2 )
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (x*z0) * dx, (-z0*z1 + z0)/x^2 )
hol_form (x*z0) * dx
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
( (0) * dx, (-z0^2*z1 + z0^2 - z1^2)/x^2 )
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [54], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:79, in coordinates(self, threshold, basis)
ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-z0^2*z1 + z0^2 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAx^2[?7h[?12l[?25h[?25l[?7lSx^2[?7h[?12l[?25h[?25l[?7l.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz1^2)/AS.x^2[?7h[?12l[?25h[?25l[?7lSz1^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l.z1^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz0^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7lSz0^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l.z0^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz0^2*z1 + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7lSz0^2*z1 + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l.z0^2*z1 + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0^2*z1 + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2*z1 + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz1 + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7lSz1 + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l.z1 + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1 + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (-AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [55], in <cell line: 1>()
----> 1 (-AS.z[Integer(0)]**Integer(2)*AS.z[Integer(1)] + AS.z[Integer(0)]**Integer(2) - AS.z[Integer(1)]**Integer(2))/AS.x**Integer(2)
TypeError: bad operand type for unary -: 'as_function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-1AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l()*AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((-1)*AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2
[?7h[?12l[?25h[?2004l[?7h(-z0^2*z1 + z0^2 - z1^2)/x^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-1)*AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lsage: (((-1)*AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2).expansion_at_infty()
[?7h[?12l[?25h[?2004l[?7ht^-6 + 2*t^2 + 2*t^10 + 2*t^14 + 2*t^18 + t^26 + 2*t^30 + 2*t^38 + 2*t^46 + 2*t^54 + t^58 + t^62 + t^66 + 2*t^78 + 2*t^90 + 2*t^94 + t^98 + 2*t^102 + t^118 + t^122 + 2*t^134 + 2*t^138 + 2*t^142 + 2*t^146 + 2*t^154 + t^158 + 2*t^162 + 2*t^166 + t^170 + 2*t^182 + 2*t^186 + t^190 + 2*t^202 + 2*t^206 + 2*t^218 + t^222 + t^230 + 2*t^234 + t^238 + t^246 + 2*t^250 + 2*t^262 + 2*t^266 + t^278 + 2*t^282 + t^286 + 2*t^298 + t^310 + 2*t^314 + 2*t^318 + t^326 + 2*t^330 + 2*t^334 + t^338 + 2*t^346 + t^350 + t^354 + t^370 + 2*t^374 + t^382 + 2*t^386 + t^390 + 2*t^394 + t^402 + 2*t^410 + 2*t^414 + t^418 + t^422 + t^426 + 2*t^434 + t^446 + 2*t^450 + t^458 + 2*t^462 + t^466 + 2*t^470 + 2*t^474 + 2*t^478 + 2*t^482 + 2*t^486 + t^490 + t^494 + t^498 + 2*t^510 + 2*t^514 + t^522 + 2*t^526 + 2*t^530 + 2*t^538 + 2*t^542 + 2*t^546 + 2*t^554 + 2*t^558 + 2*t^562 + 2*t^574 + 2*t^578 + 2*t^586 + 2*t^590 + 2*t^594 + 2*t^602 + 2*t^606 + 2*t^610 + t^618 + 2*t^622 + 2*t^638 + 2*t^642 + 2*t^650 + 2*t^654 + 2*t^670 + t^682 + 2*t^686 + 2*t^698 + 2*t^702 + t^714 + 2*t^718 + t^730 + 2*t^734 + t^746 + 2*t^750 + t^762 + 2*t^766 + 2*t^770 + t^778 + 2*t^782 + 2*t^786 + 2*t^798 + 2*t^802 + 2*t^814 + t^818 + t^826 + 2*t^830 + 2*t^834 + t^842 + 2*t^846 + 2*t^850 + t^858 + 2*t^862 + 2*t^866 + t^874 + 2*t^878 + 2*t^882 + t^890 + 2*t^894 + 2*t^898 + t^906 + 2*t^910 + t^914 + t^922 + 2*t^926 + t^930 + 2*t^942 + t^946 + 2*t^958 + 2*t^966 + t^970 + t^978 + t^982 + 2*t^986 + O(t^994)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: (((-1)*AS.z[0]^2*AS.z[1] + AS.z[0]^2)/AS.x^2).expansion_at_infty()
[?7h[?12l[?25h[?2004l[?7h2*t^-6 + 2*t^-2 + 2*t^6 + t^10 + 2*t^14 + t^18 + 2*t^22 + t^30 + 2*t^34 + 2*t^38 + t^46 + 2*t^50 + t^54 + 2*t^58 + t^70 + t^74 + t^82 + t^86 + t^90 + t^98 + 2*t^102 + 2*t^106 + t^114 + t^122 + 2*t^126 + 2*t^130 + t^134 + t^138 + 2*t^146 + t^154 + t^162 + t^166 + t^174 + t^178 + 2*t^182 + t^194 + t^198 + 2*t^206 + t^210 + 2*t^214 + t^222 + t^226 + t^242 + t^246 + t^258 + t^270 + t^274 + 2*t^278 + t^286 + t^290 + t^294 + t^302 + t^306 + 2*t^322 + 2*t^326 + t^330 + 2*t^338 + 2*t^342 + t^346 + t^350 + 2*t^358 + t^362 + 2*t^366 + t^374 + 2*t^378 + 2*t^382 + t^386 + 2*t^394 + t^398 + t^402 + t^406 + 2*t^410 + t^414 + t^418 + t^422 + 2*t^430 + t^434 + t^438 + t^442 + t^446 + 2*t^454 + 2*t^458 + t^462 + 2*t^470 + t^478 + t^486 + t^490 + t^502 + 2*t^506 + 2*t^514 + t^518 + t^534 + t^546 + t^550 + t^554 + t^566 + t^582 + t^586 + t^594 + t^598 + t^602 + t^610 + t^614 + 2*t^618 + t^626 + t^630 + t^642 + t^646 + t^650 + t^662 + 2*t^666 + t^674 + t^678 + t^694 + t^698 + 2*t^706 + t^710 + 2*t^722 + t^726 + 2*t^738 + t^742 + t^754 + t^758 + 2*t^762 + t^770 + t^774 + 2*t^778 + t^790 + 2*t^794 + t^806 + t^810 + 2*t^818 + t^822 + t^826 + 2*t^834 + t^838 + t^842 + 2*t^850 + t^854 + t^858 + 2*t^866 + t^870 + t^874 + 2*t^882 + t^886 + t^890 + t^898 + t^902 + t^914 + t^918 + t^934 + t^950 + 2*t^954 + 2*t^962 + 2*t^966 + 2*t^990 + O(t^994)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] + AS.z[0]^2)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l-1)*AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l-AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
---------------------------------------------------------------------------
IndexError Traceback (most recent call last)
Input In [59], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:55, in coordinates(self, threshold, basis)
IndexError: list assignment index out of range
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [60], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:61, in coordinates(self, threshold, basis)
File <string>:61, in <listcomp>(.0)
File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:493, in sage.modules.free_module_element.vector()
 491 pass
 492 else:
--> 493 v = arg0_vector_(arg1)
 494 if immutable:
 495 v.set_immutable()
TypeError: IntegerMod_int._vector_() takes no arguments (1 given)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [61], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:61, in coordinates(self, threshold, basis)
File <string>:61, in <listcomp>(.0)
File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:493, in sage.modules.free_module_element.vector()
 491 pass
 492 else:
--> 493 v = arg0_vector_(arg1)
 494 if immutable:
 495 v.set_immutable()
TypeError: IntegerMod_int._vector_() takes no arguments (1 given)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (1) * dx, 0 ) []
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z1) * dx, 0 ) []
hol_form (z1) * dx
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) []
hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0 + 1) * dx, 0 ) []
hol_form (z0 + 1) * dx
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0*z1 + z1) * dx, 0 ) []
hol_form (z0*z1 + z1) * dx
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0^2 - z0 + 1) * dx, 0 ) []
hol_form (z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x) * dx, 0 ) []
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) []
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x*z0 + x) * dx, 0 ) []
hol_form (x*z0 + x) * dx
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2) * dx, 0 ) []
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, 0 ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, 0 ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2) * dx, 0 ) []
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2 + z0*z1 - z1) * dx, 0 ) []
hol_form (-x^2 + z0*z1 - z1) * dx
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2) * dx, 0 ) []
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2*z0 - z0^2*z1 - z1^2) * dx, 0 ) []
hol_form (-x^2*z0 - z0^2*z1 - z1^2) * dx
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0 + x) * dx, 0 ) []
hol_form (-x*z0 + x) * dx
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z1) * dx, 0 ) []
hol_form (-x*z0^2 + x*z1) * dx
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) []
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-z0*z1 + z1) * dx, (x^2*z1 - z0*z1^2 + z1^2)/x^3 ) []
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [62], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:70, in coordinates(self, threshold, basis)
NameError: name 'v_f_den' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (1) * dx, 0 ) []
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce)
 705 try:
--> 706 x, y = resolve_fractions(x0, y0)
 707 except (AttributeError, TypeError):
File /ext/sage/9.7/src/sage/rings/fraction_field.py:683, in FractionField_generic._element_constructor_.<locals>.resolve_fractions(x, y)
 682 def resolve_fractions(x, y):
--> 683 xn = x.numerator()
 684 xd = x.denominator()
AttributeError: 'function' object has no attribute 'numerator'
During handling of the above exception, another exception occurred:
TypeError Traceback (most recent call last)
Input In [63], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:69, in coordinates(self, threshold, basis)
File <string>:14, in __init__(self, C, g)
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
 895 if mor is not None:
 896 if no_extra_args:
--> 897 return mor._call_(x)
 898 else:
 899 return mor._call_with_args(x, args, kwds)
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
 159 print(type(C), C)
 160 print(type(C._element_constructor), C._element_constructor)
--> 161 raise
 162
 163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
 154 cdef Parent C = self._codomain
 155 try:
--> 156 return C._element_constructor(x)
 157 except Exception:
 158 if print_warnings:
File /ext/sage/9.7/src/sage/rings/fraction_field.py:708, in FractionField_generic._element_constructor_(self, x, y, coerce)
 706 x, y = resolve_fractions(x0, y0)
 707 except (AttributeError, TypeError):
--> 708 raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
 709 x0, y0, self))
 710 try:
 711 return self._element_class(self, x, y, coerce=coerce)
TypeError: cannot convert <function denominator at 0x7f71d01e8820>/1 to an element of Fraction Field of Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (1) * dx, 0 ) []
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z1) * dx, 0 ) []
hol_form (z1) * dx
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) []
hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0 + 1) * dx, 0 ) []
hol_form (z0 + 1) * dx
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0*z1 + z1) * dx, 0 ) []
hol_form (z0*z1 + z1) * dx
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0^2 - z0 + 1) * dx, 0 ) []
hol_form (z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x) * dx, 0 ) []
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) []
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x*z0 + x) * dx, 0 ) []
hol_form (x*z0 + x) * dx
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2) * dx, 0 ) []
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, 0 ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, 0 ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2) * dx, 0 ) []
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2 + z0*z1 - z1) * dx, 0 ) []
hol_form (-x^2 + z0*z1 - z1) * dx
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2) * dx, 0 ) []
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2*z0 - z0^2*z1 - z1^2) * dx, 0 ) []
hol_form (-x^2*z0 - z0^2*z1 - z1^2) * dx
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0 + x) * dx, 0 ) []
hol_form (-x*z0 + x) * dx
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z1) * dx, 0 ) []
hol_form (-x*z0^2 + x*z1) * dx
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) []
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-z0*z1 + z1) * dx, (x^2*z1 - z0*z1^2 + z1^2)/x^3 ) []
hol_form (-z0*z1 + z1) * dx
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (1) * dx, 0 ) []
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z1 + 1) * dx, 0 ) []
hol_form (z1 + 1) * dx
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 ) []
hol_form (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0) * dx, 0 ) []
hol_form (z0) * dx
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0*z1 + z0) * dx, 0 ) []
hol_form (z0*z1 + z0) * dx
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0^2) * dx, 0 ) []
hol_form (z0^2) * dx
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x) * dx, 0 ) []
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z1 + x) * dx, 0 ) []
hol_form (-x*z0^2 + x*z1 + x) * dx
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x*z0) * dx, 0 ) []
hol_form (x*z0) * dx
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2) * dx, 0 ) []
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, 1/x ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2) * dx, 1/x ) []
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, z0/x ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-z0^2) * dx, z0/x ) []
hol_form (-z0^2) * dx
(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, (z0^2 - z1)/x ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0*z1 - z0) * dx, (z0^2 - z1)/x ) []
hol_form (z0*z1 - z0) * dx
(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, (-z1 + 1)/x^2 ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x*z0) * dx, (-z0*z1 + z0)/x^2 ) []
hol_form (x*z0) * dx
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, (-z0^2*z1 + z0^2 - z1^2)/x^2 ) []
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [64], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:82, in coordinates(self, threshold, basis)
ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] + AS.z[0]^2)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l - AS.z[1]^2)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] + AS.z[0]^2)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (1) * dx, 0 ) []
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z1) * dx, 0 ) []
hol_form (z1) * dx
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) []
hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0 + 1) * dx, 0 ) []
hol_form (z0 + 1) * dx
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0*z1 + z1) * dx, 0 ) []
hol_form (z0*z1 + z1) * dx
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0^2 - z0 + 1) * dx, 0 ) []
hol_form (z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x) * dx, 0 ) []
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) []
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x*z0 + x) * dx, 0 ) []
hol_form (x*z0 + x) * dx
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2) * dx, 0 ) []
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, 0 ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, 0 ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2) * dx, 0 ) []
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2 + z0*z1 - z1) * dx, 0 ) []
hol_form (-x^2 + z0*z1 - z1) * dx
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2) * dx, 0 ) []
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2*z0 - z0^2*z1 - z1^2) * dx, 0 ) []
hol_form (-x^2*z0 - z0^2*z1 - z1^2) * dx
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0 + x) * dx, 0 ) []
hol_form (-x*z0 + x) * dx
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z1) * dx, 0 ) []
hol_form (-x*z0^2 + x*z1) * dx
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) []
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-z0*z1 + z1) * dx, (x^2*z1 - z0*z1^2 + z1^2)/x^3 ) []
hol_form (-z0*z1 + z1) * dx
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (1) * dx, 0 ) []
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z1 + 1) * dx, 0 ) []
hol_form (z1 + 1) * dx
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 ) []
hol_form (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0) * dx, 0 ) []
hol_form (z0) * dx
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0*z1 + z0) * dx, 0 ) []
hol_form (z0*z1 + z0) * dx
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0^2) * dx, 0 ) []
hol_form (z0^2) * dx
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x) * dx, 0 ) []
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z1 + x) * dx, 0 ) []
hol_form (-x*z0^2 + x*z1 + x) * dx
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x*z0) * dx, 0 ) []
hol_form (x*z0) * dx
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2) * dx, 0 ) []
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, 1/x ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2) * dx, 1/x ) []
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, z0/x ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-z0^2) * dx, z0/x ) []
hol_form (-z0^2) * dx
(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, (z0^2 - z1)/x ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0*z1 - z0) * dx, (z0^2 - z1)/x ) []
hol_form (z0*z1 - z0) * dx
(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, (-z1 + 1)/x^2 ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x*z0) * dx, (-z0*z1 + z0)/x^2 ) []
hol_form (x*z0) * dx
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, (-z0^2*z1 + z0^2 - z1^2)/x^2 ) []
( (0) * dx, (-z0^2*z1 - z1^2)/x^2 )
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [65], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:83, in coordinates(self, threshold, basis)
ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.quo_rem(f)[?7h[?12l[?25h[?25l[?7lg =[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAx^2[?7h[?12l[?25h[?25l[?7lSx^2[?7h[?12l[?25h[?25l[?7l.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz1^2)/AS.x^2[?7h[?12l[?25h[?25l[?7lSz1^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l.z1^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lAz0^2*z1 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7lSz0^2*z1 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l.z0^2*z1 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0^2*z1 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2*z1 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz1 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7lSz1 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l/z1 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz1 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l.z1 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (-AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [66], in <cell line: 1>()
----> 1 (-AS.z[Integer(0)]**Integer(2)*AS.z[Integer(1)] - AS.z[Integer(1)]**Integer(2))/AS.x**Integer(2)
TypeError: bad operand type for unary -: 'as_function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l()AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-1)AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((-1)AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2
[?7h[?12l[?25h[?2004l Input In [67]
 ((-Integer(1))AS.z[Integer(0)]**Integer(2)*AS.z[Integer(1)] - AS.z[Integer(1)]**Integer(2))/AS.x**Integer(2)
 ^
SyntaxError: invalid syntax. Perhaps you forgot a comma?
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-1)AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7lsage: ((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2
[?7h[?12l[?25h[?2004l[?7h(-z0^2*z1 - z1^2)/x^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l2.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2.expansion_at_infty()
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [69], in <cell line: 1>()
----> 1 ((-Integer(1))*AS.z[Integer(0)]**Integer(2)*AS.z[Integer(1)] - AS.z[Integer(1)]**Integer(2))/AS.x**Integer(2).expansion_at_infty()
File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
 493 """
--> 494 return self.getattr_from_category(name)
 495
 496 cdef getattr_from_category(self, name):
File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
 505 else:
 506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
 508
 509 def __dir__(self):
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
 359 dummy_error_message.cls = type(self)
 360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
 362 attribute = <object>attr
 363 # Check for a descriptor (__get__ in Python)
AttributeError: 'sage.rings.integer.Integer' object has no attribute 'expansion_at_infty'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: (((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).expansion_at_infty()
[?7h[?12l[?25h[?2004l[?7ht^-6 + 2*t^2 + 2*t^6 + 2*t^10 + 2*t^14 + 2*t^18 + 2*t^22 + t^26 + 2*t^30 + t^38 + 2*t^42 + 2*t^46 + 2*t^54 + t^62 + t^66 + 2*t^74 + t^98 + 2*t^102 + t^106 + t^110 + 2*t^114 + t^118 + 2*t^122 + t^126 + 2*t^130 + 2*t^134 + 2*t^138 + t^146 + 2*t^154 + 2*t^158 + 2*t^162 + 2*t^166 + t^170 + t^174 + 2*t^182 + 2*t^190 + 2*t^198 + 2*t^214 + t^246 + 2*t^254 + 2*t^262 + 2*t^270 + t^278 + t^294 + 2*t^302 + 2*t^310 + t^318 + 2*t^326 + t^330 + t^334 + t^338 + t^342 + t^346 + t^354 + t^358 + 2*t^362 + 2*t^366 + t^370 + t^378 + 2*t^386 + t^390 + 2*t^398 + t^422 + 2*t^426 + t^430 + t^434 + 2*t^438 + t^442 + 2*t^446 + t^450 + 2*t^454 + 2*t^458 + 2*t^462 + t^470 + 2*t^474 + 2*t^478 + t^482 + 2*t^486 + t^490 + t^494 + t^514 + t^522 + t^530 + 2*t^538 + 2*t^546 + 2*t^554 + 2*t^562 + t^570 + 2*t^578 + 2*t^618 + t^626 + t^634 + t^658 + t^666 + t^674 + 2*t^682 + 2*t^762 + 2*t^770 + 2*t^778 + 2*t^786 + t^794 + 2*t^802 + 2*t^810 + t^818 + 2*t^906 + 2*t^914 + 2*t^922 + 2*t^930 + t^938 + 2*t^946 + 2*t^954 + t^962 + 2*t^966 + t^974 + t^978 + t^982 + t^986 + t^990 + O(t^994)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_atinfty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: (((-1)*AS.z[0]^2*AS.z[1])/AS.x^2).expansion_at_infty()
[?7h[?12l[?25h[?2004l[?7h2*t^-6 + 2*t^-2 + t^6 + t^10 + 2*t^14 + t^18 + t^22 + t^30 + 2*t^34 + t^38 + 2*t^42 + t^46 + 2*t^50 + t^54 + t^58 + t^70 + t^78 + t^82 + t^86 + 2*t^90 + t^94 + t^98 + 2*t^102 + t^110 + 2*t^122 + t^130 + t^134 + t^138 + t^142 + t^146 + t^154 + t^158 + t^162 + t^166 + 2*t^174 + t^178 + 2*t^182 + t^186 + t^190 + t^194 + t^202 + t^210 + t^214 + t^218 + t^226 + 2*t^230 + t^234 + 2*t^238 + t^242 + t^246 + t^250 + 2*t^254 + t^258 + t^266 + t^274 + 2*t^278 + t^282 + t^290 + 2*t^294 + t^298 + t^306 + t^310 + t^314 + 2*t^318 + 2*t^322 + 2*t^334 + 2*t^338 + t^366 + 2*t^374 + t^382 + t^386 + t^406 + 2*t^414 + t^422 + t^426 + 2*t^442 + 2*t^446 + 2*t^450 + t^454 + t^462 + 2*t^466 + t^470 + t^478 + 2*t^482 + t^486 + t^490 + 2*t^498 + t^502 + 2*t^506 + t^510 + t^514 + t^518 + t^526 + 2*t^530 + t^534 + t^542 + t^546 + t^550 + t^554 + t^558 + t^566 + t^570 + t^574 + t^582 + 2*t^586 + t^590 + 2*t^594 + t^598 + 2*t^602 + t^606 + 2*t^610 + t^614 + t^622 + 2*t^626 + t^630 + t^634 + t^638 + 2*t^642 + t^646 + 2*t^650 + t^654 + t^658 + t^662 + t^670 + 2*t^674 + t^678 + t^682 + t^686 + t^694 + 2*t^698 + t^702 + 2*t^706 + t^710 + 2*t^714 + t^718 + 2*t^722 + t^726 + 2*t^730 + t^734 + 2*t^738 + t^742 + 2*t^746 + t^750 + t^754 + t^758 + t^766 + t^770 + t^774 + t^782 + t^790 + t^798 + t^806 + t^814 + 2*t^818 + t^822 + t^830 + t^838 + t^846 + t^854 + t^862 + t^870 + t^878 + t^886 + t^894 + 2*t^898 + t^902 + t^906 + t^910 + 2*t^914 + t^918 + t^922 + t^926 + t^930 + t^934 + t^938 + t^942 + t^946 + t^950 + t^954 + t^958 + 2*t^966 + 2*t^970 + t^974 + 2*t^986 + O(t^994)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1])/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l - AS.z[1]^2)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).diffn()
[?7h[?12l[?25h[?2004l[?7h((x^4*z0^2 - x^4*z1 + x^2*z0*z1 - z0^2*z1 - z1^2)/x^3) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_nty()[?7h[?12l[?25h[?25l[?7l - AS.z[1]^2)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lAS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l-AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] + AS.z[0]^2)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (1) * dx, 0 ) []
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z1) * dx, 0 ) []
hol_form (z1) * dx
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) []
hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0 + 1) * dx, 0 ) []
hol_form (z0 + 1) * dx
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0*z1 + z1) * dx, 0 ) []
hol_form (z0*z1 + z1) * dx
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0^2 - z0 + 1) * dx, 0 ) []
hol_form (z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x) * dx, 0 ) []
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) []
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x*z0 + x) * dx, 0 ) []
hol_form (x*z0 + x) * dx
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2) * dx, 0 ) []
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, 0 ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, 0 ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2) * dx, 0 ) []
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2 + z0*z1 - z1) * dx, 0 ) []
hol_form (-x^2 + z0*z1 - z1) * dx
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2) * dx, 0 ) []
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2*z0 - z0^2*z1 - z1^2) * dx, 0 ) []
hol_form (-x^2*z0 - z0^2*z1 - z1^2) * dx
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0 + x) * dx, 0 ) []
hol_form (-x*z0 + x) * dx
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z1) * dx, 0 ) []
hol_form (-x*z0^2 + x*z1) * dx
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) []
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-z0*z1 + z1) * dx, (x^2*z1 - z0*z1^2 + z1^2)/x^3 ) []
hol_form (-z0*z1 + z1) * dx
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (1) * dx, 0 ) []
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z1 + 1) * dx, 0 ) []
hol_form (z1 + 1) * dx
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 ) []
hol_form (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0) * dx, 0 ) []
hol_form (z0) * dx
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0*z1 + z0) * dx, 0 ) []
hol_form (z0*z1 + z0) * dx
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0^2) * dx, 0 ) []
hol_form (z0^2) * dx
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x) * dx, 0 ) []
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z1 + x) * dx, 0 ) []
hol_form (-x*z0^2 + x*z1 + x) * dx
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x*z0) * dx, 0 ) []
hol_form (x*z0) * dx
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2) * dx, 0 ) []
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, 1/x ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2) * dx, 1/x ) []
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, z0/x ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-z0^2) * dx, z0/x ) []
hol_form (-z0^2) * dx
(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, (z0^2 - z1)/x ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0*z1 - z0) * dx, (z0^2 - z1)/x ) []
hol_form (z0*z1 - z0) * dx
(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, (-z1 + 1)/x^2 ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x*z0) * dx, (-z0*z1 + z0)/x^2 ) []
hol_form (x*z0) * dx
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, (-z0^2*z1 + z0^2 - z1^2)/x^2 ) []
( (0) * dx, (-z0^2*z1 - z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [73], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:83, in coordinates(self, threshold, basis)
ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_nty()[?7h[?12l[?25h[?25l[?7l - AS.z[1]^2)/AS.x^2).dfn()[?7h[?12l[?25h[?25l[?7lsage: (((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).diffn()
[?7h[?12l[?25h[?2004l[?7h((x^4*z0^2 - x^4*z1 + x^2*z0*z1 - z0^2*z1 - z1^2)/x^3) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (1) * dx, 0 ) []
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z1) * dx, 0 ) []
hol_form (z1) * dx
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) []
hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0 + 1) * dx, 0 ) []
hol_form (z0 + 1) * dx
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0*z1 + z1) * dx, 0 ) []
hol_form (z0*z1 + z1) * dx
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0^2 - z0 + 1) * dx, 0 ) []
hol_form (z0^2 - z0 + 1) * dx
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x) * dx, 0 ) []
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) []
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x*z0 + x) * dx, 0 ) []
hol_form (x*z0 + x) * dx
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2) * dx, 0 ) []
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, 0 ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, 0 ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2) * dx, 0 ) []
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2 + z0*z1 - z1) * dx, 0 ) []
hol_form (-x^2 + z0*z1 - z1) * dx
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2) * dx, 0 ) []
hol_form (-x^2) * dx
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x^2*z0 - z0^2*z1 - z1^2) * dx, 0 ) []
hol_form (-x^2*z0 - z0^2*z1 - z1^2) * dx
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0 + x) * dx, 0 ) []
hol_form (-x*z0 + x) * dx
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z1) * dx, 0 ) []
hol_form (-x*z0^2 + x*z1) * dx
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) []
hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-z0*z1 + z1) * dx, (x^2*z1 - z0*z1^2 + z1^2)/x^3 ) []
hol_form (-z0*z1 + z1) * dx
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (1) * dx, 0 ) []
hol_form (1) * dx
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z1 + 1) * dx, 0 ) []
hol_form (z1 + 1) * dx
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 ) []
hol_form (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0) * dx, 0 ) []
hol_form (z0) * dx
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0*z1 + z0) * dx, 0 ) []
hol_form (z0*z1 + z0) * dx
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0^2) * dx, 0 ) []
hol_form (z0^2) * dx
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x) * dx, 0 ) []
hol_form (x) * dx
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-x*z0^2 + x*z1 + x) * dx, 0 ) []
hol_form (-x*z0^2 + x*z1 + x) * dx
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x*z0) * dx, 0 ) []
hol_form (x*z0) * dx
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2) * dx, 0 ) []
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, 1/x ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x^2) * dx, 1/x ) []
hol_form (x^2) * dx
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, z0/x ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (-z0^2) * dx, z0/x ) []
hol_form (-z0^2) * dx
(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, (z0^2 - z1)/x ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (z0*z1 - z0) * dx, (z0^2 - z1)/x ) []
hol_form (z0*z1 - z0) * dx
(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, (-z1 + 1)/x^2 ) []
hol_form (0) * dx
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (x*z0) * dx, (-z0*z1 + z0)/x^2 ) []
hol_form (x*z0) * dx
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, (-z0^2*z1 + z0^2 - z1^2)/x^2 ) []
( (0) * dx, (-z0^2*z1 - z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [1], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:85, in coordinates(self, threshold, basis)
ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7lSz0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-ASz0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1ASz0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l()ASz0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l()*ASz0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7lSz1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l.z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[] - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz1^2)/x^2[?7h[?12l[?25h[?25l[?7lSz1^2)/x^2[?7h[?12l[?25h[?25l[?7l.z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2)/x^2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lAx^2[?7h[?12l[?25h[?25l[?7lSx^2[?7h[?12l[?25h[?25l[?7l.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: ((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2.expansion_at_infty()
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [2], in <cell line: 1>()
----> 1 ((-Integer(1))*AS.z[Integer(0)]**Integer(2)*AS.z[Integer(1)] - AS.z[Integer(1)]**Integer(2))/AS.x**Integer(2).expansion_at_infty()
File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
 493 """
--> 494 return self.getattr_from_category(name)
 495
 496 cdef getattr_from_category(self, name):
File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
 505 else:
 506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
 508
 509 def __dir__(self):
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
 359 dummy_error_message.cls = type(self)
 360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
 362 attribute = <object>attr
 363 # Check for a descriptor (__get__ in Python)
AttributeError: 'sage.rings.integer.Integer' object has no attribute 'expansion_at_infty'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: ((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2
[?7h[?12l[?25h[?2004l[?7h(-z0^2*z1 - z1^2)/x^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2.)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().diffn()[?7h[?12l[?25h[?25l[?7lexpasion_at_infty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).diffn()
[?7h[?12l[?25h[?2004l[?7h((x^4*z0^2 - x^4*z1 + x^2*z0*z1 - z0^2*z1 - z1^2)/x^3) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis()
[?7h[?12l[?25h[?2004l[?7h[(1) * dx,
(z1) * dx,
(x^2*z0 + z0^2*z1 + z1^2) * dx,
(z0) * dx,
(z0*z1) * dx,
(z0^2) * dx,
(x) * dx,
(-x*z0^2 + x*z1) * dx,
(x*z0) * dx,
(x^2) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lv()[?7h[?12l[?25h[?25l[?7la()[?7h[?12l[?25h[?25l[?7ll()[?7h[?12l[?25h[?25l[?7lu()[?7h[?12l[?25h[?25l[?7la()[?7h[?12l[?25h[?25l[?7lt()[?7h[?12l[?25h[?25l[?7li()[?7h[?12l[?25h[?25l[?7lo()[?7h[?12l[?25h[?25l[?7ln()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (((-1)*AS.z[0]^2*AS.z[1])/AS.x^2).valuation()
[?7h[?12l[?25h[?2004l[?7h-6
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1])/AS.x^2).valuation()[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l[- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l[]- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l[- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l()- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l(- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7lsage: ((- AS.z[1]^2)/AS.x^2).diffn()
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [7], in <cell line: 1>()
----> 1 ((- AS.z[Integer(1)]**Integer(2))/AS.x**Integer(2)).diffn()
TypeError: bad operand type for unary -: 'as_function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((- AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1 AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l() AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l()* AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (((-1)* AS.z[1]^2)/AS.x^2).diffn()
[?7h[?12l[?25h[?2004l[?7h((-x^4*z1 - z1^2)/x^3) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-1)* AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (((-1)* AS.z[1]^2)/AS.x^2).valuation()
[?7h[?12l[?25h[?2004l[?7h-6
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lsage: p
[?7h[?12l[?25h[?2004l[?7h3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS
[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7lf(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l (-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l=(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l (-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7la(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7las(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7las_(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7lf(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7lu(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7ln(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7lc(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7lt(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7li(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7lo(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7ln(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l((-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7lA(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7lS(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l,(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l (-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lxf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lyf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lzf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lQf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l,f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lRf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lxf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lyf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lzf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l,f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lxf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l,f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lyf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l,f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lzf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l=f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lAf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lSf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l.f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lcf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7ltf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l_f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lif = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lef = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7llf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7ldf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l(f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l()f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l();f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: RxyzQ, Rxyz, x, y,z = AS.fct_field(); ff = as_function(AS, (-z0^2*z1 - z1^2)/x^2)
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [12], in <cell line: 1>()
----> 1 RxyzQ, Rxyz, x, y,z = AS.fct_field(); ff = as_function(AS, (-z0**Integer(2)*z1 - z1**Integer(2))/x**Integer(2))
TypeError: 'tuple' object is not callable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field(); ff = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(; f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l; f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lsage: RxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-z0^2*z1 - z1^2)/x^2)
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [13], in <cell line: 1>()
----> 1 RxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-z0**Integer(2)*z1 - z1**Integer(2))/x**Integer(2))
NameError: name 'z0' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[] - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1^2)/x^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2)/x^2)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*z[1] - z[1]^2)/x^2)[?7h[?12l[?25h[?25l[?7l3*z[1] - z[1]^2)/x^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lz[1]^2)/x^2)[?7h[?12l[?25h[?25l[?7l[z[1]^2)/x^2)[?7h[?12l[?25h[?25l[?7l[]z[1]^2)/x^2)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l0]z[1]^2)/x^2)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[]*z[1]^2)/x^2)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(x^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l*))[?7h[?12l[?25h[?25l[?7lz))[?7h[?12l[?25h[?25l[?7l[))[?7h[?12l[?25h[?25l[?7l0))[?7h[?12l[?25h[?25l[?7l]))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: RxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-z[0]^3*z[1] - z[0]*z[1]^2)/(x^2*z[0]))
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor eta in AS.de_rham_basis():[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor eta in AS.de_rham_basis():[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7las[?7h[?12l[?25h[?25l[?7las_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7las[?7h[?12l[?25h[?25l[?7las_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(),[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fff = as_cech(AS, as_form(AS, 0), ff)
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: fff.
 fff.coordinates fff.group_action
 fff.curve fff.omega0 
 fff.f fff.omega8 
 [?7h[?12l[?25h[?25l[?7lcoordinates
 fff.coordinates 
 <unknown> [?7h[?12l[?25h[?25l[?7l



[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fff.coordinates()
[?7h[?12l[?25h[?2004lz1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, (-z0^2*z1 - z1^2)/x^2 ) []
( (0) * dx, (-z0^2*z1 - z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [16], in <cell line: 1>()
----> 1 fff.coordinates()
File <string>:85, in coordinates(self, threshold, basis)
ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7l = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-z[0]^3*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7lfff = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS
[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lfct_field[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7l = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-z[0]^3*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l(z[0]^3*z[1] - z[0]*z[1]^2)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()*z[1] - z[0]*z[1]^2)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l+)*z[1] - z[0]*z[1]^2)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7lx)*z[1] - z[0]*z[1]^2)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l^)*z[1] - z[0]*z[1]^2)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l2)*z[1] - z[0]*z[1]^2)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l[]+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: RxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0]))
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7l = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lsage: fff = as_cech(AS, as_form(AS, 0), ff)
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7l = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-z[0]^3*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7l0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l(); ff= as_function(AS, (-z0^2*z1- z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l(((-1)* AS.z[1]^2)/AS.x^2).valuation()[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7l(-1)*AS.z[0]^2*AS.z[1])/AS.x^2).valuation()[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1])/AS.x^2).valuation()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7l(-1)* AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7lvaluation()[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field(); ff = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l; ff =as_function(AS, (-z0^2*z1 -z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l[0]^3*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7lfff = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7lfff = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: fff.coordinates()
[?7h[?12l[?25h[?2004lz1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, (-x^2*z1 - z0*z1^2 - z0*z1)/(x^2*z0) ) []
( (0) * dx, (-x^2*z1 - z0*z1^2)/(x^2*z0) ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [20], in <cell line: 1>()
----> 1 fff.coordinates()
File <string>:85, in coordinates(self, threshold, basis)
ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7l = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: RxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0]))
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS
[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]^ - z[0]*z[1]^2)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l2 - z[0]*z[1]^2)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l(()/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l(())/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lz))/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l[))/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l]))/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l1])/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l+))/(x^2*z[0])[?7h[?12l[?25h[?25l[?7lx))/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l^))/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l4))/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l*))[?7h[?12l[?25h[?25l[?7lz))[?7h[?12l[?25h[?25l[?7l[))[?7h[?12l[?25h[?25l[?7l1))[?7h[?12l[?25h[?25l[?7l]))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: RxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1]^2 - z[0]*(z[1]+x^4))/(x^2*z[0]*z[1]))
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1]^2 - z[0]*(z[1]+x^4))/(x^2*z[0]*z[1]))[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7l = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lsage: fff = as_cech(AS, as_form(AS, 0), ff)
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lsage: fff.coordinates()
[?7h[?12l[?25h[?2004lz1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
( (0) * dx, (-x^4*z0 - x^2*z1^2 - z0*z1^2 - z0*z1)/(x^2*z0*z1) ) []
( (0) * dx, (-x^2*z0 - z1^2)/(z0*z1) ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [25], in <cell line: 1>()
----> 1 fff.coordinates()
File <string>:85, in coordinates(self, threshold, basis)
ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen.
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()
[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd ..
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -u
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git commit -cm "praca nad as_cech coordinate; przed poprawa drugiej czecsci"
[master d77adde] praca nad as_cech coordinate; przed poprawa drugiej czesci
5 files changed, 11731 insertions(+), 54 deletions(-)
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git push
Username for 'https://git.wmi.amu.edu.pl': jgare  rnek
Password for 'https://jgarnek@git.wmi.amu.edu.pl':
Enumerating objects: 35, done.
Counting objects: 2% (1/35) Counting objects: 5% (2/35) Counting objects: 8% (3/35) Counting objects: 11% (4/35) Counting objects: 14% (5/35) Counting objects: 17% (6/35) Counting objects: 20% (7/35) Counting objects: 22% (8/35) Counting objects: 25% (9/35) Counting objects: 28% (10/35) Counting objects: 31% (11/35) Counting objects: 34% (12/35) Counting objects: 37% (13/35) Counting objects: 40% (14/35) Counting objects: 42% (15/35) Counting objects: 45% (16/35) Counting objects: 48% (17/35) Counting objects: 51% (18/35) Counting objects: 54% (19/35) Counting objects: 57% (20/35) Counting objects: 60% (21/35) Counting objects: 62% (22/35) Counting objects: 65% (23/35) Counting objects: 68% (24/35) Counting objects: 71% (25/35) Counting objects: 74% (26/35) Counting objects: 77% (27/35) Counting objects: 80% (28/35) Counting objects: 82% (29/35) Counting objects: 85% (30/35) Counting objects: 88% (31/35) Counting objects: 91% (32/35) Counting objects: 94% (33/35) Counting objects: 97% (34/35) Counting objects: 100% (35/35) Counting objects: 100% (35/35), done.
Delta compression using up to 4 threads
Compressing objects: 4% (1/23) Compressing objects: 8% (2/23) Compressing objects: 13% (3/23) Compressing objects: 17% (4/23) Compressing objects: 21% (5/23) Compressing objects: 26% (6/23) Compressing objects: 30% (7/23) Compressing objects: 34% (8/23) Compressing objects: 39% (9/23) Compressing objects: 43% (10/23) Compressing objects: 47% (11/23) Compressing objects: 52% (12/23) Compressing objects: 56% (13/23) Compressing objects: 60% (14/23) Compressing objects: 65% (15/23) Compressing objects: 69% (16/23) Compressing objects: 73% (17/23) Compressing objects: 78% (18/23) Compressing objects: 82% (19/23) Compressing objects: 86% (20/23) Compressing objects: 91% (21/23) Compressing objects: 95% (22/23) Compressing objects: 100% (23/23) Compressing objects: 100% (23/23), done.
Writing objects: 4% (1/23) Writing objects: 8% (2/23) Writing objects: 13% (3/23) Writing objects: 17% (4/23) Writing objects: 21% (5/23) Writing objects: 26% (6/23) Writing objects: 30% (7/23) Writing objects: 34% (8/23) Writing objects: 39% (9/23) Writing objects: 43% (10/23) Writing objects: 47% (11/23) Writing objects: 52% (12/23) Writing objects: 56% (13/23) Writing objects: 60% (14/23) Writing objects: 65% (15/23) Writing objects: 69% (16/23) Writing objects: 73% (17/23) Writing objects: 78% (18/23) Writing objects: 82% (19/23) Writing objects: 86% (20/23) Writing objects: 91% (21/23) Writing objects: 95% (22/23) Writing objects: 100% (23/23) Writing objects: 100% (23/23), 66.79 KiB | 250.00 KiB/s, done.
Total 23 (delta 19), reused 0 (delta 0)
remote: . Processing 1 references
remote: Processed 1 references in total
To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git
c098f37..d77adde master -> master
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ sacd sage/
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7l = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1]^2 - z[0]*(z[1]+x^4))/(x^2*z[0]*z[1]))[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7l = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7l = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-z[0]^3*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7l0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l(); ff= as_function(AS, (-z0^2*z1- z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l(((-1)* AS.z[1]^2)/AS.x^2).valuation()[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7l(-1)*AS.z[0]^2*AS.z[1])/AS.x^2).valuation()[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7l-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [1], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:83, in coordinates(self, threshold, basis)
AttributeError: 'as_cech' object has no attribute 'form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [2], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:69, in coordinates(self, threshold, basis)
File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
 1962 return y
 1963
-> 1964 return coercion_model.bin_op(left, right, operator.mul)
 1965
 1966 cpdef _mul_(self, right):
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
 1240 mul_method = getattr(y, '__r%s__'%op_name, None)
 1241 if mul_method is not None:
-> 1242 res = mul_method(x)
 1243 if res is not None and res is not NotImplemented:
 1244 return res
File /ext/sage/9.7/src/sage/structure/parent.pyx:989, in sage.structure.parent.Parent.__mul__()
 987 pass
 988 if _mul_ is None:
--> 989 raise TypeError(_LazyString("For implementing multiplication, provide the method '_mul_' for %s resp. %s", (self, x), {}))
 990 if switch:
 991 return _mul_(self, switch_sides=True)
TypeError: For implementing multiplication, provide the method '_mul_' for 10 resp. R Interpreter
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [3], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:74, in coordinates(self, threshold, basis)
NameError: name 'pr' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [4], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:72, in coordinates(self, threshold, basis)
TypeError: 'function' object cannot be interpreted as an integer
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
---------------------------------------------------------------------------
UnboundLocalError Traceback (most recent call last)
Input In [5], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:9, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:79, in coordinates(self, threshold, basis)
UnboundLocalError: local variable 'S' referenced before assignment
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
z1/x
z1^2/x
z0*z1/x
z0*z1^2/x
z0^2*z1/x
z0^2*z1^2/x
z1^2/x^2
z0*z1^2/x^2
z0^2*z1^2/x^2
z0^2*z1^2/x^3
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [6], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:30, in group_action_matrices_dR(AS, threshold)
File <string>:10, in group_action_matrices(space, list_of_group_elements, basis)
File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:580, in sage.modules.free_module_element.vector()
 578 sparse = False
 579
--> 580 v, R = prepare(v, R, degree)
 581
 582 M = FreeModule(R, len(v), bool(sparse))
File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:678, in sage.modules.free_module_element.prepare()
 676 except TypeError:
 677 pass
--> 678 v = Sequence(v, universe=R, use_sage_types=True)
 679 ring = v.universe()
 680 if not is_Ring(ring):
File /ext/sage/9.7/src/sage/structure/sequence.py:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types)
 230 if universe is None:
 231 orig_x = x
--> 232 x = list(x) # make a copy even if x is a list, we're going to change it
 234 if len(x) == 0:
 235 from sage.categories.objects import Objects
TypeError: 'NoneType' object is not iterable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 0 0 0 0 0 0 0]
[0 1 1 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 2 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 1 0 0 0 0 0 0]
[0 1 1 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 0]
[0 0 2 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 1 0 0 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0]]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [7], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:31, in group_action_matrices_dR(AS, threshold)
File <string>:11, in group_action_matrices(space, list_of_group_elements, basis)
File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:580, in sage.modules.free_module_element.vector()
 578 sparse = False
 579
--> 580 v, R = prepare(v, R, degree)
 581
 582 M = FreeModule(R, len(v), bool(sparse))
File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:678, in sage.modules.free_module_element.prepare()
 676 except TypeError:
 677 pass
--> 678 v = Sequence(v, universe=R, use_sage_types=True)
 679 ring = v.universe()
 680 if not is_Ring(ring):
File /ext/sage/9.7/src/sage/structure/sequence.py:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types)
 230 if universe is None:
 231 orig_x = x
--> 232 x = list(x) # make a copy even if x is a list, we're going to change it
 234 if len(x) == 0:
 235 from sage.categories.objects import Objects
TypeError: 'NoneType' object is not iterable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 0 [[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 0 0 [[1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 1 [[1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 0 1 [[1 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 2 [[1 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 0 2 [[1 0 0 0 0 0 0 0 0 0]
[0 1 1 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 2 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 3 [[1 0 0 0 0 0 0 0 0 0]
[0 1 1 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 2 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 0 3 [[1 0 0 1 0 0 0 0 0 0]
[0 1 1 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 0]
[0 0 2 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 4 [[1 0 0 1 0 0 0 0 0 0]
[0 1 1 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 0]
[0 0 2 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 0 4 [[1 0 0 1 0 0 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 5 [[1 0 0 1 0 0 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 0 5 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 6 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 0 6 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 7 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 0 7 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 8 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 0 8 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 9 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 0], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 0 9 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
1 0 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 1 0 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
1 1 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 1 1 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
1 2 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 1 2 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
1 3 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 1 3 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
1 4 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 1 4 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
1 5 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 1 5 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
1 6 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 1 6 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
1 7 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 1 7 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
1 8 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 1 8 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0]]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
1 9 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0]]
2: 1 9 [[1 0 0 1 0 1 0 0 0 0]
[0 1 1 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 2 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 2 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1], [1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1]]
[
RModule of dimension 1 over GF(3),
RModule of dimension 3 over GF(3),
RModule of dimension 6 over GF(3)
]
None
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
0 19 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [8], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:32, in group_action_matrices_dR(AS, threshold)
File <string>:11, in group_action_matrices(space, list_of_group_elements, basis)
File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:580, in sage.modules.free_module_element.vector()
 578 sparse = False
 579
--> 580 v, R = prepare(v, R, degree)
 581
 582 M = FreeModule(R, len(v), bool(sparse))
File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:678, in sage.modules.free_module_element.prepare()
 676 except TypeError:
 677 pass
--> 678 v = Sequence(v, universe=R, use_sage_types=True)
 679 ring = v.universe()
 680 if not is_Ring(ring):
File /ext/sage/9.7/src/sage/structure/sequence.py:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types)
 230 if universe is None:
 231 orig_x = x
--> 232 x = list(x) # make a copy even if x is a list, we're going to change it
 234 if len(x) == 0:
 235 from sage.categories.objects import Objects
TypeError: 'NoneType' object is not iterable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
2: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
0 19 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [9], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:32, in group_action_matrices_dR(AS, threshold)
File <string>:11, in group_action_matrices(space, list_of_group_elements, basis)
File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:580, in sage.modules.free_module_element.vector()
 578 sparse = False
 579
--> 580 v, R = prepare(v, R, degree)
 581
 582 M = FreeModule(R, len(v), bool(sparse))
File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:678, in sage.modules.free_module_element.prepare()
 676 except TypeError:
 677 pass
--> 678 v = Sequence(v, universe=R, use_sage_types=True)
 679 ring = v.universe()
 680 if not is_Ring(ring):
File /ext/sage/9.7/src/sage/structure/sequence.py:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types)
 230 if universe is None:
 231 orig_x = x
--> 232 x = list(x) # make a copy even if x is a list, we're going to change it
 234 if len(x) == 0:
 235 from sage.categories.objects import Objects
TypeError: 'NoneType' object is not iterable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
0 19 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
None
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [10], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:34, in group_action_matrices_dR(AS, threshold)
File <string>:13, in group_action_matrices(space, list_of_group_elements, basis)
File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:580, in sage.modules.free_module_element.vector()
 578 sparse = False
 579
--> 580 v, R = prepare(v, R, degree)
 581
 582 M = FreeModule(R, len(v), bool(sparse))
File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:678, in sage.modules.free_module_element.prepare()
 676 except TypeError:
 677 pass
--> 678 v = Sequence(v, universe=R, use_sage_types=True)
 679 ring = v.universe()
 680 if not is_Ring(ring):
File /ext/sage/9.7/src/sage/structure/sequence.py:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types)
 230 if universe is None:
 231 orig_x = x
--> 232 x = list(x) # make a copy even if x is a list, we're going to change it
 234 if len(x) == 0:
 235 from sage.categories.objects import Objects
TypeError: 'NoneType' object is not iterable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
[0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
0 19 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
None
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [11], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:34, in group_action_matrices_dR(AS, threshold)
File <string>:13, in group_action_matrices(space, list_of_group_elements, basis)
File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:580, in sage.modules.free_module_element.vector()
 578 sparse = False
 579
--> 580 v, R = prepare(v, R, degree)
 581
 582 M = FreeModule(R, len(v), bool(sparse))
File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:678, in sage.modules.free_module_element.prepare()
 676 except TypeError:
 677 pass
--> 678 v = Sequence(v, universe=R, use_sage_types=True)
 679 ring = v.universe()
 680 if not is_Ring(ring):
File /ext/sage/9.7/src/sage/structure/sequence.py:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types)
 230 if universe is None:
 231 orig_x = x
--> 232 x = list(x) # make a copy even if x is a list, we're going to change it
 234 if len(x) == 0:
 235 from sage.categories.objects import Objects
TypeError: 'NoneType' object is not iterable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
[1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
[0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
[1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
[0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
[0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
[0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
2: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3]
0 19 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2*z1) * dx, z0^2*z1^2/x^3 ) ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) None
None
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
[0]
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [12], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:34, in group_action_matrices_dR(AS, threshold)
File <string>:13, in group_action_matrices(space, list_of_group_elements, basis)
File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:580, in sage.modules.free_module_element.vector()
 578 sparse = False
 579
--> 580 v, R = prepare(v, R, degree)
 581
 582 M = FreeModule(R, len(v), bool(sparse))
File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:678, in sage.modules.free_module_element.prepare()
 676 except TypeError:
 677 pass
--> 678 v = Sequence(v, universe=R, use_sage_types=True)
 679 ring = v.universe()
 680 if not is_Ring(ring):
File /ext/sage/9.7/src/sage/structure/sequence.py:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types)
 230 if universe is None:
 231 orig_x = x
--> 232 x = list(x) # make a copy even if x is a list, we're going to change it
 234 if len(x) == 0:
 235 from sage.categories.objects import Objects
TypeError: 'NoneType' object is not iterable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
mm: 0 19 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2*z1) * dx, z0^2*z1^2/x^3 ) ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) None
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [13], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:31, in group_action_matrices_dR(AS, threshold)
File <string>:11, in group_action_matrices(space, list_of_group_elements, basis)
File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:580, in sage.modules.free_module_element.vector()
 578 sparse = False
 579
--> 580 v, R = prepare(v, R, degree)
 581
 582 M = FreeModule(R, len(v), bool(sparse))
File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:678, in sage.modules.free_module_element.prepare()
 676 except TypeError:
 677 pass
--> 678 v = Sequence(v, universe=R, use_sage_types=True)
 679 ring = v.universe()
 680 if not is_Ring(ring):
File /ext/sage/9.7/src/sage/structure/sequence.py:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types)
 230 if universe is None:
 231 orig_x = x
--> 232 x = list(x) # make a copy even if x is a list, we're going to change it
 234 if len(x) == 0:
 235 from sage.categories.objects import Objects
TypeError: 'NoneType' object is not iterable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
nowe: ( (1) * dx, 0 )
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
nowe: ( (z1) * dx, 0 )
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
nowe: ( (z0 + 1) * dx, 0 )
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
nowe: ( (z0*z1 + z1) * dx, 0 )
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
nowe: ( (z0^2 - z0 + 1) * dx, 0 )
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
nowe: ( (x) * dx, 0 )
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
nowe: ( (x*z0 + x) * dx, 0 )
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
nowe: ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
nowe: ( (0) * dx, z1/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
nowe: ( (x^2*z1) * dx, z1^2/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x )
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 )
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
mm: 0 19 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2*z1) * dx, z0^2*z1^2/x^3 ) ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) None
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [14], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:31, in group_action_matrices_dR(AS, threshold)
File <string>:11, in group_action_matrices(space, list_of_group_elements, basis)
File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:580, in sage.modules.free_module_element.vector()
 578 sparse = False
 579
--> 580 v, R = prepare(v, R, degree)
 581
 582 M = FreeModule(R, len(v), bool(sparse))
File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:678, in sage.modules.free_module_element.prepare()
 676 except TypeError:
 677 pass
--> 678 v = Sequence(v, universe=R, use_sage_types=True)
 679 ring = v.universe()
 680 if not is_Ring(ring):
File /ext/sage/9.7/src/sage/structure/sequence.py:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types)
 230 if universe is None:
 231 orig_x = x
--> 232 x = list(x) # make a copy even if x is a list, we're going to change it
 234 if len(x) == 0:
 235 from sage.categories.objects import Objects
TypeError: 'NoneType' object is not iterable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
( (1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (1) * dx, 0 )
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z1) * dx, 0 )
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
( (z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0 + 1) * dx, 0 )
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
( (z0*z1 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0*z1 + z1) * dx, 0 )
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
( (z0^2 - z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0^2 - z0 + 1) * dx, 0 )
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
( (x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x) * dx, 0 )
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (x*z0 + x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x*z0 + x) * dx, 0 )
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
( (x^2) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
( (0) * dx, z1/x ) <class '__main__.as_cech'>
nowe: ( (0) * dx, z1/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z1) * dx, z1^2/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z1) * dx, z1^2/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x )
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 )
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) <class '__main__.as_cech'>
nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
mm: 0 19 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2*z1) * dx, z0^2*z1^2/x^3 ) ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) None
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [15], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:32, in group_action_matrices_dR(AS, threshold)
File <string>:12, in group_action_matrices(space, list_of_group_elements, basis)
File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:580, in sage.modules.free_module_element.vector()
 578 sparse = False
 579
--> 580 v, R = prepare(v, R, degree)
 581
 582 M = FreeModule(R, len(v), bool(sparse))
File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:678, in sage.modules.free_module_element.prepare()
 676 except TypeError:
 677 pass
--> 678 v = Sequence(v, universe=R, use_sage_types=True)
 679 ring = v.universe()
 680 if not is_Ring(ring):
File /ext/sage/9.7/src/sage/structure/sequence.py:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types)
 230 if universe is None:
 231 orig_x = x
--> 232 x = list(x) # make a copy even if x is a list, we're going to change it
 234 if len(x) == 0:
 235 from sage.categories.objects import Objects
TypeError: 'NoneType' object is not iterable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
( (1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (1) * dx, 0 )
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z1) * dx, 0 )
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
( (z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0 + 1) * dx, 0 )
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
( (z0*z1 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0*z1 + z1) * dx, 0 )
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
( (z0^2 - z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0^2 - z0 + 1) * dx, 0 )
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
( (x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x) * dx, 0 )
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (x*z0 + x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x*z0 + x) * dx, 0 )
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
( (x^2) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
( (0) * dx, z1/x ) <class '__main__.as_cech'>
nowe: ( (0) * dx, z1/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z1) * dx, z1^2/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z1) * dx, z1^2/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x )
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 )
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) <class '__main__.as_cech'>
nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
333:
mm: 0 19 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2*z1) * dx, z0^2*z1^2/x^3 ) ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) None
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [16], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:32, in group_action_matrices_dR(AS, threshold)
File <string>:12, in group_action_matrices(space, list_of_group_elements, basis)
File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:580, in sage.modules.free_module_element.vector()
 578 sparse = False
 579
--> 580 v, R = prepare(v, R, degree)
 581
 582 M = FreeModule(R, len(v), bool(sparse))
File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:678, in sage.modules.free_module_element.prepare()
 676 except TypeError:
 677 pass
--> 678 v = Sequence(v, universe=R, use_sage_types=True)
 679 ring = v.universe()
 680 if not is_Ring(ring):
File /ext/sage/9.7/src/sage/structure/sequence.py:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types)
 230 if universe is None:
 231 orig_x = x
--> 232 x = list(x) # make a copy even if x is a list, we're going to change it
 234 if len(x) == 0:
 235 from sage.categories.objects import Objects
TypeError: 'NoneType' object is not iterable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
( (1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (1) * dx, 0 )
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z1) * dx, 0 )
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
( (z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0 + 1) * dx, 0 )
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
( (z0*z1 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0*z1 + z1) * dx, 0 )
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
( (z0^2 - z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0^2 - z0 + 1) * dx, 0 )
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
( (x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x) * dx, 0 )
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (x*z0 + x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x*z0 + x) * dx, 0 )
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
( (x^2) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
( (0) * dx, z1/x ) <class '__main__.as_cech'>
nowe: ( (0) * dx, z1/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z1) * dx, z1^2/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z1) * dx, z1^2/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x )
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 )
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) <class '__main__.as_cech'>
nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
---------------------------------------------------------------------------
IndexError Traceback (most recent call last)
Input In [17], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:32, in group_action_matrices_dR(AS, threshold)
File <string>:10, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:80, in coordinates(self, threshold, basis)
File <string>:155, in holomorphic_combinations_fcts(S, pole_order)
IndexError: list index out of range
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
( (1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (1) * dx, 0 )
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z1) * dx, 0 )
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
( (z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0 + 1) * dx, 0 )
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
( (z0*z1 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0*z1 + z1) * dx, 0 )
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
( (z0^2 - z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0^2 - z0 + 1) * dx, 0 )
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
( (x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x) * dx, 0 )
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (x*z0 + x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x*z0 + x) * dx, 0 )
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
( (x^2) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
( (0) * dx, z1/x ) <class '__main__.as_cech'>
nowe: ( (0) * dx, z1/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z1) * dx, z1^2/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z1) * dx, z1^2/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x )
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 )
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) <class '__main__.as_cech'>
nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
A0: 0
---------------------------------------------------------------------------
IndexError Traceback (most recent call last)
Input In [18], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:32, in group_action_matrices_dR(AS, threshold)
File <string>:10, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:81, in coordinates(self, threshold, basis)
File <string>:155, in holomorphic_combinations_fcts(S, pole_order)
IndexError: list index out of range
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
( (1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (1) * dx, 0 )
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z1) * dx, 0 )
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
( (z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0 + 1) * dx, 0 )
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
( (z0*z1 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0*z1 + z1) * dx, 0 )
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
( (z0^2 - z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0^2 - z0 + 1) * dx, 0 )
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
( (x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x) * dx, 0 )
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (x*z0 + x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x*z0 + x) * dx, 0 )
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
( (x^2) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
( (0) * dx, z1/x ) <class '__main__.as_cech'>
nowe: ( (0) * dx, z1/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z1) * dx, z1^2/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z1) * dx, z1^2/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x )
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 )
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) <class '__main__.as_cech'>
nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
10 1 [[0, 1, 2], [0, 1, 2]]
A0: 0
---------------------------------------------------------------------------
IndexError Traceback (most recent call last)
Input In [19], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:32, in group_action_matrices_dR(AS, threshold)
File <string>:10, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:82, in coordinates(self, threshold, basis)
File <string>:155, in holomorphic_combinations_fcts(S, pole_order)
IndexError: list index out of range
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
( (1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (1) * dx, 0 )
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z1) * dx, 0 )
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
( (z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0 + 1) * dx, 0 )
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
( (z0*z1 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0*z1 + z1) * dx, 0 )
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
( (z0^2 - z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0^2 - z0 + 1) * dx, 0 )
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
( (x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x) * dx, 0 )
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (x*z0 + x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x*z0 + x) * dx, 0 )
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
( (x^2) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
( (0) * dx, z1/x ) <class '__main__.as_cech'>
nowe: ( (0) * dx, z1/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z1) * dx, z1^2/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z1) * dx, z1^2/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x )
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 )
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) <class '__main__.as_cech'>
nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
10 1 [[0, 1, 2], [0, 1, 2]]
A0: 0
---------------------------------------------------------------------------
IndexError Traceback (most recent call last)
Input In [20], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:32, in group_action_matrices_dR(AS, threshold)
File <string>:10, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:83, in coordinates(self, threshold, basis)
File <string>:155, in holomorphic_combinations_fcts(S, pole_order)
IndexError: list index out of range
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lrint(len(AS1.at_most_poles(M, threshold=20)))[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lsage: product
[?7h[?12l[?25h[?2004l[?7h<function symbolic_prod at 0x7f38b8be4e50>
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7lor eta in AS.de_rham_basis():[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: for k in product(*pr):
....: [?7h[?12l[?25h[?25l[?7lprint(eta.omega0, eta.omega8.valuation())[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lnt(eta.omega0, eta.omega8.valuation())[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l....:  print(k)
....: [?7h[?12l[?25h[?25l[?7lsage: for k in product(*pr):
....:  print(k)
....: 
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [22], in <cell line: 1>()
----> 1 for k in product(*pr):
 2 print(k)
NameError: name 'pr' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for k in product(*pr):
....:  print(k)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lproduct
 [?7h[?12l[?25h[?25l[?7lloa('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
( (1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (1) * dx, 0 )
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z1) * dx, 0 )
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
( (z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0 + 1) * dx, 0 )
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
( (z0*z1 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0*z1 + z1) * dx, 0 )
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
( (z0^2 - z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0^2 - z0 + 1) * dx, 0 )
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
( (x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x) * dx, 0 )
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (x*z0 + x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x*z0 + x) * dx, 0 )
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
( (x^2) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
( (0) * dx, z1/x ) <class '__main__.as_cech'>
nowe: ( (0) * dx, z1/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z1) * dx, z1^2/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z1) * dx, z1^2/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x )
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 )
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) <class '__main__.as_cech'>
nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
10 1 [[0, 1, 2], [0, 1, 2]]
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A0: 90
A: 1
B: 2
333:
mm: 0 19 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2*z1) * dx, z0^2*z1^2/x^3 ) ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) None
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [23], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:32, in group_action_matrices_dR(AS, threshold)
File <string>:12, in group_action_matrices(space, list_of_group_elements, basis)
File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:580, in sage.modules.free_module_element.vector()
 578 sparse = False
 579
--> 580 v, R = prepare(v, R, degree)
 581
 582 M = FreeModule(R, len(v), bool(sparse))
File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:678, in sage.modules.free_module_element.prepare()
 676 except TypeError:
 677 pass
--> 678 v = Sequence(v, universe=R, use_sage_types=True)
 679 ring = v.universe()
 680 if not is_Ring(ring):
File /ext/sage/9.7/src/sage/structure/sequence.py:232, in Sequence(x, universe, check, immutable, cr, cr_str, use_sage_types)
 230 if universe is None:
 231 orig_x = x
--> 232 x = list(x) # make a copy even if x is a list, we're going to change it
 234 if len(x) == 0:
 235 from sage.categories.objects import Objects
TypeError: 'NoneType' object is not iterable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
( (1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (1) * dx, 0 )
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z1) * dx, 0 )
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
( (z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0 + 1) * dx, 0 )
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
( (z0*z1 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0*z1 + z1) * dx, 0 )
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
( (z0^2 - z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0^2 - z0 + 1) * dx, 0 )
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
( (x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x) * dx, 0 )
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (x*z0 + x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x*z0 + x) * dx, 0 )
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
( (x^2) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
( (0) * dx, z1/x ) <class '__main__.as_cech'>
nowe: ( (0) * dx, z1/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z1) * dx, z1^2/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z1) * dx, z1^2/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x )
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 )
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) <class '__main__.as_cech'>
nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [24], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:32, in group_action_matrices_dR(AS, threshold)
File <string>:10, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:86, in coordinates(self, threshold, basis)
TypeError: unsupported operand type(s) for -: 'sage.rings.fraction_field_element.FractionFieldElement' and 'as_function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
( (1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (1) * dx, 0 )
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z1) * dx, 0 )
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
( (z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0 + 1) * dx, 0 )
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
( (z0*z1 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0*z1 + z1) * dx, 0 )
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
( (z0^2 - z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0^2 - z0 + 1) * dx, 0 )
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
( (x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x) * dx, 0 )
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (x*z0 + x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x*z0 + x) * dx, 0 )
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
( (x^2) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
( (0) * dx, z1/x ) <class '__main__.as_cech'>
nowe: ( (0) * dx, z1/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z1) * dx, z1^2/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z1) * dx, z1^2/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x )
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 )
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) <class '__main__.as_cech'>
nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [25], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:32, in group_action_matrices_dR(AS, threshold)
File <string>:10, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:88, in coordinates(self, threshold, basis)
NameError: name 'coordinates' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
( (1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (1) * dx, 0 )
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z1) * dx, 0 )
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 1 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z1) * dx, 0 ) ( (z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 2 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
( (z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0 + 1) * dx, 0 )
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 3 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0) * dx, 0 ) ( (z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
( (z0*z1 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0*z1 + z1) * dx, 0 )
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 4 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0*z1) * dx, 0 ) ( (z0*z1 + z1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
( (z0^2 - z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0^2 - z0 + 1) * dx, 0 )
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 5 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2) * dx, 0 ) ( (z0^2 - z0 + 1) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
( (x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x) * dx, 0 )
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 6 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x) * dx, 0 ) ( (x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 7 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x*z0^2 + x*z1) * dx, 0 ) ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (x*z0 + x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x*z0 + x) * dx, 0 )
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 8 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0) * dx, 0 ) ( (x*z0 + x) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
( (x^2) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2) * dx, 0 )
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 9 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2) * dx, 0 ) ( (x^2) * dx, 0 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
( (0) * dx, z1/x ) <class '__main__.as_cech'>
nowe: ( (0) * dx, z1/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 10 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (0) * dx, z1/x ) ( (0) * dx, z1/x ) [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (x^2*z1) * dx, z1^2/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z1) * dx, z1^2/x )
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 11 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z1) * dx, z1^2/x ) ( (x^2*z1) * dx, z1^2/x ) [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 12 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0) * dx, z0*z1/x ) ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x )
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 13 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx, z0*z1^2/x ) ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 14 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (-x^2*z0^2) * dx, z0^2*z1/x ) ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) [1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 15 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x^2*z0^2*z1 - z0*z1^2) * dx, z0^2*z1^2/x ) ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) [0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 )
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 16 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2) * dx, z1^2/x^2 ) ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 17 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0*z1) * dx, z0*z1^2/x^2 ) ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 18 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (x*z0^2*z1 - x*z0^2) * dx, z0^2*z1^2/x^2 ) ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) <class '__main__.as_cech'>
nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
nowe: ( (-z0*z1 + z1) * dx, 0 )
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0]
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: [2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0]
nowe: ( (-z0*z1 + z1) * dx, 0 )
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0]
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 19 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (z0^2*z1) * dx, z0^2*z1^2/x^3 ) ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) [2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0]
---------------------------------------------------------------------------
IndexError Traceback (most recent call last)
Input In [26], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:32, in group_action_matrices_dR(AS, threshold)
File <string>:12, in group_action_matrices(space, list_of_group_elements, basis)
File /ext/sage/9.7/src/sage/matrix/matrix0.pyx:1504, in sage.matrix.matrix0.Matrix.__setitem__()
 1502 raise IndexError("value does not have the right number of columns")
 1503 elif single_col and row_list_len != len(value_list):
-> 1504 raise IndexError("value does not have the right number of rows")
 1505 else:
 1506 if row_list_len != len(value_list):
IndexError: value does not have the right number of rows
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
( (1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (1) * dx, 0 )
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
mm: 0 0 [20 x 20 dense matrix over Finite Field of size 3, 20 x 20 dense matrix over Finite Field of size 3] ( (1) * dx, 0 ) ( (1) * dx, 0 ) (1, 0, 0, 0, 0, 0, 0, 0, 0, 0)
---------------------------------------------------------------------------
IndexError Traceback (most recent call last)
Input In [27], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:32, in group_action_matrices_dR(AS, threshold)
File <string>:12, in group_action_matrices(space, list_of_group_elements, basis)
File /ext/sage/9.7/src/sage/matrix/matrix0.pyx:1504, in sage.matrix.matrix0.Matrix.__setitem__()
 1502 raise IndexError("value does not have the right number of columns")
 1503 elif single_col and row_list_len != len(value_list):
-> 1504 raise IndexError("value does not have the right number of rows")
 1505 else:
 1506 if row_list_len != len(value_list):
IndexError: value does not have the right number of rows
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
( (1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (1) * dx, 0 )
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (1, 0, 0, 0, 0, 0, 0, 0, 0, 0)
---------------------------------------------------------------------------
IndexError Traceback (most recent call last)
Input In [28], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:32, in group_action_matrices_dR(AS, threshold)
File <string>:12, in group_action_matrices(space, list_of_group_elements, basis)
File /ext/sage/9.7/src/sage/matrix/matrix0.pyx:1504, in sage.matrix.matrix0.Matrix.__setitem__()
 1502 raise IndexError("value does not have the right number of columns")
 1503 elif single_col and row_list_len != len(value_list):
-> 1504 raise IndexError("value does not have the right number of rows")
 1505 else:
 1506 if row_list_len != len(value_list):
IndexError: value does not have the right number of rows
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
( (1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [29], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:32, in group_action_matrices_dR(AS, threshold)
File <string>:10, in group_action_matrices(space, list_of_group_elements, basis)
File <string>:94, in coordinates(self, threshold, basis)
File /ext/sage/9.7/src/sage/structure/element.pyx:1233, in sage.structure.element.Element.__add__()
 1231 # Left and right are Sage elements => use coercion model
 1232 if BOTH_ARE_ELEMENT(cl):
-> 1233 return coercion_model.bin_op(left, right, add)
 1234
 1235 cdef long value
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op()
 1246 # We should really include the underlying error.
 1247 # This causes so much headache.
-> 1248 raise bin_op_exception(op, x, y)
 1249
 1250 cpdef canonical_coercion(self, x, y):
TypeError: unsupported operand parent(s) for +: 'Vector space of dimension 10 over Finite Field of size 3' and 'Vector space of dimension 20 over Finite Field of size 3'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
( (1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 1, 1, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0 + 1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (z0*z1 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0*z1 + z1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (z0^2 - z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0^2 - z0 + 1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (1, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x*z0 + x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x*z0 + x) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x^2) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (0) * dx, z1/x ) <class '__main__.as_cech'>
nowe: ( (0) * dx, z1/x )
cc: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x^2*z1) * dx, z1^2/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z1) * dx, z1^2/x )
cc: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0)
( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x )
cc: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0] 20
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0)
( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x )
cc: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0] 20
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 2, 0, 0, 1, 0, 0, 0, 0, 2, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0)
( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
cc: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0] 20
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0)
( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
cc: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0] 20
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0)
( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 )
cc: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0] 20
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0)
( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
cc: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0] 20
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0)
( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
cc: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0] 20
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0)
( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) <class '__main__.as_cech'>
nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
cc: [2, 0, 0, 0, 0, 0, 0, 0, 0, 1] 20
nowe: ( (-z0*z1 + z1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0]
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1)
nowe: ( (-z0*z1 + z1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0]
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1)
( (1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (z1 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z1 + 1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 1, 0, 0, 0, 0]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (1, 2, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (z0) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (z0*z1 + z0) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0*z1 + z0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (z0^2) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (-x*z0^2 + x*z1 + x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (-x*z0^2 + x*z1 + x) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x*z0) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x*z0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x^2) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (0) * dx, (z1 + 1)/x ) <class '__main__.as_cech'>
nowe: ( (0) * dx, (z1 + 1)/x )
cc: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
nowe: ( (0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0)
nowe: ( (0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x^2*z1 + x^2) * dx, (z1^2 - z1 + 1)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z1 + x^2) * dx, (z1^2 - z1 + 1)/x )
cc: [2, 1, 0, 0, 0, 0, 0, 0, 0, 0] 20
nowe: ( (x^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0)
nowe: ( (x^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0)
( (-x^2*z0) * dx, (z0*z1 + z0)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0) * dx, (z0*z1 + z0)/x )
cc: [0, 0, 1, 0, 0, 0, 0, 0, 0, 0] 20
nowe: ( (0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0)
nowe: ( (0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0)
( (x^2*z0*z1 - z0^2*z1 - z0^2) * dx, (z0*z1^2 - z0*z1 + z0)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0*z1 - z0^2*z1 - z0^2) * dx, (z0*z1^2 - z0*z1 + z0)/x )
cc: [0, 0, 2, 1, 0, 0, 0, 0, 0, 0] 20
nowe: ( (-z0^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0]
(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0)
nowe: ( (-z0^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0]
(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0)
( (-x^2*z0^2) * dx, (z0^2*z1 + z0^2)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0^2) * dx, (z0^2*z1 + z0^2)/x )
cc: [1, 0, 0, 0, 1, 0, 0, 0, 0, 0] 20
nowe: ( (0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0)
nowe: ( (0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0)
( (x^2*z0^2*z1 + x^2*z0^2 - z0*z1^2 + z0*z1 - z0) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0^2*z1 + x^2*z0^2 - z0*z1^2 + z0*z1 - z0) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x )
cc: [1, 0, 0, 0, 2, 1, 0, 0, 0, 0] 20
nowe: ( (z0*z1 - z0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0]
(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 0)
nowe: ( (z0*z1 - z0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0]
(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 0)
( (x*z0^2) * dx, (z1^2 - z1 + 1)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2) * dx, (z1^2 - z1 + 1)/x^2 )
cc: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0] 20
nowe: ( (0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0)
nowe: ( (0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0)
( (x*z0*z1 + x*z0) * dx, (z0*z1^2 - z0*z1 + z0)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0*z1 + x*z0) * dx, (z0*z1^2 - z0*z1 + z0)/x^2 )
cc: [0, 0, 0, 0, 0, 0, 0, 1, 0, 0] 20
nowe: ( (x*z0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0)
nowe: ( (x*z0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0)
( (x*z0^2*z1) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2*z1) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^2 )
cc: [0, 0, 0, 0, 0, 0, 1, 0, 1, 0] 20
nowe: ( (0) * dx, z0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(-x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0]
(-x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0)
nowe: ( (0) * dx, z0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(-x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0]
(-x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0)
( (z0^2*z1 + z0^2) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^3 ) <class '__main__.as_cech'>
nowe: ( (z0^2*z1 + z0^2) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^3 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 1] 20
nowe: ( (z0^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1)
nowe: ( (z0^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1)
[
RModule of dimension 6 over GF(3),
RModule of dimension 14 over GF(3)
]
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [30], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:17, in <module>
TypeError: 'text' is an invalid keyword argument for print()
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
( (1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 1, 1, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0 + 1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (z0*z1 + z1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0*z1 + z1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (z0^2 - z0 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0^2 - z0 + 1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (1, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x*z0 + x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x*z0 + x) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x^2) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (0) * dx, z1/x ) <class '__main__.as_cech'>
nowe: ( (0) * dx, z1/x )
cc: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x^2*z1) * dx, z1^2/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z1) * dx, z1^2/x )
cc: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0)
( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0 - x^2) * dx, (z0*z1 + z1)/x )
cc: [1, 0, 1, 0, 0, 0, 0, 0, 0, 0] 20
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0)
( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0*z1 - x^2*z0 + x^2*z1 - z0^2*z1 - x^2 + z0*z1 - z1) * dx, (z0*z1^2 + z1^2)/x )
cc: [0, 1, 0, 1, 0, 0, 0, 0, 0, 0] 20
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 2, 0, 0, 1, 0, 0, 0, 0, 2, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0)
( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0^2 + x^2*z0 - x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x )
cc: [1, 0, 2, 0, 1, 0, 0, 0, 0, 0] 20
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0)
( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0^2*z1 - x^2*z0*z1 + x^2*z1 - z0*z1^2 - z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x )
cc: [0, 1, 0, 2, 0, 1, 0, 0, 0, 0] 20
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0)
( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2 - x*z0 + x) * dx, z1^2/x^2 )
cc: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0] 20
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0)
( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0*z1 + x*z1) * dx, (z0*z1^2 + z1^2)/x^2 )
cc: [0, 0, 0, 0, 0, 0, 1, 1, 0, 0] 20
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0)
( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2*z1 - x*z0^2 - x*z0*z1 + x*z0 + x*z1 - x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 )
cc: [0, 0, 0, 0, 0, 0, 1, 2, 1, 0] 20
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0)
( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) <class '__main__.as_cech'>
nowe: ( (z0^2*z1 - z0*z1 + z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 )
cc: [2, 0, 0, 0, 0, 0, 0, 0, 0, 1] 20
nowe: ( (-z0*z1 + z1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0]
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1)
nowe: ( (-z0*z1 + z1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0]
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1)
( (1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (z1 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z1 + 1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 1, 0, 0, 0, 0]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (1, 2, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (z0) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (z0*z1 + z0) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0*z1 + z0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (z0^2) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (z0^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (-x*z0^2 + x*z1 + x) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (-x*z0^2 + x*z1 + x) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x*z0) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x*z0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x^2) * dx, 0 ) <class '__main__.as_cech'>
nowe: ( (x^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (0) * dx, (z1 + 1)/x ) <class '__main__.as_cech'>
nowe: ( (0) * dx, (z1 + 1)/x )
cc: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
nowe: ( (0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0)
nowe: ( (0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0)
( (x^2*z1 + x^2) * dx, (z1^2 - z1 + 1)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z1 + x^2) * dx, (z1^2 - z1 + 1)/x )
cc: [2, 1, 0, 0, 0, 0, 0, 0, 0, 0] 20
nowe: ( (x^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0)
nowe: ( (x^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0)
( (-x^2*z0) * dx, (z0*z1 + z0)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0) * dx, (z0*z1 + z0)/x )
cc: [0, 0, 1, 0, 0, 0, 0, 0, 0, 0] 20
nowe: ( (0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0)
nowe: ( (0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0)
( (x^2*z0*z1 - z0^2*z1 - z0^2) * dx, (z0*z1^2 - z0*z1 + z0)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0*z1 - z0^2*z1 - z0^2) * dx, (z0*z1^2 - z0*z1 + z0)/x )
cc: [0, 0, 2, 1, 0, 0, 0, 0, 0, 0] 20
nowe: ( (-z0^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0]
(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0)
nowe: ( (-z0^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0]
(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0)
( (-x^2*z0^2) * dx, (z0^2*z1 + z0^2)/x ) <class '__main__.as_cech'>
nowe: ( (-x^2*z0^2) * dx, (z0^2*z1 + z0^2)/x )
cc: [1, 0, 0, 0, 1, 0, 0, 0, 0, 0] 20
nowe: ( (0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0)
nowe: ( (0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0)
( (x^2*z0^2*z1 + x^2*z0^2 - z0*z1^2 + z0*z1 - z0) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x ) <class '__main__.as_cech'>
nowe: ( (x^2*z0^2*z1 + x^2*z0^2 - z0*z1^2 + z0*z1 - z0) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x )
cc: [1, 0, 0, 0, 2, 1, 0, 0, 0, 0] 20
nowe: ( (z0*z1 - z0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0]
(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 0)
nowe: ( (z0*z1 - z0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0]
(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 0)
( (x*z0^2) * dx, (z1^2 - z1 + 1)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2) * dx, (z1^2 - z1 + 1)/x^2 )
cc: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0] 20
nowe: ( (0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0)
nowe: ( (0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0)
( (x*z0*z1 + x*z0) * dx, (z0*z1^2 - z0*z1 + z0)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0*z1 + x*z0) * dx, (z0*z1^2 - z0*z1 + z0)/x^2 )
cc: [0, 0, 0, 0, 0, 0, 0, 1, 0, 0] 20
nowe: ( (x*z0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0)
nowe: ( (x*z0) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0)
( (x*z0^2*z1) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^2 ) <class '__main__.as_cech'>
nowe: ( (x*z0^2*z1) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^2 )
cc: [0, 0, 0, 0, 0, 0, 1, 0, 1, 0] 20
nowe: ( (0) * dx, z0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(-x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0]
(-x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0)
nowe: ( (0) * dx, z0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(-x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0]
(-x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0)
( (z0^2*z1 + z0^2) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^3 ) <class '__main__.as_cech'>
nowe: ( (z0^2*z1 + z0^2) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^3 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 1] 20
nowe: ( (z0^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
111: (0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1)
nowe: ( (z0^2) * dx, 0 )
cc: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 20
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
222: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
20 wek: (0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1)
[
RModule of dimension 6 over GF(3),
RModule of dimension 14 over GF(3)
]
None
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^4
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(-x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx]
[
RModule of dimension 6 over GF(3),
RModule of dimension 14 over GF(3)
]
None
[?2004h[?25l[?7lsage: [?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ git add -u
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ git commit -m ""o"b"l"i"c"z"e""a"n"i"e" "d"z"i"a"l"a"n"i"a" "n"a" "d"R" "c"h"y"b"a" "d"z"i"a"l"a"
[master f7a04c6] obliczanie dzialania na dR chyba dziala
3 files changed, 7256 insertions(+), 23 deletions(-)
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^3
z1^2 - z1 = x^5
(1) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(x*z0 + x + z1) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(x*z0 + z1 + 1) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
[
RModule of dimension 1 over GF(2),
RModule of dimension 4 over GF(2)
]
(1) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(x*z0 + x + z1) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(z0 + 1) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(x*z0 + z1 + 1) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(z0) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(x^2) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(x) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(1) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
(0) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A
[?7h[?12l[?25h[?2004l[?7h[1 0 1 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0]
[0 1 0 1 0 0 0 0 0 1]
[0 0 0 0 1 0 0 0 1 0]
[0 0 0 0 0 1 0 1 0 0]
[0 0 0 0 0 0 1 0 1 0]
[0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l^2 == identity_matrix(F, 6)[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l.coefficient_matrix()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.dimensions()
[?7h[?12l[?25h[?2004l[?7h(10, 10)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.dimensions()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus()
[?7h[?12l[?25h[?2004l[?7h5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7l.dimenions()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l.dimensions()[?7h[?12l[?25h[?25l[?7lS.genu()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7l^2 == identity_matrix(F, 6)[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lid[?7h[?12l[?25h[?25l[?7lide[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A^p == identity_matrix(10)
[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA^p == identity_matrix(10)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^p = identity_matrix(10)[?7h[?12l[?25h[?25l[?7lB^p = identity_matrix(10)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B^p == identity_matrix(10)
[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA^p == identity_matrix(10)[?7h[?12l[?25h[?25l[?7l*BB*A[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l== B*A[?7h[?12l[?25h[?25l[?7lsage: A*B == B*A
[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA*B == B*A[?7h[?12l[?25h[?25l[?7lB^pidentity_matrix(10)[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS.genus()[?7h[?12l[?25h[?25l[?7l.dimenions()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^7
z1^2 - z1 = x^5
(1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x*z1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x^2*z1 + x*z0 + x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x^3) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x*z1 + x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x^2*z1 + x^2 + x*z0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x^3) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
[
RModule of dimension 1 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 4 over GF(2)
]
(1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x*z1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x^2*z1 + x*z0 + x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x^3) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x^3) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x*z1 + x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x^2*z1 + x^2 + x*z0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x^3) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x^3) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^7
z1^2 - z1 = x^9
(1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^2*z0 + x^2 + x*z1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^3*z0 + x^3 + x^2*z1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^3) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^4) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^5) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^2*z0 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^3*z0 + x^2*z1 + x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^3) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^4) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^5) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
[
RModule of dimension 1 over GF(2),
RModule of dimension 1 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 6 over GF(2)
]
(1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(z1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(z0 + 1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^2*z0 + x^2 + x*z1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x*z0 + x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^3*z0 + x^3 + x^2*z1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^3) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^4) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^5) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^5 + x^4) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^4) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^3 + x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(z1 + 1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(z0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^2*z0 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x*z0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^3*z0 + x^2*z1 + x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^3) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^4) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^5) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^5) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^3) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
(1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lA*B == B*A[?7h[?12l[?25h[?25l[?7lB^pidentity_matrix(10)[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS.genus()[?7h[?12l[?25h[?25l[?7l.dimenions()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lsage: A
[?7h[?12l[?25h[?2004l[?7h22 x 22 dense matrix over Finite Field of size 2 (use the '.str()' method to see the entries)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^11
z1^2 - z1 = x^9
[
RModule of dimension 1 over GF(2),
RModule of dimension 1 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 6 over GF(2)
]
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [11], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:29, in group_action_matrices_dR(AS, threshold)
File <string>:378, in de_rham_basis(self, threshold)
File <string>:366, in lift_to_de_rham(self, fct, threshold)
ValueError: Increase threshold!
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^11
z1^2 - z1 = x^9
[
RModule of dimension 1 over GF(2),
RModule of dimension 1 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 6 over GF(2)
]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 5 with the equation:
z^5 - z = x^3
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [1], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:14, in <module>
ValueError: not enough values to unpack (expected 2, got 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 5 with the equation:
z^5 - z = x^3
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [2], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File /ext/sage/9.7/src/sage/matrix/special.py:922, in identity_matrix(ring, n, sparse)
 920 n = ring
 921 ring = ZZ
--> 922 return matrix_space.MatrixSpace(ring, n, n, sparse)(1)
File /ext/sage/9.7/src/sage/misc/classcall_metaclass.pyx:320, in sage.misc.classcall_metaclass.ClasscallMetaclass.__call__()
 318 """
 319 if cls.classcall is not None:
--> 320 return cls.classcall(cls, *args, **kwds)
 321 else:
 322 # Fast version of type.__call__(cls, *args, **kwds)
File /ext/sage/9.7/src/sage/matrix/matrix_space.py:561, in MatrixSpace.__classcall__(cls, base_ring, nrows, ncols, sparse, implementation, **kwds)
 516 """
 517 Normalize the arguments to call the ``__init__`` constructor.
 518
 (...)
 558  False
 559 """
 560 if base_ring not in _Rings:
--> 561 raise TypeError("base_ring (=%s) must be a ring"%base_ring)
 562 nrows = int(nrows)
 563 if ncols is None:
TypeError: base_ring (=8) must be a ring
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 5 with the equation:
z^5 - z = x^3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l.dimensions()[?7h[?12l[?25h[?25l[?7lj[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l.dimensions()[?7h[?12l[?25h[?25l[?7lj[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.jordan_form()
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [4], in <cell line: 1>()
----> 1 A.jordan_form()
AttributeError: 'list' object has no attribute 'jordan_form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_form()[?7h[?12l[?25h[?25l[?7lsage: A
[?7h[?12l[?25h[?2004l[?7h[
[1 1 1 0 0 0 0 3]
[0 1 2 0 0 0 0 4]
[0 0 1 0 0 0 0 4]
[0 0 0 1 4 1 3 0]
[0 0 0 0 1 3 1 0]
[0 0 0 0 0 1 4 0]
[0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 1]
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l = AS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: A = A[0]
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = A[0][?7h[?12l[?25h[?25l[?7l.jordan_form()[?7h[?12l[?25h[?25l[?7lj[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldan_form()[?7h[?12l[?25h[?25l[?7lan_form()[?7h[?12l[?25h[?25l[?7lsage: A.jordan_form()
[?7h[?12l[?25h[?2004l[?7h[1 1 0 0|0 0 0 0]
[0 1 1 0|0 0 0 0]
[0 0 1 1|0 0 0 0]
[0 0 0 1|0 0 0 0]
[-------+-------]
[0 0 0 0|1 1 0 0]
[0 0 0 0|0 1 1 0]
[0 0 0 0|0 0 1 1]
[0 0 0 0|0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_form()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lb()[?7h[?12l[?25h[?25l[?7ll()[?7h[?12l[?25h[?25l[?7lo()[?7h[?12l[?25h[?25l[?7lc()[?7h[?12l[?25h[?25l[?7lk()[?7h[?12l[?25h[?25l[?7ls()[?7h[?12l[?25h[?25l[?7lsage: A.jordan_blocks()
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [8], in <cell line: 1>()
----> 1 A.jordan_blocks()
File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
 493 """
--> 494 return self.getattr_from_category(name)
 495
 496 cdef getattr_from_category(self, name):
File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
 505 else:
 506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
 508
 509 def __dir__(self):
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
 359 dummy_error_message.cls = type(self)
 360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
 362 attribute = <object>attr
 363 # Check for a descriptor (__get__ in Python)
AttributeError: 'sage.matrix.matrix_modn_dense_float.Matrix_modn_dense_float' object has no attribute 'jordan_blocks'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_blocks()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lsage: A.jordan_blocks()
 A.C A.QR A.add_multiple_of_row A.adjoint_classical 
 A.H A.T A.add_to_entry A.adjugate 
 A.LLL_gram A.act_on_polynomial A.additive_order A.anticommutator >
 A.LU A.add_multiple_of_column A.adjoint A.antitranspose 
 [?7h[?12l[?25h[?25l[?7lC
 A.C 
 <unknown> [?7h[?12l[?25h[?25l[?7lQR
 A.C  A.QR [?7h[?12l[?25h[?25l[?7lC
 A.C  A.QR [?7h[?12l[?25h[?25l[?7l




[?7h[?12l[?25h[?25l[?7ljordan_blocks()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_blocks()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: A.jordan_blocks()[0]
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [9], in <cell line: 1>()
----> 1 A.jordan_blocks()[Integer(0)]
File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
 493 """
--> 494 return self.getattr_from_category(name)
 495
 496 cdef getattr_from_category(self, name):
File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
 505 else:
 506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
 508
 509 def __dir__(self):
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
 359 dummy_error_message.cls = type(self)
 360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
 362 attribute = <object>attr
 363 # Check for a descriptor (__get__ in Python)
AttributeError: 'sage.matrix.matrix_modn_dense_float.Matrix_modn_dense_float' object has no attribute 'jordan_blocks'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_blocks()[0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[0][?7h[?12l[?25h[?25l[?7l()[0][?7h[?12l[?25h[?25l[?7l()[0][?7h[?12l[?25h[?25l[?7l()[0][?7h[?12l[?25h[?25l[?7l()[0][?7h[?12l[?25h[?25l[?7l()[0][?7h[?12l[?25h[?25l[?7lf()[0][?7h[?12l[?25h[?25l[?7lo()[0][?7h[?12l[?25h[?25l[?7lr()[0][?7h[?12l[?25h[?25l[?7lm()[0][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A.jordan_form()[0]
[?7h[?12l[?25h[?2004l[?7h(1, 1, 0, 0, 0, 0, 0, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_form()[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm()[0][?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lsage: A.jordan_form(sub
 subdivide= 
 subfactorial
 subsets 
 [?7h[?12l[?25h[?25l[?7ldivide=
 subdivide= 
 <unknown> [?7h[?12l[?25h[?25l[?7l



[?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lTrue[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.jordan_form(subdivide=True)
[?7h[?12l[?25h[?2004l[?7h[1 1 0 0|0 0 0 0]
[0 1 1 0|0 0 0 0]
[0 0 1 1|0 0 0 0]
[0 0 0 1|0 0 0 0]
[-------+-------]
[0 0 0 0|1 1 0 0]
[0 0 0 0|0 1 1 0]
[0 0 0 0|0 0 1 1]
[0 0 0 0|0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_form(subdivide=True)[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: A.jordan_form(subdivide=True)[0]
[?7h[?12l[?25h[?2004l[?7h(1, 1, 0, 0, 0, 0, 0, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_form(subdivide=True)[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.jordan_form(subdivide=True)
[?7h[?12l[?25h[?2004l[?7h[1 1 0 0|0 0 0 0]
[0 1 1 0|0 0 0 0]
[0 0 1 1|0 0 0 0]
[0 0 0 1|0 0 0 0]
[-------+-------]
[0 0 0 0|1 1 0 0]
[0 0 0 0|0 1 1 0]
[0 0 0 0|0 0 1 1]
[0 0 0 0|0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_form(subdivide=True)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_form(subdivide=True)[?7h[?12l[?25h[?25l[?7l()[0][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.jordan_form(subdivide=True)
[?7h[?12l[?25h[?2004l[?7h[1 1 0 0|0 0 0 0]
[0 1 1 0|0 0 0 0]
[0 0 1 1|0 0 0 0]
[0 0 0 1|0 0 0 0]
[-------+-------]
[0 0 0 0|1 1 0 0]
[0 0 0 0|0 1 1 0]
[0 0 0 0|0 0 1 1]
[0 0 0 0|0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_form(subdivide=True)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltA.jordan_form(subdivide=True)[?7h[?12l[?25h[?25l[?7lyA.jordan_form(subdivide=True)[?7h[?12l[?25h[?25l[?7lpA.jordan_form(subdivide=True)[?7h[?12l[?25h[?25l[?7leA.jordan_form(subdivide=True)[?7h[?12l[?25h[?25l[?7ltype(A.jordan_form(subdivide=True)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: type(A.jordan_form(subdivide=True))
[?7h[?12l[?25h[?2004l[?7h<class 'sage.matrix.matrix_modn_dense_float.Matrix_modn_dense_float'>
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(A.jordan_form(subdivide=True))[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: type(A.jordan_form(subdivide=True))[0]
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [16], in <cell line: 1>()
----> 1 type(A.jordan_form(subdivide=True))[Integer(0)]
TypeError: 'sage.misc.inherit_comparison.InheritComparisonMetaclass' object is not subscriptable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(A.jordan_form(subdivide=True))[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lTru[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: type(A.jordan_form(
 base_ring= subdivide= AA 
 check_input= transformation= AS 
 eigenvalues= %%! AbelianGroup >
 sparse= A AbelianGroupMorphism 
 [?7h[?12l[?25h[?25l[?7lbase_ring=
 base_ring= 
 <unknown> [?7h[?12l[?25h[?25l[?7lsubdivde
 base_ring=  subdivide= [?7h[?12l[?25h[?25l[?7lAA
 subdivide=  AA [?7h[?12l[?25h[?25l[?7lbelianGroupWithValues
 subdivdeAA belianGroupWithValues
 transformaion=AS belianVariety
<%%! AbelianGroupdditiveAbelianGroup
 A belianGroupMorphismdditiveAbelianGroupWrapper[?7h[?12l[?25h[?25l[?7ldditiveAbelianGroupWrapperElement
AA belianGroupWithValuesdditiveAbelianGroupWrapperElement
AS belianVarietydditiveMagmas
AbelianGroupdditiveAbelianGroupffneCryptosystem 
belianGroupMorphismdditiveAbelianGroupWrapperffneGroup [?7h[?12l[?25h[?25l[?7lbelianGroupWithValues
 AbelianGroupWithValues  AdditiveAbelianGroupWrapperElement [?7h[?12l[?25h[?25l[?7ldditiveAbelianGroupWrapperElement
 AbelianGroupWithValues  AdditiveAbelianGroupWrapperElement [?7h[?12l[?25h[?25l[?7lffneHypersurface
belianGroupWithValuesdditiveAbelianGroupWrapperElementffneHypersurface 
belianVarietydditiveMagmasffneNilTeperleyLiebTypeA
dditiveAbelianGroupffneCryptosystem PermutationGroup
dditiveAbelianGroupWrapperffneGroup Space[?7h[?12l[?25h[?25l[?7lToricVaiety
dditiveAbelianGroupWrapperElementffneHypersurface ToricVaiety
dditiveMagmasffneNilTeperleyLiebTypeAWeylGroups 
ffneCryptosystem PermutationGrouplarmInterrup 
ffneGroup Spacelgebra [?7h[?12l[?25h[?25l[?7llgebraIdeals
ffneHypersurface ToricVaietylgebraIdeals 
ffneNilTeperleyLiebTypeAWeylGroups lgebraModules 
PermutationGrouplarmInterrup gebraicField
Spacelgebra icNumber[?7h[?12l[?25h[?25l[?7licReal
ToricVaietylgebraIdeals icReal
WeylGroups lgebraModules icRealField
larmInterrup gebraicFields 
lgebra icNumbersWithBasis[?7h[?12l[?25h[?25l[?7llCusps
lgebraIdeals icReallCusps 
lgebraModules icRealFieldlExactCovers 
gebraicFields phabet
icNumbersWithBasisphabeticString[?7h[?12l[?25h[?25l[?7lternatingGroup
icReallCusps ternatingGroup
icRealFieldlExactCovers ternaingSignMatrices
s phabetternaingSignMatrix
sWithBasisphabeticStringrithmEror [?7h[?12l[?25h[?25l[?7llCusps
 AllCusps  AlternatingGroup [?7h[?12l[?25h[?25l[?7lternatingGroup
 AllCusps  AlternatingGroup [?7h[?12l[?25h[?25l[?7lrithmecSubgroup_Permutation
lCusps ternatingGrouprithmecSubgroup_Permutation
lExactCovers ternaingSignMatricesrrangemets 
phabetternaingSignMatrixrinGroup 
phabeticStringrithmEror ssertionEror [?7h[?12l[?25h[?25l[?7lssionGroupS
ternatingGrouprithmecSubgroup_PermutationssionGroupS 
ternaingSignMatricesrrangemets ssionGroupU
ternaingSignMatrixrinGroup symptoticRing
rithmEror ssertionEror tkinModulaCorrespondenceDatabase[?7h[?12l[?25h[?25l[?7lrithmeticSubgroup_Permutation
 ArithmeticSubgroup_Permutation  AssionGroupS [?7h[?12l[?25h[?25l[?7llternangGroup
 AlternatingGroup  ArithmeticSubgroup_Permutation [?7h[?12l[?25h[?25l[?7lrithmecSubgroup_Permutation
 AlternatingGroup  ArithmeticSubgroup_Permutation [?7h[?12l[?25h[?25l[?7lssionGroupS
 ArithmeticSubgroup_Permutation  AssionGroupS [?7h[?12l[?25h[?25l[?7ltknModularPolynomialDatabase
rithmecSubgroup_PermutationssionGroupS tknModularPolynomialDatabase
rrangemets ssionGroupUttributeError
rinGroup symptoticRingugentedLatticeDiagramFilling
ssertionEror tkinModulaCorrespondenceDatabaseutomaton [?7h[?12l[?25h[?25l[?7lxiom
ssionGroupS tknModularPolynomialDatabasexiom 
ssionGroupUttributeErrorBackslashOperator
symptoticRingugentedLatticeDiagramFillingBaseExcption 
tkinModulaCorrespondenceDatabaseutomaton BaxterPermutations[?7h[?12l[?25h[?25l[?7lBerkovich_Cp_Affine
tknModularPolynomialDatabasexiom Berkovich_Cp_Affine
ttributeErrorBackslashOperatorerovic_Cp_Prjective
ugentedLatticeDiagramFillingBaseExcption esel 
utomaton BaxterPermutationsezoutianQadraticForm[?7h[?12l[?25h[?25l[?7lialgebras
xiom Berkovich_Cp_Affineialgebras 
BackslashOperatorerovic_Cp_PrjectiveialgebrasWithBasis 
BaseExcption esel imodules
BaxterPermutationsezoutianQadraticForminaryQF [?7h[?12l[?25h[?25l[?7lnaryQF_reduced_representatives
Berkovich_Cp_Affineialgebras naryQF_reduced_representatives
erovic_Cp_PrjectiveialgebrasWithBasis naryRecurrenceSequence
esel imodulesnaryStrings
ezoutianQadraticForminaryQF Tree[?7h[?12l[?25h[?25l[?7lTrees
ialgebras naryQF_reduced_representativesTrees 
ialgebrasWithBasis naryRecurrenceSequenceptiteGaph 
imodulesnaryStringstset 
inaryQF TreelockDesign[?7h[?12l[?25h[?25l[?7lBlockingIOError
naryQF_reduced_representativesTrees lockingIOError
naryRecurrenceSequenceptiteGaph ooleanPolynomialRing
naryStringstset raidGroup
TreelockDesignranchingRule[?7h[?12l[?25h[?25l[?7lBrandtModule
Trees lockingIOErrorrandtModule 
ptiteGaph ooleanPolynomialRingraurAlgebra 
tset raidGroupokenPipeError
lockDesignranchingRuleuhatTitsQuotient[?7h[?12l[?25h[?25l[?7lBufferError
lockingIOErrorrandtModule ufferError 
ooleanPolynomialRingraurAlgebra ytesWarning 
raidGroupokenPipeErrorCBF 
ranchingRuleuhatTitsQuotientCC [?7h[?12l[?25h[?25l[?7lCDF
randtModule ufferError CDF 
raurAlgebra ytesWarning CFiniteSequence
okenPipeErrorCBF FiniteSequences
uhatTitsQuotientCC IF[?7h[?12l[?25h[?25l[?7lL
ufferError CDF L
ytesWarning CFiniteSequencePRFanoToricVariety
CBF FiniteSequencesRT 
CC IFRT_basis[?7h[?12l[?25h[?25l[?7lRT_list
CDF LRT_list
CFiniteSequencePRFanoToricVarietyRT_vects 
FiniteSequencesRT _super
IFRT_basisachedFunction[?7h[?12l[?25h[?25l[?7lallableSymbolicExpressionRing
LRT_listallableSymbolicExpressionRing
PRFanoToricVarietyRT_vects artanMatix
RT _superartanType
RT_basisachedFunctiontegory [?7h[?12l[?25h[?25l[?7lhainComplex
RT_listallableSymbolicExpressionRinghainComplex 
RT_vects artanMatixhainCompleMorphism
_superartanTypehainComlexes
achedFunctiontegory hi [?7h[?12l[?25h[?25l[?7lChildProcessError
allableSymbolicExpressionRinghainComplex ildProcessError
artanMatixhainCompleMorphismi 
artanTypehainComlexeslssFunction 
tegory hi lassicalCrystals[?7h[?12l[?25h[?25l[?7lClassicalModularPolynomialDatabase
hainComplex ildProcessErrorlassicalModularPolynomialDatabase
hainCompleMorphismi liffordAlgebra
hainComlexeslssFunction uterAlgebra
hi lassicalCrystalsuterComplex [?7h[?12l[?25h[?25l[?7luterQuiver
ildProcessErrorlassicalModularPolynomialDatabaseuterQuiver 
i liffordAlgebrausteSeed 
lssFunction uterAlgebraoalgbras 
lassicalCrystalsuterComplex oalgbrasWithBasis[?7h[?12l[?25h[?25l[?7lolor
lassicalModularPolynomialDatabaseuterQuiver olor 
liffordAlgebrausteSeed olordPrmutations
uterAlgebraoalgbras mbinations
uterComplex oalgbrasWithBasismbinatorialCls [?7h[?12l[?25h[?25l[?7lmbinatorialFreeModule
uterQuiver olor mbinatorialFreeModule
usteSeed olordPrmutationsmbinatoialObject
oalgbras mbinationsorialPolyhedron
oalgbrasWithBasismbinatorialCls Species[?7h[?12l[?25h[?25l[?7lmutiveAdditiveGroups
olor mbinatorialFreeModulemutiveAdditiveGroups
olordPrmutationsmbinatoialObjectmutiveAdditiveMonoids
mbinationsorialPolyhedronmutiveAdditivSemigroups
mbinatorialCls SpeciesmutiveAgebraElement[?7h[?12l[?25h[?25l[?7llgebraIdeals
mbinatorialFreeModulemutiveAdditiveGroupslgebraIdeals 
mbinatoialObjectmutiveAdditiveMonoidslgebras 
orialPolyhedronmutiveAdditivSemigroupsRing 
SpeciesmutiveAgebraElementRingElement [?7h[?12l[?25h[?25l[?7lRingIdeals
mutiveAdditiveGroupslgebraIdeals RingIdeals 
mutiveAdditiveMonoidslgebras Rings 
mutiveAdditivSemigroupsRing pleteDiscreteValuationFields
mutiveAgebraElementRingElement pleteDiscreteValuaionRings[?7h[?12l[?25h[?25l[?7lAlgebraIdeals
 CommutativeAlgebraIdeals  CommutativeRingIdeals [?7h[?12l[?25h[?25l[?7ldditiveGroups
 CommutativeAdditiveGroups  CommutativeAlgebraIdeals [?7h[?12l[?25h[?25l[?7lbinorialFreeModule
binorialFreeModule dditiveGroupsAlgebraIdeals
binorialObject dditiveMonoidsAlgebras
binorialPolyhdron AdditiveSemigroupsmutativeRing 
binoriaSpecies AlgebraElementmutativeRingElemen [?7h[?12l[?25h[?25l[?7llor
lor binorialFreeModule dditiveGroups
loredPemutationsbinorialObject dditiveMonoids
ions binorialPolyhdron AdditiveSemigroups
Class binoriaSpecies AlgebraElement[?7h[?12l[?25h[?25l[?7llusterQuiver
lusterQuiverlor binorialFreeModule 
lustrSed loredPemutationsbinorialObject 
algebras ions binorialPolyhdron 
algebrasWithBisClass binoriaSpecies [?7h[?12l[?25h[?25l[?7lasicalModularPolynomialDatabase
asicalModularPolynomialDatabaselusterQuiverlor 
iffodAlgebralustrSed loredPemutations
lustrAlgebraalgebras ions 
lustrComplex algebrasWithBisClass [?7h[?12l[?25h[?25l[?7lChildProcessError
hildProcessError asicalModularPolynomialDatabaselusterQuiver
i iffodAlgebralustrSed 
asFunction lustrAlgebraalgebras 
asicalCrystalslustrComplex algebrasWithBis[?7h[?12l[?25h[?25l[?7lChainComplex
ainComplex hildProcessError asicalModularPolynomialDatabase
hainComplexMorphismi iffodAlgebra
hinComplexesasFunction lustrAlgebra
hi asicalCrystalslustrComplex [?7h[?12l[?25h[?25l[?7lallableSymbolicExpressionRing
allableSymbolicExpressionRingainComplex hildProcessError 
artanMatri hainComplexMorphismi 
artanTye hinComplexesasFunction 
ategoryhi asicalCrystals[?7h[?12l[?25h[?25l[?7lRT_list
RT_list allableSymbolicExpressionRingainComplex 
RT_vectos artanMatri hainComplexMorphism
_super artanTye hinComplexes
chedFunctionategoryhi [?7h[?12l[?25h[?25l[?7lLF
LF RT_list allableSymbolicExpressionRing
PRFanoTicVarietyRT_vectos artanMatri 
RT _super artanTye 
RT_basis chedFunctionategory[?7h[?12l[?25h[?25l[?7lD
DLF RT_list 
FiniteSequence PRFanoTicVarietyRT_vectos 
FiniteSequencesRT _super 
IF RT_basis chedFunction[?7h[?12l[?25h[?25l[?7lBufferError
BufferErrorDLF 
BytesWarning FiniteSequence PRFanoTicVariety
BF FiniteSequencesRT 
C IF RT_basis [?7h[?12l[?25h[?25l[?7lBrandtModule
randtModuleBufferErrorD
rauerAlgebraBytesWarning FiniteSequence 
BrokenPipeErrorBF FiniteSequences
BruhatTitsQuotientC IF [?7h[?12l[?25h[?25l[?7lBlockingIOError
lockingIOErrorrandtModuleBufferError
oolanPolynomialRingrauerAlgebraBytesWarning 
aidGroup BrokenPipeErrorBF 
anchingRule BruhatTitsQuotientC [?7h[?12l[?25h[?25l[?7lBlockingIOErro




[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lvision([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: type(A.jordan_form().subdivision())
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [17], in <cell line: 1>()
----> 1 type(A.jordan_form().subdivision())
File /ext/sage/9.7/src/sage/matrix/matrix2.pyx:8845, in sage.matrix.matrix2.Matrix.subdivision()
 8843 self._subdivisions = (l_row, l_col)
 8844
-> 8845 def subdivision(self, i, j):
 8846 """
 8847 Returns an immutable copy of the (i,j)th submatrix of self,
TypeError: subdivision() takes exactly 2 positional arguments (0 given)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(A.jordan_form().subdivision())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7li))[?7h[?12l[?25h[?25l[?7l,))[?7h[?12l[?25h[?25l[?7l ))[?7h[?12l[?25h[?25l[?7li))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, i)[?7h[?12l[?25h[?25l[?7l1, i)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l1))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: type(A.jordan_form().subdivision(1, 1))
[?7h[?12l[?25h[?2004l[?7h<class 'sage.matrix.matrix_modn_dense_float.Matrix_modn_dense_float'>
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(A.jordan_form().subdivision(1, 1))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7ltyp(A.jordan_form().subdivision(1, 1))[?7h[?12l[?25h[?25l[?7l(A.jordan_form().subdivision(1, 1))[?7h[?12l[?25h[?25l[?7l(A.jordan_form().subdivision(1, 1))[?7h[?12l[?25h[?25l[?7l(A.jordan_form().subdivision(1, 1))[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls(A.jordan_form().subdivision(1, 1))[?7h[?12l[?25h[?25l[?7lt(A.jordan_form().subdivision(1, 1))[?7h[?12l[?25h[?25l[?7lstr(A.jordan_form().subdivision(1, 1))[?7h[?12l[?25h[?25l[?7lsage: str(A.jordan_form().subdivision(1, 1))
[?7h[?12l[?25h[?2004l[?7h'[1 1 0 0]\n[0 1 1 0]\n[0 0 1 1]\n[0 0 0 1]'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 2^2 with the equation:
z^2 - z = x^3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 2^2 with the equations:
z0^2 - z0 = x^3
z1^2 - z1 = a*x^3
/ext/sage/9.7/src/sage/rings/polynomial/polynomial_singular_interface.py:372:
********************************************************************************
Denominators of fraction field elements are sometimes dropped without warning.
This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696.
********************************************************************************
>> A := MatrixAlgebra<GF(4),6|[1, a + 1, 0, 0, 0, a, 0, 1, 0, 0, 0, 0, 0, 0, 1
^
User error: Identifier 'a' has not been declared or assigned
>> , 0, 1, 0, 0, 0, 0, 0, 0, 1]>;M := RModule(RSpace(GF(4),6), A);Indecomposab
^
User error: Identifier 'A' has not been declared or assigned
>> ,6), A);IndecomposableSummands(M);
^
User error: Identifier 'M' has not been declared or assigned
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 2^2 with the equations:
z0^2 - z0 = x^3
z1^2 - z1 = a*x^3
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [3], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:19, in <module>
NameError: name 'T' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 2^2 with the equations:
z0^2 - z0 = x^3
z1^2 - z1 = a*x^3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_form(subdivide=True)[?7h[?12l[?25h[?25l[?7lS.genus()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_form(subdivide=True)[?7h[?12l[?25h[?25l[?7lsage: A
[?7h[?12l[?25h[?2004l[?7h[ 1 a + 1 0 0 0 a]
[ 0 1 0 0 0 0]
[ 0 0 1 0 a 0]
[ 0 0 0 1 1 0]
[ 0 0 0 0 1 0]
[ 0 0 0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB^p == identity_matrix(10)[?7h[?12l[?25h[?25l[?7lsage: B
[?7h[?12l[?25h[?2004l[?7h[1 1 0 0 0 1]
[0 1 0 0 0 0]
[0 0 1 0 1 0]
[0 0 0 1 a 0]
[0 0 0 0 1 0]
[0 0 0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B, text=True)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lgmathis(A, B, text=True)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B, text=True)
[?7h[?12l[?25h[?2004l[?7h'A := MatrixAlgebra<GF(4),6|[1, a + 1, 0, 0, 0, a, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, a, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1],[1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, a, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1]>;M := RModule(RSpace(GF(4),6), A);IndecomposableSummands(M);'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS.genus()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus()
[?7h[?12l[?25h[?2004l[?7h3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lmagmathis(A, B, text=True)[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^3
z1^2 - z1 = x^13
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lare_equivalent_matrix(A1, A2, q)[?7h[?12l[?25h[?25l[?7lsage: q = 5
....: p = q.factor()[0][0]
....: n = 2
....: A1 = matrix(ZZ, [[1, 3], [3, 4]])
....: A2 = matrix(ZZ, [[2, 3], [2, 2]])
....: print((identity_matrix(n) + A1.transpose()*A1).determinant()%p)
....: print((identity_matrix(n) + A2.transpose()*A2).determinant()%p)[?7h[?12l[?25h[?25l[?7lare_equivalent_matrix(A1, A2, q)
 
 
 
 
 
 [?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llista_np = [2*i+1 for i in range(q//2)][?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = x^5
[
RModule of dimension 6 over GF(3),
RModule of dimension 6 over GF(3),
RModule of dimension 14 over GF(3)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA2 = matrix(ZZ, [[2, 3], [2, 2]])[?7h[?12l[?25h[?25l[?7lS.genus()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lmagical_element()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lgical_element()[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element()
[?7h[?12l[?25h[?2004l[?7h[x^4*z0 + x^3*z1 + z0^2*z1^2]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lare_equivalent_matrix(A1, A2, q)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004lno 20 -th root; divide by 2
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [3], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:13, in <module>
File <string>:44, in __init__(self, C, list_of_fcts, prec)
ValueError: not enough values to unpack (expected 4, got 2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004lno 14 -th root; divide by 2
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [4], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:13, in <module>
File <string>:44, in __init__(self, C, list_of_fcts, prec)
ValueError: not enough values to unpack (expected 4, got 2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^5
z1^3 - z1 = x^11
I haven't found all forms.
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [5], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:17, in <module>
File <string>:29, in group_action_matrices_dR(AS, threshold)
File <string>:145, in holomorphic_differentials_basis(self, threshold)
NameError: name 'holomorphic_differentials_basis' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^5
z1^3 - z1 = x^11
I haven't found all forms.
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [6], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:17, in <module>
File <string>:29, in group_action_matrices_dR(AS, threshold)
File <string>:145, in holomorphic_differentials_basis(self, threshold)
NameError: name 'holomorphic_differentials_basis' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^5
z1^3 - z1 = x^11
I haven't found all forms.
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [7], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:17, in <module>
File <string>:29, in group_action_matrices_dR(AS, threshold)
File <string>:145, in holomorphic_differentials_basis(self, threshold)
NameError: name 'holomorphic_differentials_basis' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004lno 20 -th root; divide by 2
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [8], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:13, in <module>
File <string>:44, in __init__(self, C, list_of_fcts, prec)
ValueError: not enough values to unpack (expected 4, got 2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = 2*x^8
[
RModule of dimension 6 over GF(3),
RModule of dimension 6 over GF(3),
RModule of dimension 6 over GF(3),
RModule of dimension 6 over GF(3),
RModule of dimension 6 over GF(3),
RModule of dimension 14 over GF(3)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
z0^3 - z0 = x^2
z1^3 - z1 = 2*x^11
[
RModule of dimension 6 over GF(3),
RModule of dimension 6 over GF(3),
RModule of dimension 6 over GF(3),
RModule of dimension 6 over GF(3),
RModule of dimension 6 over GF(3),
RModule of dimension 6 over GF(3),
RModule of dimension 6 over GF(3),
RModule of dimension 6 over GF(3),
RModule of dimension 14 over GF(3)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 5 with the equations:
z0^5 - z0 = x^2
z1^5 - z1 = x^7
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS
[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 5 with the equations:
z0^5 - z0 = x^2
z1^5 - z1 = x^7
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.magical_element()[?7h[?12l[?25h[?25l[?7lmagical_element()[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element()
[?7h[?12l[?25h[?2004l[?7h[x^6*z0^3 + x^5*z0^2*z1 + z0^4*z1^4 + x^4*z0*z1^2 + x^3*z1^3]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rhmbasis()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis()
[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
( (z1) * dx, 0 ),
( (z1^2) * dx, 0 ),
( (z1^3) * dx, 0 ),
( (2*x^4*z0^4 - 2*x^3*z0^3*z1 - x^2*z0^2*z1^2 + z1^4) * dx, 0 ),
( (z0) * dx, 0 ),
( (z0*z1) * dx, 0 ),
( (z0*z1^2) * dx, 0 ),
( (z0*z1^3) * dx, 0 ),
( (x^3*z0^4*z1 + x^2*z0^3*z1^2 + x^6 + x*z0^2*z1^3 + z0*z1^4) * dx, 0 ),
( (z0^2) * dx, 0 ),
( (z0^2*z1) * dx, 0 ),
( (z0^2*z1^2) * dx, 0 ),
( (-x^5 + z0^2*z1^3) * dx, 0 ),
( (z0^3) * dx, 0 ),
( (z0^3*z1) * dx, 0 ),
( (z0^3*z1^2) * dx, 0 ),
( (2*x^5*z0 + z0^3*z1^3 + 2*x^4*z1) * dx, 0 ),
( (z0^4) * dx, 0 ),
( (z0^4*z1) * dx, 0 ),
( (z0^4*z1^2) * dx, 0 ),
( (-x^5*z0^2 + z0^4*z1^3 - 2*x^4*z0*z1 + 2*x^3*z1^2) * dx, 0 ),
( (x) * dx, 0 ),
( (x*z1) * dx, 0 ),
( (x*z1^2) * dx, 0 ),
( (-x^4*z0^3 + x*z1^3) * dx, 0 ),
( (x*z0) * dx, 0 ),
( (x*z0*z1) * dx, 0 ),
( (x*z0*z1^2) * dx, 0 ),
( (-x^4*z0^4 - 2*x^3*z0^3*z1 + 2*x^2*z0^2*z1^2 + x*z0*z1^3) * dx, 0 ),
( (x*z0^2) * dx, 0 ),
( (x*z0^2*z1) * dx, 0 ),
( (x*z0^2*z1^2) * dx, 0 ),
( (x*z0^3) * dx, 0 ),
( (x*z0^3*z1) * dx, 0 ),
( (x*z0^3*z1^2 - x^5) * dx, 0 ),
( (x*z0^4) * dx, 0 ),
( (x*z0^4*z1) * dx, 0 ),
( (x*z0^4*z1^2 + x^5*z0 - 2*x^4*z1) * dx, 0 ),
( (x^2) * dx, 0 ),
( (x^2*z1) * dx, 0 ),
( (x^2*z1^2) * dx, 0 ),
( (x^2*z0) * dx, 0 ),
( (x^2*z0*z1) * dx, 0 ),
( (-x^4*z0^3 + x^2*z0*z1^2) * dx, 0 ),
( (x^2*z0^2) * dx, 0 ),
( (x^2*z0^2*z1) * dx, 0 ),
( (x^2*z0^3) * dx, 0 ),
( (x^2*z0^3*z1) * dx, 0 ),
( (x^2*z0^4) * dx, 0 ),
( (x^2*z0^4*z1 - x^5) * dx, 0 ),
( (x^3) * dx, 0 ),
( (x^3*z1) * dx, 0 ),
( (x^3*z0) * dx, 0 ),
( (x^3*z0*z1) * dx, 0 ),
( (x^3*z0^2) * dx, 0 ),
( (-x^4*z0^3 + x^3*z0^2*z1) * dx, 0 ),
( (x^3*z0^3) * dx, 0 ),
( (x^3*z0^4) * dx, 0 ),
( (x^4) * dx, 0 ),
( (x^4*z0) * dx, 0 ),
( (x^4*z0^2) * dx, 0 ),
( (-2*x^5) * dx, z1/x ),
( (x^5*z1) * dx, z1^2/x ),
( (-x^5*z1^2) * dx, z1^3/x ),
( (2*x^5*z1^3) * dx, z1^4/x ),
( (-2*x^5*z0) * dx, z0*z1/x ),
( (x^5*z0*z1) * dx, z0*z1^2/x ),
( (-x^5*z0*z1^2) * dx, z0*z1^3/x ),
( (2*x^5*z0*z1^3 - x^4*z0^4 + x^3*z0^3*z1 - 2*x^2*z0^2*z1^2) * dx, z0*z1^4/x ),
( (-2*x^5*z0^2) * dx, z0^2*z1/x ),
( (x^5*z0^2*z1) * dx, z0^2*z1^2/x ),
( (-x^5*z0^2*z1^2) * dx, z0^2*z1^3/x ),
( (2*x^5*z0^2*z1^3 - x^3*z0^4*z1 - x^2*z0^3*z1^2 - x^6 - x*z0^2*z1^3) * dx, z0^2*z1^4/x ),
( (0) * dx, z0^3/x ),
( (-2*x^5*z0^3) * dx, z0^3*z1/x ),
( (x^5*z0^3*z1) * dx, z0^3*z1^2/x ),
( (-x^5*z0^3*z1^2 - x^5) * dx, z0^3*z1^3/x ),
( (2*x^5*z0^3*z1^3 - z0^2*z1^4) * dx, z0^3*z1^4/x ),
( (0) * dx, z0^4/x ),
( (-2*x^5*z0^4) * dx, z0^4*z1/x ),
( (x^5*z0^4*z1) * dx, z0^4*z1^2/x ),
( (-x^5*z0^4*z1^2 + x^5*z0 + x^4*z1) * dx, z0^4*z1^3/x ),
( (2*x^5*z0^4*z1^3 - x^4*z0^3 + 2*z0^3*z1^4) * dx, z0^4*z1^4/x ),
( (x^4*z1) * dx, z1^2/x^2 ),
( (-x^4*z1^2) * dx, z1^3/x^2 ),
( (2*x^4*z1^3) * dx, z1^4/x^2 ),
( (x^4*z0*z1) * dx, z0*z1^2/x^2 ),
( (-x^4*z0*z1^2) * dx, z0*z1^3/x^2 ),
( (2*x^4*z0*z1^3) * dx, z0*z1^4/x^2 ),
( (x^4*z0^2*z1) * dx, z0^2*z1^2/x^2 ),
( (-x^4*z0^2*z1^2) * dx, z0^2*z1^3/x^2 ),
( (2*x^4*z0^2*z1^3 + x^5) * dx, z0^2*z1^4/x^2 ),
( (-2*x^4*z0^3) * dx, z0^3*z1/x^2 ),
( (x^4*z0^3*z1) * dx, z0^3*z1^2/x^2 ),
( (-x^4*z0^3*z1^2) * dx, z0^3*z1^3/x^2 ),
( (2*x^4*z0^3*z1^3 - 2*x^5*z0 + x^4*z1) * dx, z0^3*z1^4/x^2 ),
( (-2*x^4*z0^4) * dx, z0^4*z1/x^2 ),
( (x^4*z0^4*z1) * dx, z0^4*z1^2/x^2 ),
( (-x^4*z0^4*z1^2) * dx, z0^4*z1^3/x^2 ),
( (2*x^4*z0^4*z1^3 + x^5*z0^2 - x^4*z0*z1 + 2*x^3*z1^2) * dx, z0^4*z1^4/x^2 ),
( (-x^3*z1^2) * dx, z1^3/x^3 ),
( (2*x^3*z1^3) * dx, z1^4/x^3 ),
( (-x^3*z0*z1^2) * dx, z0*z1^3/x^3 ),
( (2*x^3*z0*z1^3) * dx, z0*z1^4/x^3 ),
( (-x^3*z0^2*z1^2) * dx, z0^2*z1^3/x^3 ),
( (2*x^3*z0^2*z1^3) * dx, z0^2*z1^4/x^3 ),
( (x^3*z0^3*z1) * dx, z0^3*z1^2/x^3 ),
( (-x^3*z0^3*z1^2) * dx, z0^3*z1^3/x^3 ),
( (2*x^3*z0^3*z1^3) * dx, z0^3*z1^4/x^3 ),
( (x^3*z0^4*z1) * dx, z0^4*z1^2/x^3 ),
( (-x^3*z0^4*z1^2) * dx, z0^4*z1^3/x^3 ),
( (2*x^3*z0^4*z1^3) * dx, z0^4*z1^4/x^3 ),
( (2*x^2*z1^3) * dx, z1^4/x^4 ),
( (2*x^2*z0*z1^3) * dx, z0*z1^4/x^4 ),
( (-x^2*z0^2*z1^2) * dx, z0^2*z1^3/x^4 ),
( (2*x^2*z0^2*z1^3) * dx, z0^2*z1^4/x^4 ),
( (-x^2*z0^3*z1^2) * dx, z0^3*z1^3/x^4 ),
( (2*x^2*z0^3*z1^3) * dx, z0^3*z1^4/x^4 ),
( (-x^2*z0^4*z1^2) * dx, z0^4*z1^3/x^4 ),
( (2*x^2*z0^4*z1^3) * dx, z0^4*z1^4/x^4 ),
( (2*x*z0^2*z1^3) * dx, z0^2*z1^4/x^5 ),
( (2*x*z0^3*z1^3) * dx, z0^3*z1^4/x^5 ),
( (2*x*z0^4*z1^3) * dx, z0^4*z1^4/x^5 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7l, B = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l_(AS)[?7h[?12l[?25h[?25l[?7ld(AS)[?7h[?12l[?25h[?25l[?7lr(AS)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7lR(AS)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l();[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_dR(AS); magma
 magma 
 magma_free
 magmathis 
 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l
 magma 
 <unknown> [?7h[?12l[?25h[?25l[?7l_free
 magma 
 magma_free[?7h[?12l[?25h[?25l[?7lthis
 magma_free
 magmathis [?7h[?12l[?25h[?25l[?7l



[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_dR(AS); magmathis(A, B)
[?7h[?12l[?25h[?2004l
^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[24;1R^[[25;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R
^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[24;1R^[[25;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [1;3S[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^3
z1^2 - z1 = x^5
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_dR(AS); magmathis(A, B)[?7h[?12l[?25h[?25l[?7lS.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ljumps[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lsage: AS.jumps
[?7h[?12l[?25h[?2004l[?7h[[3, 7]]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.jumps[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lraification_jumps()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lfication_jumps()[?7h[?12l[?25h[?25l[?7lsage: AS.ramification_jumps()
[?7h[?12l[?25h[?2004l[?7h[3, 7]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.ramification_jumps()[?7h[?12l[?25h[?25l[?7ljups[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^3
z1^2 - z1 = x^7
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.ramification_jumps()[?7h[?12l[?25h[?25l[?7ljups[?7h[?12l[?25h[?25l[?7lsage: AS.jumps
[?7h[?12l[?25h[?2004l[?7h[[3, 11]]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.jumps[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l1 3 [[3, 11]] 1 5
^C---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Input In [6], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
File <string>:44, in __init__(self, C, list_of_fcts, prec)
File <string>:134, in artin_schreier_transform(power_series, prec)
File <string>:12, in new_reverse(power_series, prec)
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1831, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
 1829 if x:
 1830 raise ValueError("must not specify %s keyword and positional argument" % name)
-> 1831 a = self(kwds[name])
 1832 del kwds[name]
 1833 try:
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1852, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
 1850 x = x[0]
 1851
-> 1852 return self.__u(*x)*(x[0]**self.__n)
 1853
 1854 def __pari__(self):
File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:365, in sage.rings.power_series_poly.PowerSeries_poly.__call__()
 363 x[0] = a
 364 x = tuple(x)
--> 365 return self.__f(x)
 366
 367 def _unsafe_mutate(self, i, value):
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:898, in sage.rings.polynomial.polynomial_element.Polynomial.__call__()
 896 return result
 897 pol._compiled = CompiledPolynomialFunction(pol.list())
--> 898 return pol._compiled.eval(a)
 899
 900 def compose_trunc(self, Polynomial other, long n):
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:125, in sage.rings.polynomial.polynomial_compiled.CompiledPolynomialFunction.eval()
 123 cdef object temp
 124 try:
--> 125 pd_eval(self._dag, x, self._coeffs) #see further down
 126 temp = self._dag.value #for an explanation
 127 pd_clean(self._dag) #of these 3 lines
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
 352 if pd.value is None:
--> 353 pd.eval(vars, coeffs)
 354 pd.hits += 1
 355
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
 505
 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507 pd_eval(self.left, vars, coeffs)
 508 pd_eval(self.right, vars, coeffs)
 509 self.value = self.left.value * self.right.value + coeffs[self.index]
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
 352 if pd.value is None:
--> 353 pd.eval(vars, coeffs)
 354 pd.hits += 1
 355
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
 505
 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507 pd_eval(self.left, vars, coeffs)
 508 pd_eval(self.right, vars, coeffs)
 509 self.value = self.left.value * self.right.value + coeffs[self.index]
[... skipping similar frames: sage.rings.polynomial.polynomial_compiled.pd_eval at line 353 (96 times), sage.rings.polynomial.polynomial_compiled.abc_pd.eval at line 507 (95 times)]
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
 505
 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507 pd_eval(self.left, vars, coeffs)
 508 pd_eval(self.right, vars, coeffs)
 509 self.value = self.left.value * self.right.value + coeffs[self.index]
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
 352 if pd.value is None:
--> 353 pd.eval(vars, coeffs)
 354 pd.hits += 1
 355
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:509, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
 507 pd_eval(self.left, vars, coeffs)
 508 pd_eval(self.right, vars, coeffs)
--> 509 self.value = self.left.value * self.right.value + coeffs[self.index]
 510 pd_clean(self.left)
 511 pd_clean(self.right)
File /ext/sage/9.7/src/sage/structure/element.pyx:1233, in sage.structure.element.Element.__add__()
 1231 # Left and right are Sage elements => use coercion model
 1232 if BOTH_ARE_ELEMENT(cl):
-> 1233 return coercion_model.bin_op(left, right, add)
 1234
 1235 cdef long value
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
 1202 self._record_exception()
 1203 else:
-> 1204 return PyObject_CallObject(op, xy)
 1205
 1206 if op is mul:
File /ext/sage/9.7/src/sage/structure/element.pyx:1230, in sage.structure.element.Element.__add__()
 1228 cdef int cl = classify_elements(left, right)
 1229 if HAVE_SAME_PARENT(cl):
-> 1230 return (<Element>left)._add_(right)
 1231 # Left and right are Sage elements => use coercion model
 1232 if BOTH_ARE_ELEMENT(cl):
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:764, in sage.rings.laurent_series_ring_element.LaurentSeries._add_()
 762 elif self.__n > right.__n:
 763 m = right.__n
--> 764 f1 = self.__u << self.__n - m
 765 f2 = right.__u
 766 else:
File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:583, in sage.rings.power_series_poly.PowerSeries_poly.__lshift__()
 581 """
 582 if n:
--> 583 return PowerSeries_poly(self._parent, self.__f << n, self._prec + n)
 584 else:
 585 return self
File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:44, in sage.rings.power_series_poly.PowerSeries_poly.__init__()
 42 ValueError: series has negative valuation
 43 """
---> 44 R = parent._poly_ring()
 45 if isinstance(f, Element):
 46 if (<Element>f)._parent is R:
File /ext/sage/9.7/src/sage/rings/power_series_ring.py:961, in PowerSeriesRing_generic._poly_ring(self)
 958 pass
 959 return False
--> 961 def _poly_ring(self):
 962 """
 963  Return the underlying polynomial ring used to represent elements of
 964  this power series ring.
 (...)
 970  Univariate Polynomial Ring in t over Integer Ring
 971  """
 972 return self.__poly_ring
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
KeyboardInterrupt:
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l1 3 [[3, 11]] 1 5
1 5 [[3, 11]] 1 9
1 7 [[3, 11]] 1 13
1 9 [[3, 11]] 1 17
1 11 [[3, 11]] 1 21
1 13 [[3, 11]] 1 25
3 5 [[3, 11]] 3 7
3 7 [[3, 11]] 3 11
3 9 [[3, 11]] 3 15
3 11 [[3, 11]] 3 19
3 13 [[3, 11]] 3 23
5 7 [[3, 11]] 5 9
5 9 [[3, 11]] 5 13
5 11 [[3, 11]] 5 17
5 13 [[3, 11]] 5 21
7 9 [[3, 11]] 7 11
7 11 [[3, 11]] 7 15
7 13 [[3, 11]] 7 19
9 11 [[3, 11]] 9 13
9 13 [[3, 11]] 9 17
11 13 [[3, 11]] 11 15
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l1 3 [[1, 5]] 1 5
1 5 [[1, 9]] 1 9
1 7 [[1, 13]] 1 13
1 9 [[1, 17]] 1 17
1 11 [[1, 21]] 1 21
1 13 [[1, 25]] 1 25
3 5 [[3, 7]] 3 7
3 7 [[3, 11]] 3 11
3 9 [[3, 15]] 3 15
3 11 [[3, 19]] 3 19
3 13 [[3, 23]] 3 23
5 7 [[5, 9]] 5 9
5 9 [[5, 13]] 5 13
5 11 [[5, 17]] 5 17
5 13 [[5, 21]] 5 21
7 9 [[7, 11]] 7 11
7 11 [[7, 15]] 7 15
7 13 [[7, 19]] 7 19
9 11 [[9, 13]] 9 13
9 13 [[9, 17]] 9 17
11 13 [[11, 15]] 11 15
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.jumps[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS
[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^11
z1^2 - z1 = x^13
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.jumps[?7h[?12l[?25h[?25l[?7lraification_jumps()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lfication_jumps()[?7h[?12l[?25h[?25l[?7lsage: AS.ramification_jumps()
[?7h[?12l[?25h[?2004l[?7h[11, 15]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.ramification_jumps()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lonent_of_different_prim()[?7h[?12l[?25h[?25l[?7lsage: AS.exponent_of_different_prim()
[?7h[?12l[?25h[?2004l[?7h37
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l1 3 [[1, 5]] 1 5
3 7
1 5 [[1, 9]] 1 9
7 11
1 7 [[1, 13]] 1 13
11 15
1 9 [[1, 17]] 1 17
15 19
1 11 [[1, 21]] 1 21
19 23
1 13 [[1, 25]] 1 25
23 27
3 5 [[3, 7]] 3 7
9 13
3 7 [[3, 11]] 3 11
13 17
3 9 [[3, 15]] 3 15
17 21
3 11 [[3, 19]] 3 19
21 25
3 13 [[3, 23]] 3 23
25 29
5 7 [[5, 9]] 5 9
15 19
5 9 [[5, 13]] 5 13
19 23
5 11 [[5, 17]] 5 17
23 27
5 13 [[5, 21]] 5 21
27 31
7 9 [[7, 11]] 7 11
21 25
7 11 [[7, 15]] 7 15
25 29
7 13 [[7, 19]] 7 19
29 33
9 11 [[9, 13]] 9 13
27 31
9 13 [[9, 17]] 9 17
31 35
11 13 [[11, 15]] 11 15
33 37
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l1 3 [[1, 5]] 1 5
7 7
1 5 [[1, 9]] 1 9
11 11
1 7 [[1, 13]] 1 13
15 15
1 9 [[1, 17]] 1 17
19 19
1 11 [[1, 21]] 1 21
23 23
1 13 [[1, 25]] 1 25
27 27
3 5 [[3, 7]] 3 7
13 13
3 7 [[3, 11]] 3 11
17 17
3 9 [[3, 15]] 3 15
21 21
3 11 [[3, 19]] 3 19
25 25
3 13 [[3, 23]] 3 23
29 29
5 7 [[5, 9]] 5 9
19 19
5 9 [[5, 13]] 5 13
23 23
5 11 [[5, 17]] 5 17
27 27
5 13 [[5, 21]] 5 21
31 31
7 9 [[7, 11]] 7 11
25 25
7 11 [[7, 15]] 7 15
29 29
7 13 [[7, 19]] 7 19
33 33
9 11 [[9, 13]] 9 13
31 31
9 13 [[9, 17]] 9 17
35 35
11 13 [[11, 15]] 11 15
37 37
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lzmag = AS.magical_element(threshold = 18)[0][?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7l.jorda_form(subdivide=True)[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[1]^2/AS.x*AS.dx[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]*[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: AS.z[0]*AS.z[1]
[?7h[?12l[?25h[?2004l[?7hz0*z1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[0]*AS.z[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]*AS.z[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]*AS.z[1]).norm()
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [15], in <cell line: 1>()
----> 1 (AS.z[Integer(0)]*AS.z[Integer(1)]).norm()
AttributeError: 'as_function' object has no attribute 'norm'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprint((identity_matrix(n) + A2.transpose()*A2).determinant()%p)[?7h[?12l[?25h[?25l[?7l = q.factor()[0][0][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[0]*AS.z[1][?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lmagical_element()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lal_element()[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element()
[?7h[?12l[?25h[?2004l[?7h[]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7lh)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7lh)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7ll)[?7h[?12l[?25h[?25l[?7ld)[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element(threshold=20)
[?7h[?12l[?25h[?2004l[?7h[x^12 + z0*z1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lare_equivalent_matrix(A1, A2, q)[?7h[?12l[?25h[?25l[?7lsage: a
[?7h[?12l[?25h[?2004l[?7h13
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lsage: b
[?7h[?12l[?25h[?2004l[?7h13
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]*AS.z[1]).norm()[?7h[?12l[?25h[?25l[?7la^8 + a^7 + a^5 + a^3 + a^2)^2[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: (a+b)/2
[?7h[?12l[?25h[?2004l[?7h13
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element(threshold=20)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS
[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^11
z1^2 - z1 = x^13
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a+b)/2[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: (11+13)/2
[?7h[?12l[?25h[?2004l[?7h12
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l1 3 [[1, 5]] 1 5
7 7
1 5 [[1, 9]] 1 9
11 11
1 7 [[1, 13]] 1 13
15 15
1 9 [[1, 17]] 1 17
19 19
1 11 [[1, 21]] 1 21
23 23
1 13 [[1, 25]] 1 25
27 27
3 5 [[3, 7]] 3 7
13 13
3 7 [[3, 11]] 3 11
17 17
3 9 [[3, 15]] 3 15
21 21
3 11 [[3, 19]] 3 19
25 25
3 13 [[3, 23]] 3 23
29 29
5 7 [[5, 9]] 5 9
19 19
5 9 [[5, 13]] 5 13
23 23
5 11 [[5, 17]] 5 17
27 27
5 13 [[5, 21]] 5 21
31 31
7 9 [[7, 11]] 7 11
25 25
7 11 [[7, 15]] 7 15
29 29
7 13 [[7, 19]] 7 19
33 33
9 11 [[9, 13]] 9 13
31 31
9 13 [[9, 17]] 9 17
35 35
11 13 [[11, 15]] 11 15
37 37
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.magical_element(threshold=20)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lgical_element(threshold=20)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element()
[?7h[?12l[?25h[?2004l[?7h[(a + 1)*x^3 + z0*z1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l16.factor()[0][0][?7h[?12l[?25h[?25l[?7l/(a^13 + a^12 + a^11 + a^9 + a^8 + a^4 + a^3 + a)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: 1/(a+1)
[?7h[?12l[?25h[?2004l[?7ha
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[x^6*z0 + x^5*z1 + x^4*z0 + x^4*z2 + z0*z1*z2]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[x^7*z0 + x^6*z1 + x^5*z0 + x^4*z2 + z0*z1*z2]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[x^7*z0 + x^6*z0 + x^6*z1 + x^5*z0 + x^5*z1 + x^4*z2 + z0*z1*z2]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l/ext/sage/9.7/src/sage/rings/polynomial/polynomial_singular_interface.py:372:
********************************************************************************
Denominators of fraction field elements are sometimes dropped without warning.
This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696.
********************************************************************************
>> A := MatrixAlgebra<GF(4),6|[1, a + 1, 0, 0, 0, a, 0, 1, 0, 0, 0, 0, 0, 0, 1
^
User error: Identifier 'a' has not been declared or assigned
>> , 0, 1, 0, 0, 0, 0, 0, 0, 1]>;M := RModule(RSpace(GF(4),6), A);Indecomposab
^
User error: Identifier 'A' has not been declared or assigned
>> ,6), A);IndecomposableSummands(M);
^
User error: Identifier 'M' has not been declared or assigned
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [4], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:16, in <module>
TypeError: group_action_matrices_holo() got an unexpected keyword argument 'threshold'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[
RModule of dimension 1 over GF(2^2),
RModule of dimension 2 over GF(2^2)
]
[
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[
RModule of dimension 1 over GF(2^2),
RModule of dimension 2 over GF(2^2),
RModule of dimension 3 over GF(2^2)
]
[
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[
RModule of dimension 1 over GF(2^2),
RModule of dimension 1 over GF(2^2),
RModule of dimension 2 over GF(2^2),
RModule of dimension 2 over GF(2^2),
RModule of dimension 3 over GF(2^2)
]
[
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[
RModule of dimension 1 over GF(2^2),
RModule of dimension 2 over GF(2^2)
]
[
RModule of dimension 3 over GF(2^2),
RModule of dimension 3 over GF(2^2)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[
RModule of dimension 1 over GF(2^2),
RModule of dimension 2 over GF(2^2)
]
F<a> := GF(4);A := MatrixAlgebra<GF(4),6|[1, a + 1, 0, 0, 0, a, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, a, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1],[1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, a, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1]>;M := RModule(RSpace(GF(4),6), A);IndecomposableSummands(M);
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[
RModule of dimension 1 over GF(2),
RModule of dimension 4 over GF(2)
]
F<a> := GF(4);A := MatrixAlgebra<GF(2),10|[1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],[1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]>;M := RModule(RSpace(GF(2),10), A);IndecomposableSummands(M);
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[
RModule of dimension 1 over GF(2),
RModule of dimension 4 over GF(2)
]
[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[
RModule of dimension 1 over GF(2),
RModule of dimension 4 over GF(2)
]
A := MatrixAlgebra<GF(2),10|[1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],[1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]>;M := RModule(RSpace(GF(2),10), A);IndecomposableSummands(M);
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004lWARNING: your terminal doesn't support cursor position requests (CPR).
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[
RModule of dimension 1 over GF(2),
RModule of dimension 4 over GF(2)
]
^C^C
KeyboardInterrupt
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l1 3 [[1, 5]] 1 5
7 7
1 5 [[1, 9]] 1 9
11 11
1 7 [[1, 13]] 1 13
15 15
^C---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zz_pex.pyx:280, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.__call__()
 279 try:
--> 280 if a.parent() is not K:
 281 a = K.coerce(a)
AttributeError: 'tuple' object has no attribute 'parent'
During handling of the above exception, another exception occurred:
KeyboardInterrupt Traceback (most recent call last)
Input In [2], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:26, in <module>
File <string>:44, in __init__(self, C, list_of_fcts, prec)
File <string>:134, in artin_schreier_transform(power_series, prec)
File <string>:12, in new_reverse(power_series, prec)
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1831, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
 1829 if x:
 1830 raise ValueError("must not specify %s keyword and positional argument" % name)
-> 1831 a = self(kwds[name])
 1832 del kwds[name]
 1833 try:
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1852, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
 1850 x = x[0]
 1851
-> 1852 return self.__u(*x)*(x[0]**self.__n)
 1853
 1854 def __pari__(self):
File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:365, in sage.rings.power_series_poly.PowerSeries_poly.__call__()
 363 x[0] = a
 364 x = tuple(x)
--> 365 return self.__f(x)
 366
 367 def _unsafe_mutate(self, i, value):
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zz_pex.pyx:283, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.__call__()
 281 a = K.coerce(a)
 282 except (TypeError, AttributeError, NotImplementedError):
--> 283 return Polynomial.__call__(self, a)
 284
 285 _a = self._parent._modulus.ZZ_pE(list(a.polynomial()))
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:898, in sage.rings.polynomial.polynomial_element.Polynomial.__call__()
 896 return result
 897 pol._compiled = CompiledPolynomialFunction(pol.list())
--> 898 return pol._compiled.eval(a)
 899
 900 def compose_trunc(self, Polynomial other, long n):
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:125, in sage.rings.polynomial.polynomial_compiled.CompiledPolynomialFunction.eval()
 123 cdef object temp
 124 try:
--> 125 pd_eval(self._dag, x, self._coeffs) #see further down
 126 temp = self._dag.value #for an explanation
 127 pd_clean(self._dag) #of these 3 lines
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
 352 if pd.value is None:
--> 353 pd.eval(vars, coeffs)
 354 pd.hits += 1
 355
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
 505
 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507 pd_eval(self.left, vars, coeffs)
 508 pd_eval(self.right, vars, coeffs)
 509 self.value = self.left.value * self.right.value + coeffs[self.index]
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
 352 if pd.value is None:
--> 353 pd.eval(vars, coeffs)
 354 pd.hits += 1
 355
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
 505
 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507 pd_eval(self.left, vars, coeffs)
 508 pd_eval(self.right, vars, coeffs)
 509 self.value = self.left.value * self.right.value + coeffs[self.index]
[... skipping similar frames: sage.rings.polynomial.polynomial_compiled.pd_eval at line 353 (10 times), sage.rings.polynomial.polynomial_compiled.abc_pd.eval at line 507 (9 times)]
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
 505
 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507 pd_eval(self.left, vars, coeffs)
 508 pd_eval(self.right, vars, coeffs)
 509 self.value = self.left.value * self.right.value + coeffs[self.index]
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
 352 if pd.value is None:
--> 353 pd.eval(vars, coeffs)
 354 pd.hits += 1
 355
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:509, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
 507 pd_eval(self.left, vars, coeffs)
 508 pd_eval(self.right, vars, coeffs)
--> 509 self.value = self.left.value * self.right.value + coeffs[self.index]
 510 pd_clean(self.left)
 511 pd_clean(self.right)
File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__()
 1512 cdef int cl = classify_elements(left, right)
 1513 if HAVE_SAME_PARENT(cl):
-> 1514 return (<Element>left)._mul_(right)
 1515 if BOTH_ARE_ELEMENT(cl):
 1516 return coercion_model.bin_op(left, right, mul)
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:912, in sage.rings.laurent_series_ring_element.LaurentSeries._mul_()
 910 """
 911 cdef LaurentSeries right = <LaurentSeries>right_r
--> 912 return type(self)(self._parent,
 913 self.__u * right.__u,
 914 self.__n + right.__n)
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:165, in sage.rings.laurent_series_ring_element.LaurentSeries.__init__()
 163 self.__u = f
 164 else:
--> 165 val = f.valuation()
 166 if val is infinity:
 167 self.__n = 0
File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:134, in sage.rings.power_series_poly.PowerSeries_poly.valuation()
 132 return self._prec
 133
--> 134 return self.__f.valuation()
 135
 136 def degree(self):
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:9215, in sage.rings.polynomial.polynomial_element.Polynomial.valuation()
 9213 if p is None:
 9214 for k from 0 <= k <= self.degree():
-> 9215 if self.get_unsafe(k):
 9216 return ZZ(k)
 9217 if isinstance(p, Polynomial):
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zz_pex.pyx:179, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.get_unsafe()
 177 self._parent._modulus.restore()
 178 cdef ZZ_pE_c c_pE = ZZ_pEX_coeff(self.x, i)
--> 179 return self._parent._base(ZZ_pE_c_to_list(c_pE))
 180
 181 cpdef list list(self, bint copy=True):
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
 895 if mor is not None:
 896 if no_extra_args:
--> 897 return mor._call_(x)
 898 else:
 899 return mor._call_with_args(x, args, kwds)
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
 154 cdef Parent C = self._codomain
 155 try:
--> 156 return C._element_constructor(x)
 157 except Exception:
 158 if print_warnings:
File /ext/sage/9.7/src/sage/rings/finite_rings/finite_field_givaro.py:229, in FiniteField_givaro._element_constructor_(self, e)
 211 """
 212  Return a random element of ``self``.
 213
 (...)
 225  True
 226  """
 227 return self._cache.random_element()
--> 229 def _element_constructor_(self, e):
 230 """
 231  Coerces several data types to ``self``.
 232
 (...)
 368  2*a4^3 + 2*a4^2 + 1
 369  """
 370 return self._cache.element_from_data(e)
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
KeyboardInterrupt:
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l1 2 [[1, 4]] 1 4
7 14
1 4 [[1, 10]] 1 10
13 26
^C---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zz_pex.pyx:280, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.__call__()
 279 try:
--> 280 if a.parent() is not K:
 281 a = K.coerce(a)
AttributeError: 'tuple' object has no attribute 'parent'
During handling of the above exception, another exception occurred:
KeyboardInterrupt Traceback (most recent call last)
Input In [3], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:26, in <module>
File <string>:44, in __init__(self, C, list_of_fcts, prec)
File <string>:134, in artin_schreier_transform(power_series, prec)
File <string>:12, in new_reverse(power_series, prec)
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1831, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
 1829 if x:
 1830 raise ValueError("must not specify %s keyword and positional argument" % name)
-> 1831 a = self(kwds[name])
 1832 del kwds[name]
 1833 try:
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1852, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
 1850 x = x[0]
 1851
-> 1852 return self.__u(*x)*(x[0]**self.__n)
 1853
 1854 def __pari__(self):
File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:365, in sage.rings.power_series_poly.PowerSeries_poly.__call__()
 363 x[0] = a
 364 x = tuple(x)
--> 365 return self.__f(x)
 366
 367 def _unsafe_mutate(self, i, value):
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zz_pex.pyx:283, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.__call__()
 281 a = K.coerce(a)
 282 except (TypeError, AttributeError, NotImplementedError):
--> 283 return Polynomial.__call__(self, a)
 284
 285 _a = self._parent._modulus.ZZ_pE(list(a.polynomial()))
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:898, in sage.rings.polynomial.polynomial_element.Polynomial.__call__()
 896 return result
 897 pol._compiled = CompiledPolynomialFunction(pol.list())
--> 898 return pol._compiled.eval(a)
 899
 900 def compose_trunc(self, Polynomial other, long n):
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:125, in sage.rings.polynomial.polynomial_compiled.CompiledPolynomialFunction.eval()
 123 cdef object temp
 124 try:
--> 125 pd_eval(self._dag, x, self._coeffs) #see further down
 126 temp = self._dag.value #for an explanation
 127 pd_clean(self._dag) #of these 3 lines
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
 352 if pd.value is None:
--> 353 pd.eval(vars, coeffs)
 354 pd.hits += 1
 355
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
 505
 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507 pd_eval(self.left, vars, coeffs)
 508 pd_eval(self.right, vars, coeffs)
 509 self.value = self.left.value * self.right.value + coeffs[self.index]
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
 352 if pd.value is None:
--> 353 pd.eval(vars, coeffs)
 354 pd.hits += 1
 355
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
 505
 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507 pd_eval(self.left, vars, coeffs)
 508 pd_eval(self.right, vars, coeffs)
 509 self.value = self.left.value * self.right.value + coeffs[self.index]
[... skipping similar frames: sage.rings.polynomial.polynomial_compiled.pd_eval at line 353 (13 times), sage.rings.polynomial.polynomial_compiled.abc_pd.eval at line 507 (12 times)]
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
 505
 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507 pd_eval(self.left, vars, coeffs)
 508 pd_eval(self.right, vars, coeffs)
 509 self.value = self.left.value * self.right.value + coeffs[self.index]
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
 352 if pd.value is None:
--> 353 pd.eval(vars, coeffs)
 354 pd.hits += 1
 355
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:509, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
 507 pd_eval(self.left, vars, coeffs)
 508 pd_eval(self.right, vars, coeffs)
--> 509 self.value = self.left.value * self.right.value + coeffs[self.index]
 510 pd_clean(self.left)
 511 pd_clean(self.right)
File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__()
 1512 cdef int cl = classify_elements(left, right)
 1513 if HAVE_SAME_PARENT(cl):
-> 1514 return (<Element>left)._mul_(right)
 1515 if BOTH_ARE_ELEMENT(cl):
 1516 return coercion_model.bin_op(left, right, mul)
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:913, in sage.rings.laurent_series_ring_element.LaurentSeries._mul_()
 911 cdef LaurentSeries right = <LaurentSeries>right_r
 912 return type(self)(self._parent,
--> 913 self.__u * right.__u,
 914 self.__n + right.__n)
 915
File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__()
 1512 cdef int cl = classify_elements(left, right)
 1513 if HAVE_SAME_PARENT(cl):
-> 1514 return (<Element>left)._mul_(right)
 1515 if BOTH_ARE_ELEMENT(cl):
 1516 return coercion_model.bin_op(left, right, mul)
File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:539, in sage.rings.power_series_poly.PowerSeries_poly._mul_()
 537 19*w^10 + 323*w^11 + O(w^12)
 538 """
--> 539 prec = self._mul_prec(right_r)
 540 return PowerSeries_poly(self._parent,
 541 self.__f * (<PowerSeries_poly>right_r).__f,
File /ext/sage/9.7/src/sage/rings/power_series_ring_element.pyx:949, in sage.rings.power_series_ring_element.PowerSeries._mul_prec()
 947 prec = sp + right.valuation()
 948 else:
--> 949 prec = min(rp + self.valuation(), sp + right.valuation())
 950 # endif
 951 return prec
File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:131, in sage.rings.power_series_poly.PowerSeries_poly.valuation()
 129 +Infinity
 130 """
--> 131 if self.__f == 0:
 132 return self._prec
 133
File /ext/sage/9.7/src/sage/structure/element.pyx:1112, in sage.structure.element.Element.__richcmp__()
 1110 return (<Element>self)._richcmp_(other, op)
 1111 else:
-> 1112 return coercion_model.richcmp(self, other, op)
 1113
 1114 cpdef _richcmp_(left, right, int op):
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1973, in sage.structure.coerce.CoercionModel.richcmp()
 1971 # Coerce to a common parent
 1972 try:
-> 1973 x, y = self.canonical_coercion(x, y)
 1974 except (TypeError, NotImplementedError):
 1975 pass
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1315, in sage.structure.coerce.CoercionModel.canonical_coercion()
 1313 x_elt = x
 1314 if y_map is not None:
-> 1315 y_elt = (<Map>y_map)._call_(y)
 1316 else:
 1317 y_elt = y
File /ext/sage/9.7/src/sage/categories/map.pyx:1692, in sage.categories.map.FormalCompositeMap._call_()
 1690 """
 1691 for f in self.__list:
-> 1692 x = f._call_(x)
 1693 return x
 1694
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:153, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
 151 argument is assumed to be bound to the codomain).
 152 """
--> 153 cpdef Element _call_(self, x):
 154 cdef Parent C = self._codomain
 155 try:
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
 154 cdef Parent C = self._codomain
 155 try:
--> 156 return C._element_constructor(x)
 157 except Exception:
 158 if print_warnings:
File /ext/sage/9.7/src/sage/rings/finite_rings/finite_field_givaro.py:229, in FiniteField_givaro._element_constructor_(self, e)
 211 """
 212  Return a random element of ``self``.
 213
 (...)
 225  True
 226  """
 227 return self._cache.random_element()
--> 229 def _element_constructor_(self, e):
 230 """
 231  Coerces several data types to ``self``.
 232
 (...)
 368  2*a4^3 + 2*a4^2 + 1
 369  """
 370 return self._cache.element_from_data(e)
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
KeyboardInterrupt:
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004lTraceback (most recent call last):
File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
exec(code_obj, self.user_global_ns, self.user_ns)
Input In [4] in <cell line: 1>
load('init.sage')
File sage/misc/persist.pyx:175 in sage.misc.persist.load
sage.repl.load.load(filename, globals())
File /ext/sage/9.7/src/sage/repl/load.py:272 in load
exec(preparse_file(f.read()) + "\n", globals)
File <string>:21 in <module>
File sage/misc/persist.pyx:175 in sage.misc.persist.load
sage.repl.load.load(filename, globals())
 File /ext/sage/9.7/src/sage/repl/load.py:272 in load
 exec(preparse_file(f.read()) + "\n", globals)
 File <string>:28
 print((p-_sage_const_1 )*(a+p*b, AS.exponent_of_different_prim())
 ^
SyntaxError: '(' was never closed
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l1 2 [[1, 4]] 1 4
14 14
1 4 [[1, 10]] 1 10
26 26
1 5 [[1, 13]] 1 13
32 32
1 7 [[1, 19]] 1 19
44 44
1 8 [[1, 22]] 1 22
50 50
1 10 [[1, 28]] 1 28
62 62
1 11 [[1, 31]] 1 31
68 68
^C---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zz_pex.pyx:280, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.__call__()
 279 try:
--> 280 if a.parent() is not K:
 281 a = K.coerce(a)
AttributeError: 'tuple' object has no attribute 'parent'
During handling of the above exception, another exception occurred:
KeyboardInterrupt Traceback (most recent call last)
Input In [5], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:26, in <module>
File <string>:44, in __init__(self, C, list_of_fcts, prec)
File <string>:134, in artin_schreier_transform(power_series, prec)
File <string>:12, in new_reverse(power_series, prec)
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1831, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
 1829 if x:
 1830 raise ValueError("must not specify %s keyword and positional argument" % name)
-> 1831 a = self(kwds[name])
 1832 del kwds[name]
 1833 try:
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1852, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
 1850 x = x[0]
 1851
-> 1852 return self.__u(*x)*(x[0]**self.__n)
 1853
 1854 def __pari__(self):
File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:365, in sage.rings.power_series_poly.PowerSeries_poly.__call__()
 363 x[0] = a
 364 x = tuple(x)
--> 365 return self.__f(x)
 366
 367 def _unsafe_mutate(self, i, value):
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zz_pex.pyx:283, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.__call__()
 281 a = K.coerce(a)
 282 except (TypeError, AttributeError, NotImplementedError):
--> 283 return Polynomial.__call__(self, a)
 284
 285 _a = self._parent._modulus.ZZ_pE(list(a.polynomial()))
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:898, in sage.rings.polynomial.polynomial_element.Polynomial.__call__()
 896 return result
 897 pol._compiled = CompiledPolynomialFunction(pol.list())
--> 898 return pol._compiled.eval(a)
 899
 900 def compose_trunc(self, Polynomial other, long n):
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:125, in sage.rings.polynomial.polynomial_compiled.CompiledPolynomialFunction.eval()
 123 cdef object temp
 124 try:
--> 125 pd_eval(self._dag, x, self._coeffs) #see further down
 126 temp = self._dag.value #for an explanation
 127 pd_clean(self._dag) #of these 3 lines
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
 352 if pd.value is None:
--> 353 pd.eval(vars, coeffs)
 354 pd.hits += 1
 355
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
 505
 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507 pd_eval(self.left, vars, coeffs)
 508 pd_eval(self.right, vars, coeffs)
 509 self.value = self.left.value * self.right.value + coeffs[self.index]
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
 352 if pd.value is None:
--> 353 pd.eval(vars, coeffs)
 354 pd.hits += 1
 355
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
 505
 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507 pd_eval(self.left, vars, coeffs)
 508 pd_eval(self.right, vars, coeffs)
 509 self.value = self.left.value * self.right.value + coeffs[self.index]
[... skipping similar frames: sage.rings.polynomial.polynomial_compiled.pd_eval at line 353 (5 times), sage.rings.polynomial.polynomial_compiled.abc_pd.eval at line 507 (4 times)]
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
 505
 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507 pd_eval(self.left, vars, coeffs)
 508 pd_eval(self.right, vars, coeffs)
 509 self.value = self.left.value * self.right.value + coeffs[self.index]
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
 352 if pd.value is None:
--> 353 pd.eval(vars, coeffs)
 354 pd.hits += 1
 355
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:509, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
 507 pd_eval(self.left, vars, coeffs)
 508 pd_eval(self.right, vars, coeffs)
--> 509 self.value = self.left.value * self.right.value + coeffs[self.index]
 510 pd_clean(self.left)
 511 pd_clean(self.right)
File /ext/sage/9.7/src/sage/structure/element.pyx:1233, in sage.structure.element.Element.__add__()
 1231 # Left and right are Sage elements => use coercion model
 1232 if BOTH_ARE_ELEMENT(cl):
-> 1233 return coercion_model.bin_op(left, right, add)
 1234
 1235 cdef long value
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1200, in sage.structure.coerce.CoercionModel.bin_op()
 1198 # Now coerce to a common parent and do the operation there
 1199 try:
-> 1200 xy = self.canonical_coercion(x, y)
 1201 except TypeError:
 1202 self._record_exception()
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1315, in sage.structure.coerce.CoercionModel.canonical_coercion()
 1313 x_elt = x
 1314 if y_map is not None:
-> 1315 y_elt = (<Map>y_map)._call_(y)
 1316 else:
 1317 y_elt = y
File /ext/sage/9.7/src/sage/categories/morphism.pyx:601, in sage.categories.morphism.SetMorphism._call_()
 599 3
 600 """
--> 601 return self._function(x)
 602
 603 cpdef Element _call_with_args(self, x, args=(), kwds={}):
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:919, in sage.rings.laurent_series_ring_element.LaurentSeries._lmul_()
 917 return type(self)(self._parent, self.__u._rmul_(c), self.__n)
 918
--> 919 cpdef _lmul_(self, Element c):
 920 return type(self)(self._parent, self.__u._lmul_(c), self.__n)
 921
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:920, in sage.rings.laurent_series_ring_element.LaurentSeries._lmul_()
 918
 919 cpdef _lmul_(self, Element c):
--> 920 return type(self)(self._parent, self.__u._lmul_(c), self.__n)
 921
 922 def __pow__(_self, r, dummy):
File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:569, in sage.rings.power_series_poly.PowerSeries_poly._lmul_()
 567 2 + 6*t^4 + O(t^120)
 568 """
--> 569 return PowerSeries_poly(self._parent, c * self.__f, self._prec, check=False)
 570
 571 def __lshift__(PowerSeries_poly self, n):
File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
 1514 return (<Element>left)._mul_(right)
 1515 if BOTH_ARE_ELEMENT(cl):
-> 1516 return coercion_model.bin_op(left, right, mul)
 1517
 1518 cdef long value
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1194, in sage.structure.coerce.CoercionModel.bin_op()
 1192 if action is not None:
 1193 if (<Action>action)._is_left:
-> 1194 return (<Action>action)._act_(x, y)
 1195 else:
 1196 return (<Action>action)._act_(y, x)
File /ext/sage/9.7/src/sage/structure/coerce_actions.pyx:612, in sage.structure.coerce_actions.LeftModuleAction._act_()
 610 if self.extended_base is not None:
 611 a = <ModuleElement?>self.extended_base(a)
--> 612 return (<ModuleElement>a)._rmul_(<Element>g) # g * a
 613
 614
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:400, in sage.rings.polynomial.polynomial_element.Polynomial._rmul_()
 398 if not right:
 399 return self._parent.zero()
--> 400 return self * self._parent(right)
 401
 402 def subs(self, *x, **kwds):
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
 895 if mor is not None:
 896 if no_extra_args:
--> 897 return mor._call_(x)
 898 else:
 899 return mor._call_with_args(x, args, kwds)
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:12221, in sage.rings.polynomial.polynomial_element.PolynomialBaseringInjection._call_()
 12219 Univariate Polynomial Ring in x over Integer Ring
 12220 """
> 12221 return self._new_constant_poly_(x, self._codomain)
 12222
 12223 cpdef Element _call_with_args(self, x, args=(), kwds={}):
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:5449, in sage.rings.polynomial.polynomial_element.Polynomial._new_constant_poly()
 5447 return self.get_unsafe(0)
 5448
-> 5449 cpdef Polynomial _new_constant_poly(self, a, Parent P):
 5450 """
 5451 Create a new constant polynomial from a in P, which MUST be an
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:5463, in sage.rings.polynomial.polynomial_element.Polynomial._new_constant_poly()
 5461 """
 5462 t = type(self)
-> 5463 return t(P, [a] if a else [], check=False)
 5464
 5465 def is_monic(self):
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zz_pex.pyx:151, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.__init__()
 149 # not do K.coerce(e) but K(e).
 150 e = K(e)
--> 151 d = parent._modulus.ZZ_pE(list(e.polynomial()))
 152 ZZ_pEX_SetCoeff(self.x, i, d.x)
 153 return
File /ext/sage/9.7/src/sage/libs/ntl/ntl_ZZ_pEContext.pyx:149, in sage.libs.ntl.ntl_ZZ_pEContext.ntl_ZZ_pEContext_class.ZZ_pE()
 147 [4 3]
 148 """
--> 149 from .ntl_ZZ_pE import ntl_ZZ_pE
 150 return ntl_ZZ_pE(v,modulus=self)
 151
File <frozen importlib._bootstrap>:404, in parent(self)
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
KeyboardInterrupt:
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l1 2 [[1, 6]] 1 6
44 44
1 3 [[1, 11]] 1 11
64 64
1 4 [[1, 16]] 1 16
84 84
1 6 [[1, 26]] 1 26
124 124
1 7 [[1, 31]] 1 31
144 144
no 36 -th root; divide by 2
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [6], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:26, in <module>
File <string>:44, in __init__(self, C, list_of_fcts, prec)
ValueError: not enough values to unpack (expected 4, got 2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS
[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 5^2 with the equations:
z0^5 - z0 = x
z1^5 - z1 = x^7
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS
[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 5^2 with the equations:
z0^5 - z0 = x
z1^5 - z1 = x^7
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.magical_element()[?7h[?12l[?25h[?25l[?7lz[0]*AS.z[1][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0]*AS.z[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[]^*AS.z[1][?7h[?12l[?25h[?25l[?7l(*AS.z[1][?7h[?12l[?25h[?25l[?7l()*AS.z[1][?7h[?12l[?25h[?25l[?7l()p*AS.z[1][?7h[?12l[?25h[?25l[?7l-*AS.z[1][?7h[?12l[?25h[?25l[?7l*AS.z[1][?7h[?12l[?25h[?25l[?7l()*AS.z[1][?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)*AS.z[1][?7h[?12l[?25h[?25l[?7l-)*AS.z[1][?7h[?12l[?25h[?25l[?7l1)*AS.z[1][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004lno 8 -th root; divide by 2
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [9], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:37, in <module>
File <string>:44, in __init__(self, C, list_of_fcts, prec)
ValueError: not enough values to unpack (expected 4, got 2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS
[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 5 with the equations:
z0^5 - z0 = x^3
z1^5 - z1 = 3*x^4
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.magical_element()[?7h[?12l[?25h[?25l[?7lz[0]*AS.z[1][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]*AS.z[1][?7h[?12l[?25h[?25l[?7l[]^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.z[0]^(p-1)*AS.z[1]^(p-1)
[?7h[?12l[?25h[?2004l[?7hz0^4*z1^4
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[0]^(p-1)*AS.z[1]^(p-1)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.z[0]^(p-1)*AS.z[1]^(p-1).valuation()
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [13], in <cell line: 1>()
----> 1 AS.z[Integer(0)]**(p-Integer(1))*AS.z[Integer(1)]**(p-Integer(1)).valuation()
TypeError: Integer.valuation() takes exactly one argument (0 given)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[0]^(p-1)*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[]()[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[]()[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]^(p-1)*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()).valuation()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]^(p-1)*AS.z[1]^(p-1)).valuation()
[?7h[?12l[?25h[?2004l[?7h-140
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l4*Q[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[0]^(p-1)*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lmagical_element()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lcal_element()[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element()
[?7h[?12l[?25h[?2004l[?7h[z0^4*z1^4 + 2*x^3*z0^3*z1 - 2*x^2*z0^2*z1^3 + x^5*z0 - x^4*z1^2]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lonent_of_different_prim()[?7h[?12l[?25h[?25l[?7lsage: AS.exponent_of_different_prim()
[?7h[?12l[?25h[?2004l[?7h92
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[0]^(p-1)*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]^3*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lA)[?7h[?12l[?25h[?25l[?7lS)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lz)[?7h[?12l[?25h[?25l[?7l[)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]^3*AS.z[1]).valuation()
[?7h[?12l[?25h[?2004l[?7h-65
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]^3*AS.z[1]).valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l^).valuation()[?7h[?12l[?25h[?25l[?7l3).valuation()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*AS.z[1]^3).valuation()[?7h[?12l[?25h[?25l[?7l2*AS.z[1]^3).valuation()[?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]^2*AS.z[1]^3).valuation()
[?7h[?12l[?25h[?2004l[?7h-90
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004lno 18 -th root; divide by 3
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [19], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:37, in <module>
File <string>:44, in __init__(self, C, list_of_fcts, prec)
ValueError: not enough values to unpack (expected 4, got 2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l\[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l\[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(AS.z[0]^2*AS.z[1]^3).valuation()[?7h[?12l[?25h[?25l[?7l3).valuation()[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim[?7h[?12l[?25h[?25l[?7lsage: AS.exponent_of_different_prim()
[?7h[?12l[?25h[?2004l[?7h132
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lmagical_element()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lcal_element()[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element()
[?7h[?12l[?25h[?2004l[?7h[x^6*z0^2 - x^3*z0^3*z1^2 + z0^4*z1^4 - 2*x^6*z1 + 2*x^3*z0*z1^3]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]^2*AS.z[1]^3).valuation()[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.z[0]^2*AS.z[1]^3).valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*AS.z[1]^3).valuation()[?7h[?12l[?25h[?25l[?7l3*AS.z[1]^3).valuation()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l2).valuation()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]^3*AS.z[1]^2).valuation()
[?7h[?12l[?25h[?2004l[?7h-105
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]^3*AS.z[1]^2).valuation()[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7lexponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.magical_element()[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element()
[?7h[?12l[?25h[?2004l[?7h[]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7lh)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7lh)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7ll)[?7h[?12l[?25h[?25l[?7ld)[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element(threshold=20)
[?7h[?12l[?25h[?2004l[?7h[x^8 + x^6*z0*z1 + x^4*z0^2*z1^2 + x^2*z0^3*z1^3 + z0^4*z1^4]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element(threshold=20)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(AS.z[0]^3*AS.z[1]^2).valuation()[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7lexponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lsage: AS.exponent_of_different_prim()
[?7h[?12l[?25h[?2004l[?7h152
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lmagical_element(threshold=20)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(AS.z[0]^3*AS.z[1]^2).valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l3).valuation()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]^3*AS.z[1]^3).valuation()
[?7h[?12l[?25h[?2004l[?7h-150
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lmagical_element(threshold=20)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lgical_element(threshold=20)[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element(threshold=20)
[?7h[?12l[?25h[?2004l[?7h[x^8 + x^4*z0*z1 + z0^2*z1^2]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element(threshold=20)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.magical_element(threshold=20)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.magical_element(threshold=20)[?7h[?12l[?25h[?25l[?7lexponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lonent_of_different_prim()[?7h[?12l[?25h[?25l[?7lsage: AS.exponent_of_different_prim()
[?7h[?12l[?25h[?2004l[?7h52
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[0]^(p-1)*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0]^(p-1)*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()).valuation()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]^(p-1)*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[]()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l[]*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(().valuation()[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l().valuation()[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]*AS.z[1]).valuation()
[?7h[?12l[?25h[?2004l[?7h-36
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(AS.z[0]*AS.z[1]).valuation()[?7h[?12l[?25h[?25l[?7lAS.exponent_of_differen_prim()[?7h[?12l[?25h[?25l[?7lmagical_element(threshold=20)[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element(threshold=20)
[?7h[?12l[?25h[?2004l[?7h[x^6*z0 + x^5*z1 + z0^2*z1^2]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element(threshold=20)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_differentias_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis()
[?7h[?12l[?25h[?2004l[?7h[(1) * dx,
(x^3*z0 + z1) * dx,
(z0) * dx,
(x) * dx,
(x*z0) * dx,
(x^2) * dx,
(x^2*z0) * dx,
(x^3) * dx,
(x^4) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS
[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
z0^2 - z0 = x^3
z1^2 - z1 = x^9
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lus()[?7h[?12l[?25h[?25l[?7lsage: AS.genus()
[?7h[?12l[?25h[?2004l[?7h3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis()
[?7h[?12l[?25h[?2004l[?7h[(1) * dx, ((a + 1)*z0 + z1) * dx, (x) * dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis()
[?7h[?12l[?25h[?2004l/ext/sage/9.7/src/sage/rings/polynomial/polynomial_singular_interface.py:372:
********************************************************************************
Denominators of fraction field elements are sometimes dropped without warning.
This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696.
********************************************************************************
[?7h[( (1) * dx, 0 ),
( ((a + 1)*z0 + z1) * dx, 0 ),
( (x) * dx, 0 ),
( (0) * dx, z1/x ),
( (a*x*z0 + x*z1) * dx, z0*z1/x ),
( (a*z0 + z1) * dx, z0*z1/x^2 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1/(a+1)[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l(+1)[?7h[?12l[?25h[?25l[?7lsage: 1/(a+1)
[?7h[?12l[?25h[?2004l[?7ha
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1/(a+1)[?7h[?12l[?25h[?25l[?7lsage: 1/(a+1)
[?7h[?12l[?25h[?2004l[?7ha
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1/(a+1)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004lno 3 -th root; divide by a^2 + a + 1
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [4], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:14, in <module>
File <string>:44, in __init__(self, C, list_of_fcts, prec)
ValueError: not enough values to unpack (expected 4, got 2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis()
[?7h[?12l[?25h[?2004l/ext/sage/9.7/src/sage/rings/polynomial/polynomial_singular_interface.py:372:
********************************************************************************
Denominators of fraction field elements are sometimes dropped without warning.
This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696.
********************************************************************************
[?7h[( (1) * dx, 0 ),
( ((a^2 + a)*z0 + z1) * dx, 0 ),
( (x) * dx, 0 ),
( (0) * dx, z1/x ),
( (a*x*z0 + x*z1) * dx, z0*z1/x ),
( (a*z0 + z1) * dx, z0*z1/x^2 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1/(a+1)[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l^3 + a^12 + a^11 + a^9 + a^8 + a^4 + a^3 + a)[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: 1/(a^2+a)
[?7h[?12l[?25h[?2004l[?7ha + 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l^3[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: a^2
[?7h[?12l[?25h[?2004l[?7ha^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la^2[?7h[?12l[?25h[?25l[?7l1/(a^2+a)[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: 1/(a^2+a)^2
[?7h[?12l[?25h[?2004l[?7ha^2 + 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1/(a^2+a)^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(a^2+a)^2[?7h[?12l[?25h[?25l[?7l(a^2+a)^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (a^2+a)^2
[?7h[?12l[?25h[?2004l[?7ha
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: AS.dx
[?7h[?12l[?25h[?2004l[?7h(1) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.dx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lty[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.dx.expansion_at_infty()
[?7h[?12l[?25h[?2004l[?7h(a + 1)*t^4 + a*t^16 + t^22 + a^2*t^52 + t^64 + (a^2 + 1)*t^70 + (a^2 + a + 1)*t^76 + (a + 1)*t^88 + a^2*t^94 + (a^2 + 1)*t^196 + (a^2 + a)*t^208 + (a + 1)*t^214 + (a^2 + a + 1)*t^244 + (a + 1)*t^256 + a^2*t^262 + a*t^268 + (a^2 + 1)*t^280 + (a^2 + a + 1)*t^286 + (a^2 + a)*t^292 + O(t^295)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.dx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS
[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 2^3 with the equations:
z0^2 - z0 = x^3
z1^2 - z1 = a*x^3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.dx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7l.dx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: AS.x.expansion_at_infty()
[?7h[?12l[?25h[?2004l[?7ha*t^-4 + t^2 + (a + 1)*t^5 + (a^2 + 1)*t^8 + a*t^17 + (a^2 + a)*t^20 + t^23 + t^44 + (a^2 + 1)*t^50 + a^2*t^53 + (a^2 + a + 1)*t^56 + t^65 + (a^2 + 1)*t^71 + a^2*t^74 + (a^2 + a + 1)*t^77 + a*t^80 + (a + 1)*t^89 + (a^2 + 1)*t^92 + a^2*t^95 + (a^2 + a)*t^188 + (a + 1)*t^194 + (a^2 + 1)*t^197 + a^2*t^200 + (a^2 + a)*t^209 + t^212 + (a + 1)*t^215 + (a + 1)*t^236 + a^2*t^242 + (a^2 + a + 1)*t^245 + a*t^248 + (a + 1)*t^257 + a^2*t^263 + (a^2 + a + 1)*t^266 + a*t^269 + (a^2 + a)*t^272 + (a^2 + 1)*t^281 + (a^2 + a + 1)*t^287 + a*t^290 + (a^2 + a)*t^293 + O(t^296)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.x.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexponet_fdifferent_prim()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lonent_of_different_prim()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.exponent_of_differen()
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [15], in <cell line: 1>()
----> 1 AS.exponent_of_differen()
AttributeError: 'as_cover' object has no attribute 'exponent_of_differen'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_differen()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lt()[?7h[?12l[?25h[?25l[?7lsage: AS.exponent_of_different()
[?7h[?12l[?25h[?2004l[?7h12
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lS.exponent_of_different()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[0]^(p-1)*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.z[0].valuation()
[?7h[?12l[?25h[?2004l[?7h-6
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[0].valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l].valuation()[?7h[?12l[?25h[?25l[?7l1].valuation()[?7h[?12l[?25h[?25l[?7lsage: AS.z[1].valuation()
[?7h[?12l[?25h[?2004l[?7h-6
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[1].valuation()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.z[1].valuation()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: AS.z[1]/AS.x
[?7h[?12l[?25h[?2004l[?7hz1/x
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[1]/AS.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[1]/AS.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?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: (AS.z[1]/AS.x).diffn()
[?7h[?12l[?25h[?2004l[?7h((a*x^3 + z1)/x^2) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[1]/AS.x[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS
[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 2^3 with the equations:
z0^2 - z0 = x^3
z1^2 - z1 = a*x^3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7l(AS.z[1]/AS.x).diffn()[?7h[?12l[?25h[?25l[?7lAS.z[1]/AS.x[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()aa[?7h[?12l[?25h[?25l[?7laa[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7l.dx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_differen()[?7h[?12l[?25h[?25l[?7lt()[?7h[?12l[?25h[?25l[?7lz[0].valuation()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l/AS.x[?7h[?12l[?25h[?25l[?7l(AS.z[1]/AS.x).diffn()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?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[?7ltio[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (AS.z[1]/AS.x).diffn().valuation()
[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[1]/AS.x).diffn().valuation()[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7l(AS.z[1]/AS.x).diffn().valuation()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l]/AS.x).difn([?7h[?12l[?25h[?25l[?7l0]/AS.x).difn([?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[]*/AS.x).difn([?7h[?12l[?25h[?25l[?7lA/AS.x).difn([?7h[?12l[?25h[?25l[?7lS/AS.x).difn([?7h[?12l[?25h[?25l[?7l./AS.x).difn([?7h[?12l[?25h[?25l[?7lz/AS.x).difn([?7h[?12l[?25h[?25l[?7l[/AS.x).difn([?7h[?12l[?25h[?25l[?7l1/AS.x).difn([?7h[?12l[?25h[?25l[?7l[]/AS.x).difn([?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)([?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]*AS.z[1]/AS.x).diffn()
[?7h[?12l[?25h[?2004l[?7h((a*x^3*z0 + x^3*z1 + z0*z1)/x^2) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]*AS.z[1]/AS.x).diffn()[?7h[?12l[?25h[?25l[?7l1/x).diffn(valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7l(AS.z[1]/AS.x).diffn().valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l0*z[1]/AS.xdiffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.x).difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()^.difn()[?7h[?12l[?25h[?25l[?7l2.difn()[?7h[?12l[?25h[?25l[?7l(2).difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]*AS.z[1]/(AS.x)^2).diffn()
[?7h[?12l[?25h[?2004l[?7h(a*z0 + z1) * dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7l, B = group_action_matrices_dR(AS); magmathis(A, B)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l = group_action_matrices_dR(AS); magmathis(A, B)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l(); magmathis(A, B)[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_dR(AS)
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lsage: A
[?7h[?12l[?25h[?2004l[?7h[ 1 a^2 + a 0 0 0 a]
[ 0 1 0 0 0 0]
[ 0 0 1 0 a 0]
[ 0 0 0 1 1 0]
[ 0 0 0 0 1 0]
[ 0 0 0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lenumerate(lll)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7las[?7h[?12l[?25h[?25l[?7las_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lAx)[?7h[?12l[?25h[?25l[?7lSx)[?7h[?12l[?25h[?25l[?7l.x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[1]/AS.x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: e1 = as_cech(AS, 0*AS.dx, (AS.z[1]/AS.x)^2)
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le1 = as_cech(AS, 0*AS.dx, (AS.z[1]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: e1
[?7h[?12l[?25h[?2004l[?7h( (0) * dx, z1^2/x^2 )
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: e1.coordinates()
[?7h[?12l[?25h[?2004l[?7h(a, 0, 0, 0, 0, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le1.coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = as_cech(AS, 0*AS.dx, (AS.z[1]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l0]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]*/AS.x)^2)[?7h[?12l[?25h[?25l[?7lA/AS.x)^2)[?7h[?12l[?25h[?25l[?7lS/AS.x)^2)[?7h[?12l[?25h[?25l[?7l./AS.x)^2)[?7h[?12l[?25h[?25l[?7lz/AS.x)^2)[?7h[?12l[?25h[?25l[?7lp/AS.x)^2)[?7h[?12l[?25h[?25l[?7l[/AS.x)^2)[?7h[?12l[?25h[?25l[?7l/AS.x)^2)[?7h[?12l[?25h[?25l[?7l/AS.x)^2)[?7h[?12l[?25h[?25l[?7l[/AS.x)^2)[?7h[?12l[?25h[?25l[?7l1/AS.x)^2)[?7h[?12l[?25h[?25l[?7l[]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: e1 = as_cech(AS, 0*AS.dx, (AS.z[0]*AS.z[1]/AS.x)^2)
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le1 = as_cech(AS, 0*AS.dx, (AS.z[0]*AS.z[1]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = as_cech(AS, 0*AS.dx, (AS.z[1]/AS.x)^2)[?7h[?12l[?25h[?25l[?7lsage: e1 = as_cech(AS, 0*AS.dx, (AS.z[1]/AS.x)^2)
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le1 = as_cech(AS, 0*AS.dx, (AS.z[1]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l0*z[1]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = as_cech(AS, 0*AS.dx, (AS.z[0]*AS.z[1]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l2 = as_cech(AS, 0*AS.dx, (AS.z[0]*AS.z[1]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: e2 = as_cech(AS, 0*AS.dx, (AS.z[0]*AS.z[1]/AS.x)^2)
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le2 = as_cech(AS, 0*AS.dx, (AS.z[0]*AS.z[1]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ldinates[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: e2.coordinates()
[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, 0, 0, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le2.coordinates()[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7las[?7h[?12l[?25h[?25l[?7las_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7las[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le2.coordinates()[?7h[?12l[?25h[?25l[?7l = as_cech(AS, 0*AS.dx, (AS.z[0]*AS.z[1]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l^)^2)[?7h[?12l[?25h[?25l[?7l2)^2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = as_cech(AS, 0*AS.dx, (AS.z[0]*AS.z[1]/AS.x^2)^2)[?7h[?12l[?25h[?25l[?7l3 = as_cech(AS, 0*AS.dx, (AS.z[0]*AS.z[1]/AS.x^2)^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: e3 = as_cech(AS, 0*AS.dx, (AS.z[0]*AS.z[1]/AS.x^2)^2)
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le3 = as_cech(AS, 0*AS.dx, (AS.z[0]*AS.z[1]/AS.x^2)^2)[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: e3.coordinates()
[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, a^2 + a + 1, 0, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la^2 + a + 1[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a^2 + a + 1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: (a^2 + a + 1)^2
[?7h[?12l[?25h[?2004l[?7ha + 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a^2 + a + 1)^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1(a^2 + a + 1)^2[?7h[?12l[?25h[?25l[?7l/(a^2 + a + 1)^2[?7h[?12l[?25h[?25l[?7lsage: 1/(a^2 + a + 1)^2
[?7h[?12l[?25h[?2004l[?7ha^2 + a
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1/(a^2 + a + 1)^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(a^2 + a + 1)^2[?7h[?12l[?25h[?25l[?7l(a^2 + a + 1)^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.z[1]/AS.x[?7h[?12l[?25h[?25l[?7ldx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7le_rham_basis()[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis()
[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
( ((a^2 + a)*z0 + z1) * dx, 0 ),
( (x) * dx, 0 ),
( (0) * dx, z1/x ),
( (a*x*z0 + x*z1) * dx, z0*z1/x ),
( (a*z0 + z1) * dx, z0*z1/x^2 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmatrix(v0).transpose()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lgmathis(A, B, text=True)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lathis(A, B, text=True)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lTru)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l")[?7h[?12l[?25h[?25l[?7l")[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lG")[?7h[?12l[?25h[?25l[?7lF")[?7h[?12l[?25h[?25l[?7l")[?7h[?12l[?25h[?25l[?7l")[?7h[?12l[?25h[?25l[?7lF")[?7h[?12l[?25h[?25l[?7l,")[?7h[?12l[?25h[?25l[?7la")[?7h[?12l[?25h[?25l[?7l.")[?7h[?12l[?25h[?25l[?7l")[?7h[?12l[?25h[?25l[?7l")[?7h[?12l[?25h[?25l[?7l")[?7h[?12l[?25h[?25l[?7l<")[?7h[?12l[?25h[?25l[?7la")[?7h[?12l[?25h[?25l[?7l>?")[?7h[?12l[?25h[?25l[?7l")[?7h[?12l[?25h[?25l[?7l ")[?7h[?12l[?25h[?25l[?7l:")[?7h[?12l[?25h[?25l[?7l=")[?7h[?12l[?25h[?25l[?7l ")[?7h[?12l[?25h[?25l[?7lG")[?7h[?12l[?25h[?25l[?7lF")[?7h[?12l[?25h[?25l[?7l(")[?7h[?12l[?25h[?25l[?7l4")[?7h[?12l[?25h[?25l[?7l()")[?7h[?12l[?25h[?25l[?7l();")[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B, prefix="F<a> := GF(4);")
[?7h[?12l[?25h[?2004l[?7h>> F<a> := GF(4);A := MatrixAlgebra<GF(8),6|[1, a^2 + a, 0, 0, 0, a, 0, 1, 0,
^
Runtime error in MatrixAlgebra< ... >: Rhs argument 1 is invalid for this constructor
>> RModule(RSpace(GF(8),6), A);IndecomposableSummands(M);
^
User error: Identifier 'A' has not been declared or assigned
>> RModule(RSpace(GF(8),6), A);IndecomposableSummands(M);
^
User error: Identifier 'M' has not been declared or assigned
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS
[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 2^3 with the equations:
z0^2 - z0 = x^3
z1^2 - z1 = a*x^3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lmagmathis(A, B, prefix="F<a> := GF(4);")[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lmagmathis(A, B, prefix="F<a> := GF(4);")[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l);")[?7h[?12l[?25h[?25l[?7l8);")[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B, prefix="F<a> := GF(8);")
[?7h[?12l[?25h[?2004l[?7h[
RModule of dimension 3 over GF(2^3),
RModule of dimension 3 over GF(2^3)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lsage: A
[?7h[?12l[?25h[?2004l[?7h[ 1 a^2 + a 0 0 0 a]
[ 0 1 0 0 0 0]
[ 0 0 1 0 a 0]
[ 0 0 0 1 1 0]
[ 0 0 0 0 1 0]
[ 0 0 0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lsage: B
[?7h[?12l[?25h[?2004l[?7h[ 1 1 0 0 0 1]
[ 0 1 0 0 0 0]
[ 0 0 1 0 1 0]
[ 0 0 0 1 a + 1 0]
[ 0 0 0 0 1 0]
[ 0 0 0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lmagmathis(A, B, prefix="F<a> := GF(8);")[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7lt=)[?7h[?12l[?25h[?25l[?7lT)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7lTrue)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B, prefix="F<a> := GF(8);", text=True)
[?7h[?12l[?25h[?2004l[?7h'F<a> := GF(8);A := MatrixAlgebra<GF(8),6|[1, a^2 + a, 0, 0, 0, a, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, a, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1],[1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, a + 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),6), A);IndecomposableSummands(M);'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l1 = matrix(ZZ, [[1, 3], [3, 4]])[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l, B = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1, B = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1 = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7lh(AS)[?7h[?12l[?25h[?25l[?7lo(AS)[?7h[?12l[?25h[?25l[?7ll(AS)[?7h[?12l[?25h[?25l[?7lo(AS)[?7h[?12l[?25h[?25l[?7lsage: A1, B1 = group_action_matrices_holo(AS)
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lmagmathis(A, B, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B, prefix="F<a> := GF(8);", text=True)
[?7h[?12l[?25h[?2004l[?7h'F<a> := GF(8);A := MatrixAlgebra<GF(8),6|[1, a^2 + a, 0, 0, 0, a, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, a, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1],[1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, a + 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),6), A);IndecomposableSummands(M);'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lTru)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B, prefix="F<a> := GF(8);")
[?7h[?12l[?25h[?2004l[?7h[
RModule of dimension 3 over GF(2^3),
RModule of dimension 3 over GF(2^3)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B, prefix="F<a> := GF(8);")[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1, B, prefix="F<a> := GF(8);")[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1, prefix="F<a> := GF(8);")[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: magmathis(A1, B1, prefix="F<a> := GF(8);")
[?7h[?12l[?25h[?2004l[?7h[
RModule of dimension 1 over GF(2^3),
RModule of dimension 2 over GF(2^3)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);")[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lxt)[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7lT)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7lTrue)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A1, B1, prefix="F<a> := GF(8);", text=True)
[?7h[?12l[?25h[?2004l[?7h'F<a> := GF(8);A := MatrixAlgebra<GF(8),3|[1, a^2 + a, 0, 0, 1, 0, 0, 0, 1],[1, 1, 0, 0, 1, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),3), A);IndecomposableSummands(M);'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l, B, prefix="F<a> := GF(8);")[?7h[?12l[?25h[?25l[?7l, text=True)[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lsage: A1, B1 = group_action_matrices_holo(AS)
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A1, B1, prefix="F<a> := GF(8);", text=True)
[?7h[?12l[?25h[?2004l[?7h'F<a> := GF(8);A := MatrixAlgebra<GF(8),3|[1, a^2 + a + 1, 0, 0, 1, 0, 0, 0, 1],[1, 1, 0, 0, 1, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),3), A);IndecomposableSummands(M);'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7ld(AS)[?7h[?12l[?25h[?25l[?7lR(AS)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A1, B1 = group_action_matrices_dR(AS)
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A1, B1, prefix="F<a> := GF(8);", text=True)
[?7h[?12l[?25h[?2004l[?7h'F<a> := GF(8);A := MatrixAlgebra<GF(8),6|[1, a^2 + a + 1, 0, 0, 0, a + 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, a + 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1],[1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, a^2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),6), A);IndecomposableSummands(M);'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lsage: A1, B1 = group_action_matrices_dR(AS)
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A1, B1, prefix="F<a> := GF(8);", text=True)
[?7h[?12l[?25h[?2004l[?7h'F<a> := GF(8);A := MatrixAlgebra<GF(8),6|[1, a^2 + a, 0, 0, 0, a, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, a, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1],[1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, a + 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),6), A);IndecomposableSummands(M);'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7lh(AS)[?7h[?12l[?25h[?25l[?7lo(AS)[?7h[?12l[?25h[?25l[?7ll(AS)[?7h[?12l[?25h[?25l[?7lo(AS)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A1, B1 = group_action_matrices_holo(AS)
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A1, B1, prefix="F<a> := GF(8);", text=True)
[?7h[?12l[?25h[?2004l[?7h'F<a> := GF(8);A := MatrixAlgebra<GF(8),3|[1, a^2 + a, 0, 0, 1, 0, 0, 0, 1],[1, 1, 0, 0, 1, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),3), A);IndecomposableSummands(M);'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lsage: A1, B1 = group_action_matrices_holo(AS)
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A1, B1, prefix="F<a> := GF(8);", text=True)
[?7h[?12l[?25h[?2004l[?7h'F<a> := GF(8);A := MatrixAlgebra<GF(8),3|[1, a^2 + a + 1, 0, 0, 1, 0, 0, 0, 1],[1, 1, 0, 0, 1, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),3), A);IndecomposableSummands(M);'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis()
[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
( ((a^2 + a)*z0 + z1) * dx, 0 ),
( (x) * dx, 0 ),
( (0) * dx, z1/x ),
( (a*x*z0 + x*z1) * dx, z0*z1/x ),
( (a*z0 + z1) * dx, z0*z1/x^2 )]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le3.coordinates()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lrham_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: eta6 = AS.de_rham_basis()[5]
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta6 = AS.de_rham_basis()[5][?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: eta6.group_action([1, 0]).coordinates()
[?7h[?12l[?25h[?2004l[?7h(a, 0, 0, 0, 0, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta6.group_action([1, 0]).coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 0]).cordinates()[?7h[?12l[?25h[?25l[?7l0, 0]).cordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]).cordinates()[?7h[?12l[?25h[?25l[?7l1]).cordinates()[?7h[?12l[?25h[?25l[?7lsage: eta6.group_action([0, 1]).coordinates()
[?7h[?12l[?25h[?2004l[?7h(1, 0, 0, 0, 0, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[
RModule M of dimension 2 over GF(2^2)
]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004lF<a> := GF(4);A := MatrixAlgebra<GF(4),2|[1, 1, 0, 1],[1, a, 0, 1]>;M := RModule(RSpace(GF(4),2), A);IndecomposableSummands(M);
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004lF<a> := GF(4);A := MatrixAlgebra<GF(4),2|[1, 0, 1, 1],[1, 0, a, 1]>;M := RModule(RSpace(GF(4),2), A);IndecomposableSummands(M);
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l/ext/sage/9.7/src/sage/rings/polynomial/polynomial_singular_interface.py:372:
********************************************************************************
Denominators of fraction field elements are sometimes dropped without warning.
This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696.
********************************************************************************
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7l, B = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l(); magmathis(A, B)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lagmathis(A, B)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l")[?7h[?12l[?25h[?25l[?7l")[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lF")[?7h[?12l[?25h[?25l[?7l<")[?7h[?12l[?25h[?25l[?7l>")[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la>")[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l:")[?7h[?12l[?25h[?25l[?7l=")[?7h[?12l[?25h[?25l[?7lG")[?7h[?12l[?25h[?25l[?7lF")[?7h[?12l[?25h[?25l[?7l(")[?7h[?12l[?25h[?25l[?7l4")[?7h[?12l[?25h[?25l[?7l()")[?7h[?12l[?25h[?25l[?7l();")[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l);")[?7h[?12l[?25h[?25l[?7l8);")[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7let6.group_action([0, 1]).coordinates()[?7h[?12l[?25h[?25l[?7llod('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004lF<a> := GF(8);A := MatrixAlgebra<GF(8),3|[1, a^2 + a, 0, 0, 1, 0, 0, 0, 1],[1, 1, 0, 0, 1, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),3), A);IndecomposableSummands(M);
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la^2[?7h[?12l[?25h[?25l[?7lsage: a
[?7h[?12l[?25h[?2004l[?7ha
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a.square_root()
[?7h[?12l[?25h[?2004l[?7ha^2 + a
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a^2 + a + 1)^2[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+a)^2[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l)^2[?7h[?12l[?25h[?25l[?7lsage: (a^2+a)^2
[?7h[?12l[?25h[?2004l[?7ha
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004lF<a> := GF(8);A := MatrixAlgebra<GF(8),3|[1, a^2 + a, 0, 0, 1, 0, 0, 0, 1],[1, 1, 0, 0, 1, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),3), A);IndecomposableSummands(M);
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004lF<a> := GF(8);A := MatrixAlgebra<GF(8),3|[1, a^2 + a, 0, 0, 1, 0, 0, 0, 1],[1, 1, 0, 0, 1, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),3), A);IndecomposableSummands(M);
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004lF<a> := GF(8);A := MatrixAlgebra<GF(8),3|[1, a^2 + a, 0, 0, 1, 0, 0, 0, 1],[1, 1, 0, 0, 1, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),3), A);IndecomposableSummands(M);
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004lF<a> := GF(4);A := MatrixAlgebra<GF(8),2|[1, 1, 0, 1],[1, a, 0, 1]>;M := RModule(RSpace(GF(8),2), A);IndecomposableSummands(M);
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004lF<a> := GF(4);A := MatrixAlgebra<GF(8),2|[1, 0, 1, 1],[1, 0, a^2 + 1, 1]>;M := RModule(RSpace(GF(8),2), A);IndecomposableSummands(M);
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004lF<a> := GF(8);A := MatrixAlgebra<GF(8),2|[1, 1, 0, 1],[1, a^2 + 1, 0, 1]>;M := RModule(RSpace(GF(8),2), A);IndecomposableSummands(M);
F<a> := GF(8);A := MatrixAlgebra<GF(8),2|[1, 0, 1, 1],[1, 0, a^2 + 1, 1]>;M := RModule(RSpace(GF(8),2), A);IndecomposableSummands(M);
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004lF<a> := GF(8);A := MatrixAlgebra<GF(8),2|[1, 1, 0, 1],[1, a, 0, 1]>;M := RModule(RSpace(GF(8),2), A);IndecomposableSummands(M);
F<a> := GF(8);A := MatrixAlgebra<GF(8),2|[1, 0, 1, 1],[1, 0, a, 1]>;M := RModule(RSpace(GF(8),2), A);IndecomposableSummands(M);
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l/ext/sage/9.7/src/sage/rings/polynomial/polynomial_singular_interface.py:372:
********************************************************************************
Denominators of fraction field elements are sometimes dropped without warning.
This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696.
********************************************************************************
F<a> := GF(8);A := MatrixAlgebra<GF(8),3|[1, a^2 + a, 0, 0, 1, 0, 0, 0, 1],[1, 1, 0, 0, 1, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),3), A);IndecomposableSummands(M);
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l{
[ 1]
}
{
[ 1 a^4]
[ 0 1],
[ 1 1]
[ 0 1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l/ext/sage/9.7/src/sage/rings/polynomial/polynomial_singular_interface.py:372:
********************************************************************************
Denominators of fraction field elements are sometimes dropped without warning.
This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696.
********************************************************************************
{
[ 1]
}
{
[ 1 a^4]
[ 0 1],
[ 1 1]
[ 0 1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l{
[1]
}
{
[1 0 1 0]
[0 1 0 0]
[0 0 1 0]
[0 1 0 1],
[1 1 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[
RModule of dimension 1 over GF(2),
RModule of dimension 4 over GF(2)
]
{
[1]
}
{
[1 0 1 0]
[0 1 0 0]
[0 0 1 0]
[0 1 0 1],
[1 1 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[
RModule of dimension 2 over GF(2),
RModule of dimension 2 over GF(2),
RModule of dimension 3 over GF(2),
RModule of dimension 3 over GF(2)
]
{
[1 1]
[0 1],
[1 0]
[0 1]
}
{
[1 0]
[1 1],
[1 0]
[0 1]
}
{
[1 1 0]
[0 1 0]
[0 0 1],
[1 1 1]
[0 1 0]
[0 0 1]
}
{
[1 0 1]
[0 1 0]
[0 0 1],
[1 0 1]
[0 1 1]
[0 0 1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004lno 7 -th root; divide by a
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [5], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:15, in <module>
File <string>:44, in __init__(self, C, list_of_fcts, prec)
ValueError: not enough values to unpack (expected 4, got 2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004lno 7 -th root; divide by a + 1
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [6], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:15, in <module>
File <string>:44, in __init__(self, C, list_of_fcts, prec)
ValueError: not enough values to unpack (expected 4, got 2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004lno 7 -th root; divide by a + 1
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [7], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:15, in <module>
File <string>:44, in __init__(self, C, list_of_fcts, prec)
ValueError: not enough values to unpack (expected 4, got 2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004lno 7 -th root; divide by a + 1
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [8], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:15, in <module>
File <string>:44, in __init__(self, C, list_of_fcts, prec)
ValueError: not enough values to unpack (expected 4, got 2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004lno 7 -th root; divide by a^2
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [9], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:15, in <module>
File <string>:44, in __init__(self, C, list_of_fcts, prec)
ValueError: not enough values to unpack (expected 4, got 2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004lno 7 -th root; divide by a^2 + a
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Input In [10], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:15, in <module>
File <string>:44, in __init__(self, C, list_of_fcts, prec)
ValueError: not enough values to unpack (expected 4, got 2)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[
RModule of dimension 2 over GF(2^3),
RModule of dimension 2 over GF(2^3),
RModule of dimension 2 over GF(2^3),
RModule of dimension 2 over GF(2^3),
RModule of dimension 3 over GF(2^3),
RModule of dimension 3 over GF(2^3)
]
{
[ 1 0]
[a^2 1],
[ 1 0]
[ 0 1]
}
{
[ 1 0]
[a^6 1],
[ 1 0]
[ 0 1]
}
{
[ 1 0]
[a^2 1],
[ 1 0]
[ 0 1]
}
{
[ 1 0]
[a^6 1],
[ 1 0]
[ 0 1]
}
{
[ 1 a^2 1]
[ 0 1 0]
[ 0 0 1],
[ 1 1 0]
[ 0 1 0]
[ 0 0 1]
}
{
[ 1 0 a^5]
[ 0 1 a^6]
[ 0 0 1],
[ 1 0 a^4]
[ 0 1 a^4]
[ 0 0 1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.square_root()[?7h[?12l[?25h[?25l[?7lsage: a
[?7h[?12l[?25h[?2004l[?7ha
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lmin[?7h[?12l[?25h[?25l[?7lmini[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: minimal_polynomial(a)
[?7h[?12l[?25h[?2004l[?7hx^3 + x + 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lminimal_polynomial(a)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(a^2+a)^2[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[
RModule of dimension 2 over GF(2^4),
RModule of dimension 2 over GF(2^4),
RModule of dimension 2 over GF(2^4),
RModule of dimension 2 over GF(2^4),
RModule of dimension 3 over GF(2^4),
RModule of dimension 3 over GF(2^4)
]
{
[ 1 0]
[ 0 1],
[ 1 0]
[ a 1]
}
{
[ 1 0]
[ 0 1],
[ 1 0]
[ 1 1]
}
{
[ 1 a^2]
[ 0 1],
[ 1 0]
[ 0 1]
}
{
[ 1 0]
[a^14 1],
[ 1 0]
[ 0 1]
}
{
[ 1 1 0]
[ 0 1 0]
[ 0 0 1],
[ 1 a^5 1]
[ 0 1 0]
[ 0 0 1]
}
{
[ 1 0 a^12]
[ 0 1 0]
[ 0 0 1],
[ 1 0 a]
[ 0 1 a^14]
[ 0 0 1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ljumps[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lsage: AS.jumps
[?7h[?12l[?25h[?2004l[?7h[[3, 11]]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.jumps[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lraification_jumps()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lmification_jumps()[?7h[?12l[?25h[?25l[?7lsage: AS.ramification_jumps()
[?7h[?12l[?25h[?2004l[?7h[3, 11]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l>> F<a> := GF(16);A := MatrixAlgebra<GF(8),12|[1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0
^
Runtime error in MatrixAlgebra< ... >: Rhs argument 1 is invalid for this constructor
>> ;M := RModule(RSpace(GF(8),12), A);L := IndecomposableSummands(M); L;for i
^
User error: Identifier 'A' has not been declared or assigned
>> ;M := RModule(RSpace(GF(8),12), A);L := IndecomposableSummands(M); L;for i
^
User error: Identifier 'M' has not been declared or assigned
>> ;M := RModule(RSpace(GF(8),12), A);L := IndecomposableSummands(M); L;for i
^
User error: Identifier 'L' has not been declared or assigned
>> ummands(M); L;for i in [1 .. #L] do print(Generators(Action(L[i]))); end fo
^
User error: Identifier 'L' has not been declared or assigned
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[
RModule of dimension 3 over GF(2^3),
RModule of dimension 3 over GF(2^3),
RModule of dimension 3 over GF(2^3),
RModule of dimension 3 over GF(2^3)
]
{
[ 1 0 a^5]
[ 0 1 a^4]
[ 0 0 1],
[ 1 0 a^3]
[ 0 1 a^5]
[ 0 0 1]
}
{
[ 1 0 a^3]
[ 0 1 a^2]
[ 0 0 1],
[ 1 0 1]
[ 0 1 a]
[ 0 0 1]
}
{
[ 1 0 1]
[ 0 1 0]
[ 0 0 1],
[ 1 1 0]
[ 0 1 0]
[ 0 0 1]
}
{
[ 1 0 1]
[ 0 1 0]
[ 0 0 1],
[ 1 1 0]
[ 0 1 0]
[ 0 0 1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.ramification_jumps()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS
[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 2^3 with the equations:
z0^2 - z0 = x^5
z1^2 - z1 = a*x^5 + x^3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.ramification_jumps()[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lus()[?7h[?12l[?25h[?25l[?7lsage: AS.genus()
[?7h[?12l[?25h[?2004l[?7h6
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7l, B = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l_(AS)[?7h[?12l[?25h[?25l[?7lh(AS)[?7h[?12l[?25h[?25l[?7lo(AS)[?7h[?12l[?25h[?25l[?7ll(AS)[?7h[?12l[?25h[?25l[?7lo(AS)[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_holo(AS)
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lminimal_polynomial(a)[?7h[?12l[?25h[?25l[?7lagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lTru)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, B)[?7h[?12l[?25h[?25l[?7l, B)[?7h[?12l[?25h[?25l[?7lA, B)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B)
[?7h[?12l[?25h[?2004l[?7h>> 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, a^2 + a, 0, 0, 0, 0, 0, 1, 0, 0, 0,
^
User error: Identifier 'a' has not been declared or assigned
>> 0, 0, 1, 0, 0, 0, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),6), A);L := Indec
^
User error: Identifier 'A' has not been declared or assigned
>> 8),6), A);L := IndecomposableSummands(M); L;for i in [1 .. #L] do print(Gen
^
User error: Identifier 'M' has not been declared or assigned
>> 8),6), A);L := IndecomposableSummands(M); L;for i in [1 .. #L] do print(Gen
^
User error: Identifier 'L' has not been declared or assigned
>> 8),6), A);L := IndecomposableSummands(M); L;for i in [1 .. #L] do print(Gen
^
User error: Identifier 'L' has not been declared or assigned
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A
[?7h[?12l[?25h[?2004l[?7h[ 1 0 1 0 0 0]
[ 0 1 0 0 0 0]
[ 0 0 1 0 0 0]
[ 0 0 0 1 a^2 + a 0]
[ 0 0 0 0 1 0]
[ 0 0 0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(A).base_ring().order()[?7h[?12l[?25h[?25l[?7lsage: parent(A).base_ring().order()
[?7h[?12l[?25h[?2004l[?7h8
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zz_pex.pyx:280, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.__call__()
 279 try:
--> 280 if a.parent() is not K:
 281 a = K.coerce(a)
AttributeError: 'tuple' object has no attribute 'parent'
During handling of the above exception, another exception occurred:
KeyboardInterrupt Traceback (most recent call last)
Input In [25], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:15, in <module>
File <string>:44, in __init__(self, C, list_of_fcts, prec)
File <string>:134, in artin_schreier_transform(power_series, prec)
File <string>:12, in new_reverse(power_series, prec)
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1831, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
 1829 if x:
 1830 raise ValueError("must not specify %s keyword and positional argument" % name)
-> 1831 a = self(kwds[name])
 1832 del kwds[name]
 1833 try:
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1852, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
 1850 x = x[0]
 1851
-> 1852 return self.__u(*x)*(x[0]**self.__n)
 1853
 1854 def __pari__(self):
File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:365, in sage.rings.power_series_poly.PowerSeries_poly.__call__()
 363 x[0] = a
 364 x = tuple(x)
--> 365 return self.__f(x)
 366
 367 def _unsafe_mutate(self, i, value):
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zz_pex.pyx:283, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.__call__()
 281 a = K.coerce(a)
 282 except (TypeError, AttributeError, NotImplementedError):
--> 283 return Polynomial.__call__(self, a)
 284
 285 _a = self._parent._modulus.ZZ_pE(list(a.polynomial()))
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:898, in sage.rings.polynomial.polynomial_element.Polynomial.__call__()
 896 return result
 897 pol._compiled = CompiledPolynomialFunction(pol.list())
--> 898 return pol._compiled.eval(a)
 899
 900 def compose_trunc(self, Polynomial other, long n):
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:125, in sage.rings.polynomial.polynomial_compiled.CompiledPolynomialFunction.eval()
 123 cdef object temp
 124 try:
--> 125 pd_eval(self._dag, x, self._coeffs) #see further down
 126 temp = self._dag.value #for an explanation
 127 pd_clean(self._dag) #of these 3 lines
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
 352 if pd.value is None:
--> 353 pd.eval(vars, coeffs)
 354 pd.hits += 1
 355
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
 505
 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507 pd_eval(self.left, vars, coeffs)
 508 pd_eval(self.right, vars, coeffs)
 509 self.value = self.left.value * self.right.value + coeffs[self.index]
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
 352 if pd.value is None:
--> 353 pd.eval(vars, coeffs)
 354 pd.hits += 1
 355
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
 505
 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507 pd_eval(self.left, vars, coeffs)
 508 pd_eval(self.right, vars, coeffs)
 509 self.value = self.left.value * self.right.value + coeffs[self.index]
[... skipping similar frames: sage.rings.polynomial.polynomial_compiled.pd_eval at line 353 (47 times), sage.rings.polynomial.polynomial_compiled.abc_pd.eval at line 507 (46 times)]
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
 505
 506 cdef int eval(abc_pd self, object vars, object coeffs) except -2:
--> 507 pd_eval(self.left, vars, coeffs)
 508 pd_eval(self.right, vars, coeffs)
 509 self.value = self.left.value * self.right.value + coeffs[self.index]
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
 351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
 352 if pd.value is None:
--> 353 pd.eval(vars, coeffs)
 354 pd.hits += 1
 355
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:509, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
 507 pd_eval(self.left, vars, coeffs)
 508 pd_eval(self.right, vars, coeffs)
--> 509 self.value = self.left.value * self.right.value + coeffs[self.index]
 510 pd_clean(self.left)
 511 pd_clean(self.right)
File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__()
 1512 cdef int cl = classify_elements(left, right)
 1513 if HAVE_SAME_PARENT(cl):
-> 1514 return (<Element>left)._mul_(right)
 1515 if BOTH_ARE_ELEMENT(cl):
 1516 return coercion_model.bin_op(left, right, mul)
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:913, in sage.rings.laurent_series_ring_element.LaurentSeries._mul_()
 911 cdef LaurentSeries right = <LaurentSeries>right_r
 912 return type(self)(self._parent,
--> 913 self.__u * right.__u,
 914 self.__n + right.__n)
 915
File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__()
 1512 cdef int cl = classify_elements(left, right)
 1513 if HAVE_SAME_PARENT(cl):
-> 1514 return (<Element>left)._mul_(right)
 1515 if BOTH_ARE_ELEMENT(cl):
 1516 return coercion_model.bin_op(left, right, mul)
File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:540, in sage.rings.power_series_poly.PowerSeries_poly._mul_()
 538 """
 539 prec = self._mul_prec(right_r)
--> 540 return PowerSeries_poly(self._parent,
 541 self.__f * (<PowerSeries_poly>right_r).__f,
 542 prec=prec,
File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:44, in sage.rings.power_series_poly.PowerSeries_poly.__init__()
 42 ValueError: series has negative valuation
 43 """
---> 44 R = parent._poly_ring()
 45 if isinstance(f, Element):
 46 if (<Element>f)._parent is R:
File /ext/sage/9.7/src/sage/rings/power_series_ring.py:961, in PowerSeriesRing_generic._poly_ring(self)
 958 pass
 959 return False
--> 961 def _poly_ring(self):
 962 """
 963  Return the underlying polynomial ring used to represent elements of
 964  this power series ring.
 (...)
 970  Univariate Polynomial Ring in t over Integer Ring
 971  """
 972 return self.__poly_ring
File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
KeyboardInterrupt:
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lparent(A).base_ring().order()[?7h[?12l[?25h[?25l[?7lmgmahis(A, B)[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lS.genus()[?7h[?12l[?25h[?25l[?7l, B = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_holo(AS)
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lparent(A).base_ring().order()[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lmagmathis(A, B)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B)
[?7h[?12l[?25h[?2004l[?7h[
RModule of dimension 1 over GF(2^3),
RModule of dimension 2 over GF(2^3),
RModule of dimension 3 over GF(2^3)
]
{
[ 1]
}
{
[ 1 a^4]
[ 0 1],
[ 1 1]
[ 0 1]
}
{
[ 1 0 1]
[ 0 1 0]
[ 0 0 1],
[ 1 1 0]
[ 0 1 0]
[ 0 0 1]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l12.factor()[1][0][?7h[?12l[?25h[?25l[?7l/(a^2 + a + 1)^2[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: 1/a
[?7h[?12l[?25h[?2004l[?7ha^2 + 1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l^2[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: a^8
[?7h[?12l[?25h[?2004l[?7ha
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ losage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x-x^3)^2 - x^2[?7h[?12l[?25h[?25l[?7l(x-x^3) + (-x^3)^3)^2-x^2[?7h[?12l[?25h[?25l[?7lR.<x> = PolynomialRing(QQ)[?7h[?12l[?25h[?25l[?7l((x-x^3) + (x-x^3)^3)^2-x^2[?7h[?12l[?25h[?25l[?7lx-x^3)^2 - ^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.derivative()[?7h[?12l[?25h[?25l[?7lpatil_fraction_decomposition()[?7h[?12l[?25h[?25l[?7l = (x^2 + 1)/(x^2*(x^3 - x))[?7h[?12l[?25h[?25l[?7lsage: F.<x> = PolynomialRing(GF(3))
....: FF = FractionField(F)[?7h[?12l[?25h[?25l[?7lf = (x^2 + 1)/(x^2*(x^3 - x)
 [?7h[?12l[?25h[?25l[?7l.partial_fraction_decomposition()[?7h[?12l[?25h[?25l[?7ldeivtive()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.derivative()[?7h[?12l[?25h[?25l[?7l = (x^2 + 1)/(x^2*(x^3 - x))[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: f = C.y
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [2], in <cell line: 1>()
----> 1 f = C.y
NameError: name 'C' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lsage: C_super
[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: C_super.x
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [4], in <cell line: 1>()
----> 1 C_super.x
AttributeError: 'superelliptic' object has no attribute 'x'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super.x[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: C_super.x
[?7h[?12l[?25h[?2004l[?7hx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y, z0, z1 = Rxyz.gens()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxC_super.x[?7h[?12l[?25h[?25l[?7lxC_super.x[?7h[?12l[?25h[?25l[?7l,C_super.x[?7h[?12l[?25h[?25l[?7l C_super.x[?7h[?12l[?25h[?25l[?7lyC_super.x[?7h[?12l[?25h[?25l[?7lyC_super.x[?7h[?12l[?25h[?25l[?7l C_super.x[?7h[?12l[?25h[?25l[?7l=C_super.x[?7h[?12l[?25h[?25l[?7l C_super.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, C.super.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = C_super.x, C.super.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, y = C_super.x, C.super.y[?7h[?12l[?25h[?25l[?7lsage: x, y = C_super.x, C.super.y
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [7], in <cell line: 1>()
----> 1 x, y = C_super.x, C.super.y
NameError: name 'C' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y = C_super.x, C.super.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuper.y[?7h[?12l[?25h[?25l[?7l_super.y[?7h[?12l[?25h[?25l[?7lsage: x, y = C_super.x, C_super.y
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = C.y[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = C.y[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: f = y+y/x^2
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = y+y/x^2[?7h[?12l[?25h[?25l[?7l.derivative()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7liscrimnant()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lerivative()[?7h[?12l[?25h[?25l[?7lrivative()[?7h[?12l[?25h[?25l[?7lsage: f.derivative()
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [10], in <cell line: 1>()
----> 1 f.derivative()
AttributeError: 'superelliptic_function' object has no attribute 'derivative'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld = f.degree()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: diffn(f)
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [11], in <cell line: 1>()
----> 1 diffn(f)
NameError: name 'diffn' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldiffn(f)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.derivative()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7liscrimnant()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f.diffn()
[?7h[?12l[?25h[?2004l[?7h((-1)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7ldiffn(f)[?7h[?12l[?25h[?25l[?7lf.derivative()[?7h[?12l[?25h[?25l[?7l = y+y/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly/x^2[?7h[?12l[?25h[?25l[?7l-y/x^2[?7h[?12l[?25h[?25l[?7lsage: f = y-y/x^2
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = y-y/x^2[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7lsage: f.diffn()
[?7h[?12l[?25h[?2004l[?7h0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.diffn()[?7h[?12l[?25h[?25l[?7l = y-y/x^2[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f = y*(x^3 + 2*x+2/x^3+1/x^5)
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [15], in <cell line: 1>()
----> 1 f = y*(x**Integer(3) + Integer(2)*x+Integer(2)/x**Integer(3)+Integer(1)/x**Integer(5))
File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
 1962 return y
 1963
-> 1964 return coercion_model.bin_op(left, right, operator.mul)
 1965
 1966 cpdef _mul_(self, right):
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op()
 1246 # We should really include the underlying error.
 1247 # This causes so much headache.
-> 1248 raise bin_op_exception(op, x, y)
 1249
 1250 cpdef canonical_coercion(self, x, y):
TypeError: unsupported operand parent(s) for *: 'Integer Ring' and '<class '__main__.superelliptic_function'>'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = y*(x^3 + 2*x+2/x^3+1/x^5)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: f = y*(x^3 + 2*x+2/x^3+1/x^5)
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [16], in <cell line: 1>()
----> 1 f = y*(x**Integer(3) + Integer(2)*x+Integer(2)/x**Integer(3)+Integer(1)/x**Integer(5))
File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
 1962 return y
 1963
-> 1964 return coercion_model.bin_op(left, right, operator.mul)
 1965
 1966 cpdef _mul_(self, right):
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op()
 1246 # We should really include the underlying error.
 1247 # This causes so much headache.
-> 1248 raise bin_op_exception(op, x, y)
 1249
 1250 cpdef canonical_coercion(self, x, y):
TypeError: unsupported operand parent(s) for *: 'Integer Ring' and '<class '__main__.superelliptic_function'>'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lf = y*(x^3 + 2*x+2/x^3+1/x^5)[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7l = y-y/x^2[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ldiffn(f)[?7h[?12l[?25h[?25l[?7lf.derivative()[?7h[?12l[?25h[?25l[?7l = y+y/x^2[?7h[?12l[?25h[?25l[?7lx, y = C_super.x, C_super.y[?7h[?12l[?25h[?25l[?7lsage: x, y = C_super.x, C_super.y
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y = C_super.x, C_super.y[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lf = y*(x^3 + 2*x+2/x^3+1/x^5)[?7h[?12l[?25h[?25l[?7lsage: f = y*(x^3 + 2*x+2/x^3+1/x^5)
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [19], in <cell line: 1>()
----> 1 f = y*(x**Integer(3) + Integer(2)*x+Integer(2)/x**Integer(3)+Integer(1)/x**Integer(5))
File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
 1962 return y
 1963
-> 1964 return coercion_model.bin_op(left, right, operator.mul)
 1965
 1966 cpdef _mul_(self, right):
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
 1240 mul_method = getattr(y, '__r%s__'%op_name, None)
 1241 if mul_method is not None:
-> 1242 res = mul_method(x)
 1243 if res is not None and res is not NotImplemented:
 1244 return res
File <string>:53, in __rmul__(self, constant)
File <string>:6, in __init__(self, C, g)
AttributeError: 'superelliptic' object has no attribute 'height'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = y*(x^3 + 2*x+2/x^3+1/x^5)[?7h[?12l[?25h[?25l[?7lx, y = C_super., C_super.y[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lf = y*(x^3 + 2*x+2/x^3+1/x^5)[?7h[?12l[?25h[?25l[?7lx, y = C_super., C_super.y[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lf = y*(x^3 + 2*x+2/x^3+1/x^5)[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7l = y-y/x^2[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ldiffn(f)[?7h[?12l[?25h[?25l[?7lf.derivative()[?7h[?12l[?25h[?25l[?7l = y+y/x^2[?7h[?12l[?25h[?25l[?7lx, y = C_super.x, C_super.y[?7h[?12l[?25h[?25l[?7lsage: x, y = C_super.x, C_super.y
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lf = y*(x^3 + 2*x+2/x^3+1/x^5)[?7h[?12l[?25h[?25l[?7lsage: f = y*(x^3 + 2*x+2/x^3+1/x^5)
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [22], in <cell line: 1>()
----> 1 f = y*(x**Integer(3) + Integer(2)*x+Integer(2)/x**Integer(3)+Integer(1)/x**Integer(5))
File /ext/sage/9.7/src/sage/rings/integer.pyx:2037, in sage.rings.integer.Integer.__truediv__()
 2035 return y
 2036
-> 2037 return coercion_model.bin_op(left, right, operator.truediv)
 2038
 2039 cpdef _div_(self, right):
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op()
 1246 # We should really include the underlying error.
 1247 # This causes so much headache.
-> 1248 raise bin_op_exception(op, x, y)
 1249
 1250 cpdef canonical_coercion(self, x, y):
TypeError: unsupported operand parent(s) for /: 'Integer Ring' and '<class '__main__.superelliptic_function'>'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = y*(x^3 + 2*x+2/x^3+1/x^5)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = y*(x^3 + 2*x+2/x^3+1/x^5)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuperelliptic_function(C, g)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_, g)[?7h[?12l[?25h[?25l[?7ls, g)[?7h[?12l[?25h[?25l[?7lu, g)[?7h[?12l[?25h[?25l[?7lp, g)[?7h[?12l[?25h[?25l[?7le, g)[?7h[?12l[?25h[?25l[?7lr, g)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7lsage: f1 = superelliptic_function(C_super, 1)
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = superelliptic_function(C_super, 1)[?7h[?12l[?25h[?25l[?7l = y*(x^3 + 2*x+2/x^3+1/x^5)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1/x^5)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf2/x^3+f1/x^5)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx^3+f1/x^5)[?7h[?12l[?25h[?25l[?7lx^3+f1/x^5)[?7h[?12l[?25h[?25l[?7l1x^3+f1/x^5)[?7h[?12l[?25h[?25l[?7l/x^3+f1/x^5)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2f1/x^3+f1/x^5)[?7h[?12l[?25h[?25l[?7l*f1/x^3+f1/x^5)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: f = y*(x^3 + 2*x+2*f1/x^3+f1/x^5)
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = y*(x^3 + 2*x+2*f1/x^3+f1/x^5)[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f.diffn()
[?7h[?12l[?25h[?2004l[?7h0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l = y*(x^3 + 2*x+2*f1/x^3+f1/x^5)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: f = y*(x^3 + 2*x)
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = y*(x^3 + 2*x)[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f.diffn()
[?7h[?12l[?25h[?2004l[?7h0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super.x[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lrham_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C_super.de_rham_basis()
[?7h[?12l[?25h[?2004lsage/rings/polynomial/polynomial_zmod_flint.pyx:7: DeprecationWarning: invalid escape sequence '\Z'
"""
sage/rings/polynomial/polynomial_zmod_flint.pyx:7: DeprecationWarning: invalid escape sequence '\Z'
"""
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [28], in <cell line: 1>()
----> 1 C_super.de_rham_basis()
File <string>:94, in de_rham_basis(self)
File <string>:86, in basis_de_rham_degrees(self)
File <string>:150, in cut(f, i)
File /ext/sage/9.7/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds)
 583 return expression.sum(*args, **kwds)
 584 elif max(len(args),len(kwds)) <= 1:
--> 585 return sum(expression, *args, **kwds)
 586 else:
 587 from sage.symbolic.ring import SR
File <string>:150, in <genexpr>(.0)
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
 895 if mor is not None:
 896 if no_extra_args:
--> 897 return mor._call_(x)
 898 else:
 899 return mor._call_with_args(x, args, kwds)
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
 159 print(type(C), C)
 160 print(type(C._element_constructor), C._element_constructor)
--> 161 raise
 162
 163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
 154 cdef Parent C = self._codomain
 155 try:
--> 156 return C._element_constructor(x)
 157 except Exception:
 158 if print_warnings:
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:469, in PolynomialRing_general._element_constructor_(self, x, check, is_gen, construct, **kwds)
 467 elif isinstance(x, sage.rings.power_series_ring_element.PowerSeries):
 468 x = x.truncate()
--> 469 return C(self, x, check, is_gen, construct=construct, **kwds)
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zmod_flint.pyx:129, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint.__init__()
 127 except AttributeError:
 128 pass
--> 129 Polynomial_template.__init__(self, parent, x, check, is_gen, construct)
 130
 131 cdef Polynomial_template _new(self):
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_template.pxi:176, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_template.__init__()
 174 self.__class__.__init__(self, parent, x, check=check, is_gen=is_gen, construct=construct)
 175 else:
--> 176 x = parent.base_ring()(x)
 177 self.__class__.__init__(self, parent, x, check=check, is_gen=is_gen, construct=construct)
 178
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
 895 if mor is not None:
 896 if no_extra_args:
--> 897 return mor._call_(x)
 898 else:
 899 return mor._call_with_args(x, args, kwds)
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
 159 print(type(C), C)
 160 print(type(C._element_constructor), C._element_constructor)
--> 161 raise
 162
 163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
 154 cdef Parent C = self._codomain
 155 try:
--> 156 return C._element_constructor(x)
 157 except Exception:
 158 if print_warnings:
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x)
 1143 """
 1144 TESTS::
 1145
 (...)
 1182  True
 1183 """
 1184 try:
-> 1185 return integer_mod.IntegerMod(self, x)
 1186 except (NotImplementedError, PariError):
 1187 raise TypeError("error coercing to finite field")
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod()
 199 return a
 200 t = modulus.element_class()
--> 201 return t(parent, value)
 202
 203
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:391, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
 389 z = value % self.__modulus.sageInteger
 390 else:
--> 391 raise
 392 self.set_from_mpz(z.value)
 393
File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:380, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
 378 else:
 379 try:
--> 380 z = integer_ring.Z(value)
 381 except (TypeError, ValueError):
 382 from sage.structure.element import Expression
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
 895 if mor is not None:
 896 if no_extra_args:
--> 897 return mor._call_(x)
 898 else:
 899 return mor._call_with_args(x, args, kwds)
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
 159 print(type(C), C)
 160 print(type(C._element_constructor), C._element_constructor)
--> 161 raise
 162
 163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
 154 cdef Parent C = self._codomain
 155 try:
--> 156 return C._element_constructor(x)
 157 except Exception:
 158 if print_warnings:
File /ext/sage/9.7/src/sage/rings/integer.pyx:717, in sage.rings.integer.Integer.__init__()
 715 return
 716
--> 717 raise TypeError("unable to coerce %s to an integer" % type(x))
 718
 719 def __reduce__(self):
TypeError: unable to coerce <class '__main__.superelliptic_function'> to an integer
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC_super.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C_super.de_rham_basis()
[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.discriminant()%8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llista += [[e, f, g]][?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [1], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:10, in <module>
AttributeError: 'superelliptic' object has no attribute 'holo_basis'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super.de_rham_basis()[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C_super.
 C_super.a_number C_super.cartier_matrix C_super.degrees_de_rham1 
 C_super.base_ring C_super.characteristic C_super.degrees_holomorphic_differentials 
 C_super.basis_de_rham_degrees C_super.de_rham_basis C_super.exponent >
 C_super.basis_holomorphic_differentials_degree C_super.degrees_de_rham0 C_super.final_type 
 [?7h[?12l[?25h[?25l[?7la_number
 C_super.a_number 
 <unknown> [?7h[?12l[?25h[?25l[?7lcartier_matrix
 C_super.a_number  C_super.cartier_matrix [?7h[?12l[?25h[?25l[?7ldegresde_ham1
 C_super.cartier_matrix  C_super.degrees_de_rham1 [?7h[?12l[?25h[?25l[?7lfrobnius_matrix
 cartier_matrixdegresde_ham1frobnius_matrix
 characteristicdegees_holomorphic_differentialsgnus 
<de_rham_basis exponent holmorphic_differentials_basis
 degrees_de_rham0 final_typ is_smooth [?7h[?12l[?25h[?25l[?7lpolynomial
degresde_ham1frobnius_matrixpolynomial  
degees_holomorphic_differentialsgnus vrschiebung_matrix 
exponent holmorphic_differentials_basisx  
final_typ is_smooth y  [?7h[?12l[?25h[?25l[?7lfrobenius_matrix
 C_super.frobenius_matrix  C_super.polynomial [?7h[?12l[?25h[?25l[?7linal_type
 C_super.frobenius_matrix 
 C_super.final_type [?7h[?12l[?25h[?25l[?7lrobenius_matrix
 C_super.frobenius_matrix 
 C_super.final_type [?7h[?12l[?25h[?25l[?7lgenus
 C_super.frobenius_matrix 
 C_super.genus [?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis
 C_super.genus 
 C_super.holomorphic_differentials_basis [?7h[?12l[?25h[?25l[?7l




[?7h[?12l[?25h[?25l[?7lsage: C_super.holomorphic_differentials_basis
[?7h[?12l[?25h[?2004l[?7h<bound method superelliptic.holomorphic_differentials_basis of Superelliptic curve with the equation y^2 = x^15 + x^13 + x^11 + 2*x^9 + 2*x^7 + 2*x^5 + 1 over Finite Field of size 3>
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 
 [?7h[?12l[?25h[?25l[?7lC_super.holomorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C_super.holomorphic_differentials_basis()
[?7h[?12l[?25h[?2004l[?7h[(1/y) dx,
(x/y) dx,
(x^2/y) dx,
(x^3/y) dx,
(x^4/y) dx,
(x^5/y) dx,
(x^6/y) dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAC_super.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7l C_super.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7l=C_super.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7l C_super.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7lsage: A = C_super.holomorphic_differentials_basis()
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = C_super.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l[:, 2] = vector([1, 1, 1])[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: A[0]
[?7h[?12l[?25h[?2004l[?7h(1/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lrun.term-0.term[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lrun.term-0.term[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom, f = AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = AS.holomophic_differentials_basis()[5]; om.serre_duality_pairing(A)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: om = A[0]
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = A[0][?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.serre_duality_pairing(A)[?7h[?12l[?25h[?25l[?7lsage: om.serre_duality_pairing(A)
 om.cartier om.expansion_at_infty om.is_regular_on_Uinfty
 om.coordinates om.form om.jth_component 
 om.curve om.is_regular_on_U0 
 [?7h[?12l[?25h[?25l[?7lcartier
 om.cartier 
 <unknown> [?7h[?12l[?25h[?25l[?7lexpansion_at_infty
 om.cartier  om.expansion_at_infty [?7h[?12l[?25h[?25l[?7lis_regular_on_Uinfty
 om.expansion_at_infty  om.is_regular_on_Uinfty[?7h[?12l[?25h[?25l[?7ljth_component
 om.is_regular_on_Uinfty
 om.jth_component [?7h[?12l[?25h[?25l[?7lform
 om.form  om.jth_component [?7h[?12l[?25h[?25l[?7lis_regular_on_U0
 om.form 
 om.is_regular_on_U0 [?7h[?12l[?25h[?25l[?7lform
 om.form 
 om.is_regular_on_U0 [?7h[?12l[?25h[?25l[?7lexpansion_at_infty
 om.expansion_at_infty 
 om.form [?7h[?12l[?25h[?25l[?7lcartier
 om.cartier  om.expansion_at_infty [?7h[?12l[?25h[?25l[?7lexpansion_at_infty
 om.cartier  om.expansion_at_infty [?7h[?12l[?25h[?25l[?7lform
 om.expansion_at_infty 
 om.form [?7h[?12l[?25h[?25l[?7l



[?7h[?12l[?25h[?25l[?7lsage: om.form
[?7h[?12l[?25h[?2004l[?7h1/y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 
 [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004lTraceback (most recent call last):
File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
exec(code_obj, self.user_global_ns, self.user_ns)
Input In [8] in <cell line: 1>
load('init.sage')
File sage/misc/persist.pyx:175 in sage.misc.persist.load
sage.repl.load.load(filename, globals())
File /ext/sage/9.7/src/sage/repl/load.py:272 in load
exec(preparse_file(f.read()) + "\n", globals)
File <string>:21 in <module>
File sage/misc/persist.pyx:175 in sage.misc.persist.load
sage.repl.load.load(filename, globals())
 File /ext/sage/9.7/src/sage/repl/load.py:272 in load
 exec(preparse_file(f.read()) + "\n", globals)
 File <string>:15
 return superelliptic_form(C1, f(x=x+_sage_const_1 , y))
 ^
SyntaxError: positional argument follows keyword argument
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[(1/y) dx, (x/y) dx, (x^2/y) dx, (x^3/y) dx, (x^4/y) dx, (x^5/y) dx, (x^6/y) dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la_lead = f.coefficients(sparse=False)[d][?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.form[?7h[?12l[?25h[?25l[?7l = A[0][?7h[?12l[?25h[?25l[?7lA[0][?7h[?12l[?25h[?25l[?7l = C_super.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: A = C_super.holomorphic_differentials_basis()
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = C_super.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = C_super.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.form[?7h[?12l[?25h[?25l[?7l = A[0][?7h[?12l[?25h[?25l[?7lA[0][?7h[?12l[?25h[?25l[?7lom = A[0][?7h[?12l[?25h[?25l[?7lsage: om = A[0]
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la_lead = f.coefficients(sparse=False)[d][?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(om)
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [12], in <cell line: 1>()
----> 1 autom(om)
File <string>:15, in autom(omega)
NameError: name 'y' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(om)[?7h[?12l[?25h[?25l[?7lom = A[0][?7h[?12l[?25h[?25l[?7lA = C_super.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004lTraceback (most recent call last):
File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
exec(code_obj, self.user_global_ns, self.user_ns)
Input In [13] in <cell line: 1>
load('init.sage')
File sage/misc/persist.pyx:175 in sage.misc.persist.load
sage.repl.load.load(filename, globals())
File /ext/sage/9.7/src/sage/repl/load.py:272 in load
exec(preparse_file(f.read()) + "\n", globals)
File <string>:21 in <module>
File sage/misc/persist.pyx:175 in sage.misc.persist.load
sage.repl.load.load(filename, globals())
 File /ext/sage/9.7/src/sage/repl/load.py:272 in load
 exec(preparse_file(f.read()) + "\n", globals)
 File <string>:21
 print [autom(omm) for omm in A]
 ^
SyntaxError: Missing parentheses in call to 'print'. Did you mean print(...)?
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [14], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File <string>:21, in <listcomp>(.0)
File <string>:16, in autom(omega)
File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
 895 if mor is not None:
 896 if no_extra_args:
--> 897 return mor._call_(x)
 898 else:
 899 return mor._call_with_args(x, args, kwds)
File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
 786 return self._call_with_args(x, args, kwds)
 787
--> 788 cpdef Element _call_(self, x):
 789 """
 790 Call method with a single argument, not implemented in the base class.
File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
 1249 return num
 1250 if check and not den.is_unit():
 1251 # This should probably be a ValueError.
 1252 # However, too much existing code is expecting this to throw a
 1253 # TypeError, so we decided to keep it for the time being.
-> 1254 raise TypeError("fraction must have unit denominator")
 1255 return num * den.inverse_of_unit()
TypeError: fraction must have unit denominator
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[(1/y) dx, ((x + 1)/y) dx, ((x^2 - x + 1)/y) dx, ((x^3 + 1)/y) dx, ((x^4 + x^3 + x + 1)/y) dx, ((x^5 - x^4 + x^3 + x^2 - x + 1)/y) dx, ((x^6 - x^3 + 1)/y) dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[(1/y) dx, ((x + 1)/y) dx, ((x^2 - x + 1)/y) dx, ((x^3 + 1)/y) dx, ((x^4 + x^3 + x + 1)/y) dx, ((x^5 - x^4 + x^3 + x^2 - x + 1)/y) dx, ((x^6 - x^3 + 1)/y) dx]
[(1, 0, 0, 0, 0, 0, 0), (1, 1, 0, 0, 0, 0, 0), (1, 2, 1, 0, 0, 0, 0), (1, 0, 0, 1, 0, 0, 0), (1, 1, 0, 1, 1, 0, 0), (1, 2, 1, 1, 2, 1, 0), (1, 0, 0, 2, 0, 0, 1)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[(1/y) dx, ((x + 1)/y) dx, ((x^2 - x + 1)/y) dx, ((x^3 + 1)/y) dx, ((x^4 + x^3 + x + 1)/y) dx, ((x^5 - x^4 + x^3 + x^2 - x + 1)/y) dx, ((x^6 - x^3 + 1)/y) dx]
[(1, 0, 0, 0, 0, 0, 0), (1, 1, 0, 0, 0, 0, 0), (1, 2, 1, 0, 0, 0, 0), (1, 0, 0, 1, 0, 0, 0), (1, 1, 0, 1, 1, 0, 0), (1, 2, 1, 1, 2, 1, 0), (1, 0, 0, 2, 0, 0, 1)]
[1 1 1 1 1 1 1]
[0 1 2 0 1 2 0]
[0 0 1 0 0 1 0]
[0 0 0 1 1 1 2]
[0 0 0 0 1 2 0]
[0 0 0 0 0 1 0]
[0 0 0 0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7lsage: M
[?7h[?12l[?25h[?2004l[?7h[1 1 1 1 1 1 1]
[0 1 2 0 1 2 0]
[0 0 1 0 0 1 0]
[0 0 0 1 1 1 2]
[0 0 0 0 1 2 0]
[0 0 0 0 0 1 0]
[0 0 0 0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l.determinant()[?7h[?12l[?25h[?25l[?7lj[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: M.jordan_form()
[?7h[?12l[?25h[?2004l[?7h[1 1 0|0 0 0|0]
[0 1 1|0 0 0|0]
[0 0 1|0 0 0|0]
[-----+-----+-]
[0 0 0|1 1 0|0]
[0 0 0|0 1 1|0]
[0 0 0|0 0 1|0]
[-----+-----+-]
[0 0 0|0 0 0|1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C
[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^15 + x^13 + x^11 + 2*x^9 + 2*x^7 + 2*x^5 + 1 over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[(1/y) dx, ((x + 1)/y) dx, ((x^2 - x + 1)/y) dx, ((x^3 + 1)/y) dx, ((x^4 + x^3 + x + 1)/y) dx, ((x^5 - x^4 + x^3 + x^2 - x + 1)/y) dx, ((x^6 - x^3 + 1)/y) dx]
[(1, 0, 0, 0, 0, 0, 0), (1, 1, 0, 0, 0, 0, 0), (1, 2, 1, 0, 0, 0, 0), (1, 0, 0, 1, 0, 0, 0), (1, 1, 0, 1, 1, 0, 0), (1, 2, 1, 1, 2, 1, 0), (1, 0, 0, 2, 0, 0, 1)]
[1 1 1 1 1 1 1]
[0 1 2 0 1 2 0]
[0 0 1 0 0 1 0]
[0 0 0 1 1 1 2]
[0 0 0 0 1 2 0]
[0 0 0 0 0 1 0]
[0 0 0 0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: Cf
[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^5 + 1 over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: Cf.genus()
[?7h[?12l[?25h[?2004l[?7h2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCf.genus()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: Cf.is_smooth()
[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCf.is_smooth()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lschiebung_matrix[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.verschiebung_matrix()
[?7h[?12l[?25h[?2004l[?7h[0 2 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0 0 0 0 0]
[1 0 0 2 0 1 0 0 0 0 0 0 0 0]
[0 0 2 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 2 0 1 0 0 0 0 0 0 0 0]
[0 1 0 0 2 0 1 0 0 0 0 0 0 0]
[0 0 0 2 0 1 0 0 0 0 0 0 0 0]
[0 1 0 2 0 0 0 0 0 0 0 0 0 0]
[2 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[1 0 2 0 0 0 0 0 0 0 0 0 0 0]
[0 1 2 0 1 0 0 0 0 0 0 0 0 0]
[0 1 0 2 0 0 0 0 0 0 0 0 0 0]
[0 2 1 0 2 0 0 0 0 0 0 0 0 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.verschiebung_matrix()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ltier_matrix[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.cartier_matrix()
[?7h[?12l[?25h[?2004l[?7h[0 2 0 1 0 0 0]
[0 0 2 0 1 0 0]
[1 0 0 2 0 1 0]
[0 0 2 0 1 0 0]
[0 0 0 2 0 1 0]
[0 1 0 0 2 0 1]
[0 0 0 2 0 1 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm = 7[?7h[?12l[?25h[?25l[?7lagmathis(A, B)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lmathis(A, B)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[(1/y) dx, ((x + 1)/y) dx, ((x^2 - x + 1)/y) dx, ((x^3 + 1)/y) dx, ((x^4 + x^3 + x + 1)/y) dx, ((x^5 - x^4 + x^3 + x^2 - x + 1)/y) dx, ((x^6 - x^3 + 1)/y) dx]
[(1, 0, 0, 0, 0, 0, 0), (1, 1, 0, 0, 0, 0, 0), (1, 2, 1, 0, 0, 0, 0), (1, 0, 0, 1, 0, 0, 0), (1, 1, 0, 1, 1, 0, 0), (1, 2, 1, 1, 2, 1, 0), (1, 0, 0, 2, 0, 0, 1)]
[1 1 1 1 1 1 1]
[0 1 2 0 1 2 0]
[0 0 1 0 0 1 0]
[0 0 0 1 1 1 2]
[0 0 0 0 1 2 0]
[0 0 0 0 0 1 0]
[0 0 0 0 0 0 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[1 1 1 1 1 1 1]
[0 1 2 0 1 2 0]
[0 0 1 0 0 1 0]
[0 0 0 1 1 1 2]
[0 0 0 0 1 2 0]
[0 0 0 0 0 1 0]
[0 0 0 0 0 0 1]
[
RModule M of dimension 7 over GF(3)
]
{
[1 1 1 1 1 1 1]
[0 1 2 0 1 2 0]
[0 0 1 0 0 1 0]
[0 0 0 1 1 1 2]
[0 0 0 0 1 2 0]
[0 0 0 0 0 1 0]
[0 0 0 0 0 0 1],
[0 2 0 1 0 0 0]
[0 0 2 0 1 0 0]
[1 0 0 2 0 1 0]
[0 0 2 0 1 0 0]
[0 0 0 2 0 1 0]
[0 1 0 0 2 0 1]
[0 0 0 2 0 1 0]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = C_super.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l[0][?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A[0].cartier()
[?7h[?12l[?25h[?2004l[?7h((x^3 - x)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[0].cartier()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A[0].cartier().coordinates()
[?7h[?12l[?25h[?2004l[?7h(0, 2, 0, 1, 0, 0, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[1 1 1 1 1 1 1]
[0 1 2 0 1 2 0]
[0 0 1 0 0 1 0]
[0 0 0 1 1 1 2]
[0 0 0 0 1 2 0]
[0 0 0 0 0 1 0]
[0 0 0 0 0 0 1]
[
RModule M of dimension 7 over GF(3)
]
{
[1 1 1 1 1 1 1]
[0 1 2 0 1 2 0]
[0 0 1 0 0 1 0]
[0 0 0 1 1 1 2]
[0 0 0 0 1 2 0]
[0 0 0 0 0 1 0]
[0 0 0 0 0 0 1],
[0 0 1 0 0 0 0]
[2 0 0 0 0 1 0]
[0 2 0 2 0 0 0]
[1 0 2 0 2 0 2]
[0 1 0 1 0 2 0]
[0 0 1 0 1 0 1]
[0 0 0 0 0 1 0]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cartier_matrix()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()
[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx),
((x/y) dx, 0, (x/y) dx),
((x^2/y) dx, 0, (x^2/y) dx),
((x^3/y) dx, 0, (x^3/y) dx),
((x^4/y) dx, 0, (x^4/y) dx),
((x^5/y) dx, 0, (x^5/y) dx),
((x^6/y) dx, 0, (x^6/y) dx),
(((x^13 - x^11 - x^7 + x^5)/y) dx, 2/x*y, ((-1)/(x^2*y)) dx),
(((-x^12 + x^8 + x^6 - x^2)/y) dx, 2/x^2*y, (1/(x^3*y)) dx),
(((x^9 - x^7 - x^3 + x)/y) dx, 2/x^3*y, 0 dx),
(((x^10 - x^8 - x^4 + x^2)/y) dx, 2/x^4*y, ((-1)/(x^5*y)) dx),
(((-x^9 + x^5 + x^3)/y) dx, 2/x^5*y, ((x^5 + 1)/(x^6*y)) dx),
(((x^6 - x^4 - 1)/y) dx, 2/x^6*y, ((-1)/(x^2*y)) dx),
(((x^7 - x^5 - x)/y) dx, 2/x^7*y, ((-x^7 - 1)/(x^8*y)) dx)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [33], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:29, in <module>
File <string>:17, in autom(omega)
AttributeError: 'superelliptic_cech' object has no attribute 'form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[0].cartier().coordinates()[?7h[?12l[?25h[?25l[?7lsage: A
[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx),
((x/y) dx, 0, (x/y) dx),
((x^2/y) dx, 0, (x^2/y) dx),
((x^3/y) dx, 0, (x^3/y) dx),
((x^4/y) dx, 0, (x^4/y) dx),
((x^5/y) dx, 0, (x^5/y) dx),
((x^6/y) dx, 0, (x^6/y) dx),
(((x^13 - x^11 - x^7 + x^5)/y) dx, 2/x*y, ((-1)/(x^2*y)) dx),
(((-x^12 + x^8 + x^6 - x^2)/y) dx, 2/x^2*y, (1/(x^3*y)) dx),
(((x^9 - x^7 - x^3 + x)/y) dx, 2/x^3*y, 0 dx),
(((x^10 - x^8 - x^4 + x^2)/y) dx, 2/x^4*y, ((-1)/(x^5*y)) dx),
(((-x^9 + x^5 + x^3)/y) dx, 2/x^5*y, ((x^5 + 1)/(x^6*y)) dx),
(((x^6 - x^4 - 1)/y) dx, 2/x^6*y, ((-1)/(x^2*y)) dx),
(((x^7 - x^5 - x)/y) dx, 2/x^7*y, ((-x^7 - 1)/(x^8*y)) dx)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[0].cartier().coordinates()[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: A[0]
[?7h[?12l[?25h[?2004l[?7h((1/y) dx, 0, (1/y) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm = 7[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: mm = A[0]
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmm = A[0][?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lsage: mm.
 mm.coordinates mm.frobenius mm.omega8 
 mm.curve mm.is_cocycle mm.verschiebung
 mm.f mm.omega0 
 [?7h[?12l[?25h[?25l[?7lf


[?7h[?12l[?25h[?25l[?7lsage: mm.f
[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 
 [?7h[?12l[?25h[?25l[?7lA[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: A[-1]
[?7h[?12l[?25h[?2004l[?7h(((x^7 - x^5 - x)/y) dx, 2/x^7*y, ((-x^7 - 1)/(x^8*y)) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 
 [?7h[?12l[?25h[?25l[?7lA[-1][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: A[-1].f
[?7h[?12l[?25h[?2004l[?7h2/x^7*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[-1].f[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lsage: A[-1].f.fct
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [40], in <cell line: 1>()
----> 1 A[-Integer(1)].f.fct
AttributeError: 'superelliptic_function' object has no attribute 'fct'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[-1].f.fct[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7luct[?7h[?12l[?25h[?25l[?7lnct[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsage: A[-1].f.function
[?7h[?12l[?25h[?2004l[?7h2/x^7*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lset(*lista2)[?7h[?12l[?25h[?25l[?7lubset_um_quadratic_form(A0, q)[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l?[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lsage: ?superelliptic_cech
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
OSError Traceback (most recent call last)
Input In [42], in <cell line: 1>()
----> 1 get_ipython().run_line_magic('pinfo', 'superelliptic_cech')
File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:2305, in InteractiveShell.run_line_magic(self, magic_name, line, _stack_depth)
 2303 kwargs['local_ns'] = self.get_local_scope(stack_depth)
 2304 with self.builtin_trap:
-> 2305 result = fn(*args, **kwargs)
 2306 return result
File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/magics/namespace.py:58, in NamespaceMagics.pinfo(self, parameter_s, namespaces)
 56 self.psearch(oname)
 57 else:
---> 58 self.shell._inspect('pinfo', oname, detail_level=detail_level,
 59  namespaces=namespaces)
File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:1685, in InteractiveShell._inspect(self, meth, oname, namespaces, **kw)
 1683 pmethod(info.obj, oname, formatter)
 1684 elif meth == 'pinfo':
-> 1685 pmethod(
 1686  info.obj,
 1687  oname,
 1688  formatter,
 1689  info,
 1690  enable_html_pager=self.enable_html_pager,
 1691  **kw,
 1692  )
 1693 else:
 1694 pmethod(info.obj, oname)
File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/oinspect.py:698, in Inspector.pinfo(self, obj, oname, formatter, info, detail_level, enable_html_pager, omit_sections)
 665 def pinfo(
 666 self,
 667 obj,
 (...)
 673 omit_sections=(),
 674 ):
 675 """Show detailed information about an object.
 676
 677  Optional arguments:
 (...)
 696  - omit_sections: set of section keys and titles to omit
 697  """
--> 698 info = self._get_info(
 699  obj, oname, formatter, info, detail_level, omit_sections=omit_sections
 700  )
 701 if not enable_html_pager:
 702 del info['text/html']
File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/oinspect.py:591, in Inspector._get_info(self, obj, oname, formatter, info, detail_level, omit_sections)
 571 def _get_info(
 572 self, obj, oname="", formatter=None, info=None, detail_level=0, omit_sections=()
 573 ):
 574 """Retrieve an info dict and format it.
 575
 576  Parameters
 (...)
 588  Titles or keys to omit from output (can be set, tuple, etc., anything supporting `in`)
 589  """
--> 591 info = self.info(obj, oname=oname, info=info, detail_level=detail_level)
 593 _mime = {
 594 'text/plain': [],
 595 'text/html': '',
 596 }
 598 def append_field(bundle, title:str, key:str, formatter=None):
File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/oinspect.py:762, in Inspector.info(self, obj, oname, info, detail_level)
 760 ds += "\nDocstring:\n" + obj.__doc__
 761 else:
--> 762 ds = getdoc(obj)
 763 if ds is None:
 764 ds = '<no docstring>'
File /ext/sage/9.7/src/sage/misc/lazy_import.pyx:391, in sage.misc.lazy_import.LazyImport.__call__()
 389 True
 390 """
--> 391 return self.get_object()(*args, **kwds)
 392
 393 def __repr__(self):
File /ext/sage/9.7/src/sage/misc/sageinspect.py:2107, in sage_getdoc(obj, obj_name, embedded)
 2105 r = sage_getdoc_original(obj)
 2106 s = sage.misc.sagedoc.format(r, embedded=embedded)
-> 2107 f = sage_getfile(obj)
 2108 if f and os.path.exists(f):
 2109 from sage.doctest.control import skipfile
File /ext/sage/9.7/src/sage/misc/sageinspect.py:1414, in sage_getfile(obj)
 1412 # No go? fall back to inspect.
 1413 try:
-> 1414 sourcefile = inspect.getabsfile(obj)
 1415 except TypeError: # this happens for Python builtins
 1416 return ''
File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/inspect.py:844, in getabsfile(object, _filename)
 839 """Return an absolute path to the source or compiled file for an object.
 840
 841 The idea is for each object to have a unique origin, so this routine
 842 normalizes the result as much as possible."""
 843 if _filename is None:
--> 844 _filename = getsourcefile(object) or getfile(object)
 845 return os.path.normcase(os.path.abspath(_filename))
File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/inspect.py:817, in getsourcefile(object)
 813 def getsourcefile(object):
 814 """Return the filename that can be used to locate an object's source.
 815  Return None if no way can be identified to get the source.
 816  """
--> 817 filename = getfile(object)
 818 all_bytecode_suffixes = importlib.machinery.DEBUG_BYTECODE_SUFFIXES[:]
 819 all_bytecode_suffixes += importlib.machinery.OPTIMIZED_BYTECODE_SUFFIXES[:]
File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/inspect.py:785, in getfile(object)
 783 return module.__file__
 784 if object.__module__ == '__main__':
--> 785 raise OSError('source code not available')
 786 raise TypeError('{!r} is a built-in class'.format(object))
 787 if ismethod(object):
OSError: source code not available
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l?superelliptic_cech[?7h[?12l[?25h[?25l[?7lA[-1].f.function[?7h[?12l[?25h[?25l[?7l?superelliptic_cech[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
UnboundLocalError Traceback (most recent call last)
Input In [43], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:44, in <module>
File <string>:33, in automdR(omega)
UnboundLocalError: local variable 'om8' referenced before assignment
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[1 1 1 1 1 1 1 0 0 0 0 0 0 0]
[0 1 2 0 1 2 0 0 0 0 0 0 0 0]
[0 0 1 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 1 1 1 2 0 0 0 0 0 0 0]
[0 0 0 0 1 2 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[
RModule of dimension 1 over GF(3),
RModule of dimension 1 over GF(3),
RModule of dimension 1 over GF(3),
RModule of dimension 1 over GF(3),
RModule of dimension 10 over GF(3)
]
{
[0]
}
{
[0]
}
{
[0]
}
{
[0]
}
{
[1 1 1 1 1 1 1 0 0 0]
[0 1 2 0 1 2 0 0 0 0]
[0 0 1 0 0 1 0 0 0 0]
[0 0 0 1 1 1 2 0 0 0]
[0 0 0 0 1 2 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0],
[0 0 1 0 0 0 0 0 2 0]
[2 0 0 0 0 1 0 1 0 1]
[0 2 0 2 0 0 0 0 1 2]
[1 0 2 0 2 0 2 2 0 0]
[0 1 0 1 0 2 0 0 0 1]
[0 0 1 0 1 0 1 0 0 0]
[0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0]
}
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [45], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:43, in <module>
File <string>:75, in coordinates(self)
File <string>:113, in degree_of_rational_fctn(f, F)
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:554, in PolynomialRing(base_ring, *args, **kwds)
 52 r"""
 53 Return the globally unique univariate or multivariate polynomial
 54 ring with given properties and variable name or names.
 (...)
 551  TypeError: unable to convert 'x' to an integer
 552 """
 553 if not ring.is_Ring(base_ring):
--> 554 raise TypeError("base_ring {!r} must be a ring".format(base_ring))
 556 n = -1 # Unknown number of variables
 557 names = None # Unknown variable names
TypeError: base_ring 3 must be a ring
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y = C_super.x, C_super.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y = C_super.x, C_super.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: C.x
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [2], in <cell line: 1>()
----> 1 C.x
NameError: name 'C' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x[?7h[?12l[?25h[?25l[?7l_super.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: C_super.x
[?7h[?12l[?25h[?2004l[?7hx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltC_super.x[?7h[?12l[?25h[?25l[?7lyC_super.x[?7h[?12l[?25h[?25l[?7lpC_super.x[?7h[?12l[?25h[?25l[?7leC_super.x[?7h[?12l[?25h[?25l[?7ltype(C_super.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: type(C_super.x)
[?7h[?12l[?25h[?2004l[?7h<class '__main__.superelliptic_function'>
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(C_super.x)[?7h[?12l[?25h[?25l[?7lC_super.x[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C_super.x.diffn()
[?7h[?12l[?25h[?2004l[?7h1 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [6], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:13, in <module>
File <string>:46, in __mul__(self, other)
AttributeError: 'superelliptic_form' object has no attribute 'function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super.x.diffn()[?7h[?12l[?25h[?25l[?7l_super.x.diffn()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7liC_super.x[?7h[?12l[?25h[?25l[?7lsC_super.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_C_super.x[?7h[?12l[?25h[?25l[?7liC_super.x[?7h[?12l[?25h[?25l[?7lsC_super.x[?7h[?12l[?25h[?25l[?7lC_super.x[?7h[?12l[?25h[?25l[?7lnC_super.x[?7h[?12l[?25h[?25l[?7lsC_super.x[?7h[?12l[?25h[?25l[?7ltC_super.x[?7h[?12l[?25h[?25l[?7laC_super.x[?7h[?12l[?25h[?25l[?7lnC_super.x[?7h[?12l[?25h[?25l[?7lcC_super.x[?7h[?12l[?25h[?25l[?7leC_super.x[?7h[?12l[?25h[?25l[?7l(C_super.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lsuper)[?7h[?12l[?25h[?25l[?7lsupere)[?7h[?12l[?25h[?25l[?7ll)[?7h[?12l[?25h[?25l[?7ll)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l_)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7lsage: is_instance(C_super.x, superelliptic_function)
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [7], in <cell line: 1>()
----> 1 is_instance(C_super.x, superelliptic_function)
NameError: name 'is_instance' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_instance(C_super.x, superelliptic_function)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lisinstance(C_super.x, supereliptic_function)[?7h[?12l[?25h[?25l[?7lsage: isinstance(C_super.x, superelliptic_function)
[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lisinstance(C_super.x, superelliptic_function)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: isinstance(C_super.x, superelliptic_function)
[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super.x.diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(C_super.x)[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7ltype[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l(C_super.x)[?7h[?12l[?25h[?25l[?7lsage: type(C_super.x)
[?7h[?12l[?25h[?2004l[?7h<class '__main__.superelliptic_function'>
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(C_super.x)[?7h[?12l[?25h[?25l[?7lisinstance(C_super.x, superelliptic_function)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsuper)[?7h[?12l[?25h[?25l[?7lsupe)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsuperelliptic_function)[?7h[?12l[?25h[?25l[?7lsage: isinstance(C_super.x, superelliptic_function)
[?7h[?12l[?25h[?2004l[?7hFalse
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
!
!
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [12], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:13, in <module>
File <string>:47, in __mul__(self, other)
AttributeError: 'superelliptic_form' object has no attribute 'function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [13], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:13, in <module>
File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
 493 """
--> 494 return self.getattr_from_category(name)
 495
 496 cdef getattr_from_category(self, name):
File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
 505 else:
 506 cls = P._abstract_element_class
--> 507 return getattr_from_other_class(self, cls, name)
 508
 509 def __dir__(self):
File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
 359 dummy_error_message.cls = type(self)
 360 dummy_error_message.name = name
--> 361 raise AttributeError(dummy_error_message)
 362 attribute = <object>attr
 363 # Check for a descriptor (__get__ in Python)
AttributeError: 'sage.rings.fraction_field_element.FractionFieldElement' object has no attribute 'diffn'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super.x.diffn()[?7h[?12l[?25h[?25l[?7l.x[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: C.dx
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [14], in <cell line: 1>()
----> 1 C.dx
AttributeError: 'superelliptic' object has no attribute 'dx'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [15], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:21, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:13, in <module>
File /ext/sage/9.7/src/sage/rings/integer.pyx:2037, in sage.rings.integer.Integer.__truediv__()
 2035 return y
 2036
-> 2037 return coercion_model.bin_op(left, right, operator.truediv)
 2038
 2039 cpdef _div_(self, right):
File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op()
 1246 # We should really include the underlying error.
 1247 # This causes so much headache.
-> 1248 raise bin_op_exception(op, x, y)
 1249
 1250 cpdef canonical_coercion(self, x, y):
TypeError: unsupported operand parent(s) for /: 'Integer Ring' and '<class '__main__.superelliptic_function'>'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004lTraceback (most recent call last):
File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
exec(code_obj, self.user_global_ns, self.user_ns)
Input In [16] in <cell line: 1>
load('init.sage')
File sage/misc/persist.pyx:175 in sage.misc.persist.load
sage.repl.load.load(filename, globals())
File /ext/sage/9.7/src/sage/repl/load.py:272 in load
exec(preparse_file(f.read()) + "\n", globals)
File <string>:1 in <module>
File sage/misc/persist.pyx:175 in sage.misc.persist.load
sage.repl.load.load(filename, globals())
 File /ext/sage/9.7/src/sage/repl/load.py:272 in load
 exec(preparse_file(f.read()) + "\n", globals)
 File <string>:21
 self.gen(1) = superelliptic_function(self, Rxy(_sage_const_1 ))
 ^
SyntaxError: cannot assign to function call here. Maybe you meant '==' instead of '='?
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
((x^11 - x^9 + x^7 - x^3 + y)/(x^5*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l((x^12 - x^10 + x^8 - x^4 - x^2 + 1)/(x^6*y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 
 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lIfactors = I.factor()[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()([?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: Integers(9)(5/2)
[?7h[?12l[?25h[?2004l[?7h7
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 
 [?7h[?12l[?25h[?25l[?7lIntegers(9)(5/2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l/2)[?7h[?12l[?25h[?25l[?7l-/2)[?7h[?12l[?25h[?25l[?7l7/2)[?7h[?12l[?25h[?25l[?7lsage: Integers(9)(-7/2)
[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^2-1)^4[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (x^2/y^3).expansion_at_infty()
[?7h[?12l[?25h[?2004l[?7ht^5 + O(t^15)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^2/y^3).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l/y^3).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l4/y^3).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: (x^4/y^3).expansion_at_infty()
[?7h[?12l[?25h[?2004l[?7ht + 2*t^5 + 2*t^9 + O(t^11)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^4/y^3).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^4/y^3).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (x^2+x^4)*y^2*y.diffn()
[?7h[?12l[?25h[?2004l[?7h((x^7 - x^3)/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = A[0][?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^2+x^4)*y^2*y.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp(x^2+x^4)*y^2*y.difn()[?7h[?12l[?25h[?25l[?7l(x^2+x^4)*y^2*y.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo(x^2+x^4)*y^2*y.difn()[?7h[?12l[?25h[?25l[?7lm(x^2+x^4)*y^2*y.difn()[?7h[?12l[?25h[?25l[?7l (x^2+x^4)*y^2*y.difn()[?7h[?12l[?25h[?25l[?7l=(x^2+x^4)*y^2*y.difn()[?7h[?12l[?25h[?25l[?7l (x^2+x^4)*y^2*y.difn()[?7h[?12l[?25h[?25l[?7lsage: om = (x^2+x^4)*y^2*y.diffn()
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = (x^2+x^4)*y^2*y.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.form[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsion_at_infty[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.expansion_at_infty()
[?7h[?12l[?25h[?2004l[?7ht^-14 + O(t^-4)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lP[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: P1
[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^1 = x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx[?7h[?12l[?25h[?25l[?7lsage: C
[?7h[?12l[?25h[?2004l[?7h(Z/p)-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equation:
z^3 - z = x^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.dx[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le_rham_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lgical_element[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.
 C.at_most_poles C.cohomology_of_structure_sheaf_basis C.exponent_of_different C.genus  
 C.at_most_poles_forms C.de_rham_basis C.exponent_of_different_prim C.group  
 C.base_ring C.dx C.fct_field C.height >
 C.characteristic C.dx_series C.functions C.holomorphic_differentials_basis  
 [?7h[?12l[?25h[?25l[?7lat_most_poles
 C.at_most_poles 
 <unknown> [?7h[?12l[?25h[?25l[?7lcohomology_of_structure_sheaf_basis
 C.at_most_poles  C.cohomology_of_structure_sheaf_basis[?7h[?12l[?25h[?25l[?7lexpnent_of_different
 C.cohomology_of_structure_sheaf_basis C.exponent_of_different [?7h[?12l[?25h[?25l[?7lgenus
 C.exponent_of_different  C.genus [?7h[?12l[?25h[?25l[?7lith_ramification_gp
 cohomology_of_structure_sheaf_basisexpnent_of_different genus ith_ramification_gp
 derhambasi exponent_of_different_primgroup jumps
<dx fct_fieldheight lift_o_de_rham
 dx_seris functionholomorphic_differentials_basismagical_element [?7h[?12l[?25h[?25l[?7lnb_of_pts_at_nfty
expnent_of_different genus ith_ramification_gpnb_of_pts_at_nfty 
exponent_of_different_primgroup jumpsprec 
fct_fieldheight lift_o_de_rhampseudo_magical_element
functionholomorphic_differentials_basismagical_element quotient [?7h[?12l[?25h[?25l[?7lramiicationjumps
genus ith_ramification_gpnb_of_pts_at_nfty ramiicationjumps
group jumpsprec uniformizer
height lift_o_de_rhampseudo_magical_elementx 
holomorphic_differentials_basismagical_element quotient x_series[?7h[?12l[?25h[?25l[?7ly
ith_ramification_gpnb_of_pts_at_nfty ramiicationjumpsy  
jumpsprec uniformizery_series  
lift_o_de_rhampseudo_magical_elementx z 
magical_element quotient x_seriesz  [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_series
 C.y 
 C.y_series [?7h[?12l[?25h[?25l[?7lz
 C.y_series 
 C.z [?7h[?12l[?25h[?25l[?7l_series
 C.z 
 C.z_series [?7h[?12l[?25h[?25l[?7l
 a_most_poles cohmology_of_structure_sheaf_basisexponent_of_differentgenus 
 at_most_poles_formsde_rham_basisexponent_of_different_primgroup  
 basering dx fct_fieldheight>
 characteristic dx_seriesfunctons C.holomorphic_differentials_basis  
[?7h[?12l[?25h[?25l[?7l



[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l
 C CFiniteSequence CPRFanoToricVariety CRT_vectors 
 CBF CFiniteSequences CRT C_super 
 CC CIF CRT_basis CachedFunction >
 CDF CLF CRT_list CallableSymbolicExpressionRing [?7h[?12l[?25h[?25l[?7l
 C 
 <unknown> [?7h[?12l[?25h[?25l[?7lFiniteSequence.
 C  CFiniteSequence [?7h[?12l[?25h[?25l[?7lPRFanoToricVariety.
 CFiniteSequence  CPRFanoToricVariety [?7h[?12l[?25h[?25l[?7l.




[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.dx[?7h[?12l[?25h[?25l[?7l
 C.at_most_poles C.cohomology_of_structure_sheaf_basis C.exponent_of_different C.genus  
 C.at_most_poles_forms C.de_rham_basis C.exponent_of_different_prim C.group  
 C.base_ring C.dx C.fct_field C.height >
 C.characteristic C.dx_series C.functions C.holomorphic_differentials_basis   [?7h[?12l[?25h[?25l[?7lat_most_poles
 C.at_most_poles 
 <unknown> [?7h[?12l[?25h[?25l[?7l_forms
 C.at_most_poles 
 C.at_most_poles_forms [?7h[?12l[?25h[?25l[?7lbase_ring
 C.at_most_poles_forms 
 C.base_ring [?7h[?12l[?25h[?25l[?7lcharacteristic
 C.base_ring 
 C.characteristic [?7h[?12l[?25h[?25l[?7lohomology_of_structure_sheaf_basis
 C.cohomology_of_structure_sheaf_basis
 C.characteristic [?7h[?12l[?25h[?25l[?7lde_rham_basis
 C.cohomology_of_structure_sheaf_basis
 C.de_rham_basis [?7h[?12l[?25h[?25l[?7lx
 C.de_rham_basis 
 C.dx [?7h[?12l[?25h[?25l[?7l_series
 C.dx 
 C.dx_series [?7h[?12l[?25h[?25l[?7leponent_of_different
 C.exponent_of_different 
 C.dx_series [?7h[?12l[?25h[?25l[?7l_prim
 C.exponent_of_different 
 C.exponent_of_different_prim [?7h[?12l[?25h[?25l[?7lfct_field
 C.exponent_of_different_prim 
 C.fct_field [?7h[?12l[?25h[?25l[?7lunctons
 C.fct_field 
 C.functions [?7h[?12l[?25h[?25l[?7lgeus
 C.genus 
 C.functions [?7h[?12l[?25h[?25l[?7lrop
 C.genus 
 C.group [?7h[?12l[?25h[?25l[?7lheight
 C.group 
 C.height [?7h[?12l[?25h[?25l[?7lolomorphic_differentials_basis
 C.height 
 C.holomorphic_differentials_basis [?7h[?12l[?25h[?25l[?7lith_ramifaton_gp
 cohomology_of_structure_sheaf_basisexpnent_of_different genus  C.ith_ramification_gp 
 derhambasi exponent_of_different_primgroup jumps
<dx fct_fieldheight lift_o_de_rham
 dx_seris functionholomorphic_differentials_basis C.magical_element [?7h[?12l[?25h[?25l[?7ljumps
 C.ith_ramification_gp 
 C.jumps [?7h[?12l[?25h[?25l[?7llift_to_de_rham
 C.jumps 
 C.lift_to_de_rham [?7h[?12l[?25h[?25l[?7lmagicalelement
 C.lift_to_de_rham 
 C.magical_element [?7h[?12l[?25h[?25l[?7lnb_of_pts_at_infty
expnent_of_different genus ith_ramification_gp C.nb_of_pts_at_infty 
exponent_of_different_primgroup jumpsprec 
fct_fieldheight lift_o_de_rhampseudo_magical_element
functionholomorphic_differentials_basismagical_element  C.quotient [?7h[?12l[?25h[?25l[?7lprec
 C.nb_of_pts_at_infty 
 C.prec [?7h[?12l[?25h[?25l[?7lsudo_magical_element
 C.prec 
 C.pseudo_magical_element [?7h[?12l[?25h[?25l[?7lquotient
 C.pseudo_magical_element 
 C.quotient [?7h[?12l[?25h[?25l[?7lramification_jumps
genus ith_ramification_gpnb_of_pts_at_nfty  C.ramification_jumps 
group jumpsprec uniformizer
height lift_o_de_rhampseudo_magical_elementx 
holomorphic_differentials_basismagical_element quotient  C.x_series [?7h[?12l[?25h[?25l[?7luniformizer
 C.ramification_jumps 
 C.uniformizer [?7h[?12l[?25h[?25l[?7lx
 C.uniformizer 
 C.x [?7h[?12l[?25h[?25l[?7l_series
 C.x 
 C.x_series [?7h[?12l[?25h[?25l[?7ly
ith_ramification_gpnb_of_pts_at_nfty ramiicationjumps C.y  
jumpsprec uniformizery_series  
lift_o_de_rhampseudo_magical_elementx z 
magical_element quotient x_series C.z_series   [?7h[?12l[?25h[?25l[?7l_series
 C.y 
 C.y_series [?7h[?12l[?25h[?25l[?7lz
 C.y_series 
 C.z [?7h[?12l[?25h[?25l[?7l_series
 C.z 
 C.z_series [?7h[?12l[?25h[?25l[?7l
 a_most_poles cohmology_of_structure_sheaf_basisexponent_of_differentgenus 
 at_most_poles_formsde_rham_basisexponent_of_different_primgroup  
 basering dx fct_fieldheight>
 characteristic dx_seriesfunctons C.holomorphic_differentials_basis  
[?7h[?12l[?25h[?25l[?7lat_most_poles
 C.at_most_poles 
 <unknown> [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcohomology_of_structure_sheaf_basis
 C.at_most_poles  C.cohomology_of_structure_sheaf_basis[?7h[?12l[?25h[?25l[?7lexpnent_of_different
 C.cohomology_of_structure_sheaf_basis C.exponent_of_different [?7h[?12l[?25h[?25l[?7lgenus
 C.exponent_of_different  C.genus [?7h[?12l[?25h[?25l[?7lith_ramification_gp
 cohomology_of_structure_sheaf_basisexpnent_of_different genus ith_ramification_gp
 derhambasi exponent_of_different_primgroup jumps
<dx fct_fieldheight lift_o_de_rham
 dx_seris functionholomorphic_differentials_basismagical_element [?7h[?12l[?25h[?25l[?7lnb_of_pts_at_nfty
expnent_of_different genus ith_ramification_gpnb_of_pts_at_nfty 
exponent_of_different_primgroup jumpsprec 
fct_fieldheight lift_o_de_rhampseudo_magical_element
functionholomorphic_differentials_basismagical_element quotient [?7h[?12l[?25h[?25l[?7lramiicationjumps
genus ith_ramification_gpnb_of_pts_at_nfty ramiicationjumps
group jumpsprec uniformizer
height lift_o_de_rhampseudo_magical_elementx 
holomorphic_differentials_basismagical_element quotient x_series[?7h[?12l[?25h[?25l[?7ly
ith_ramification_gpnb_of_pts_at_nfty ramiicationjumpsy  
jumpsprec uniformizery_series  
lift_o_de_rhampseudo_magical_elementx z 
magical_element quotient x_seriesz  [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lramification_jumps
 C.ramification_jumps  C.y [?7h[?12l[?25h[?25l[?7luniformizer
 C.ramification_jumps 
 C.uniformizer [?7h[?12l[?25h[?25l[?7lx
 C.uniformizer 
 C.x [?7h[?12l[?25h[?25l[?7lpseudo_magical_element
 C.pseudo_magical_element  C.x [?7h[?12l[?25h[?25l[?7lquotient
 C.pseudo_magical_element 
 C.quotient [?7h[?12l[?25h[?25l[?7lpseudo_magical_element
 C.pseudo_magical_element 
 C.quotient [?7h[?12l[?25h[?25l[?7lrc
 C.prec 
 C.pseudo_magical_element [?7h[?12l[?25h[?25l[?7lnb_of_pts_at_infty
 C.nb_of_pts_at_infty 
 C.prec [?7h[?12l[?25h[?25l[?7lith_ramificaton_gp
 C.ith_ramification_gp  C.nb_of_pts_at_infty [?7h[?12l[?25h[?25l[?7ljumps
 C.ith_ramification_gp 
 C.jumps [?7h[?12l[?25h[?25l[?7llift_to_de_rham
 C.jumps 
 C.lift_to_de_rham [?7h[?12l[?25h[?25l[?7lmagicalelement
 C.lift_to_de_rham 
 C.magical_element [?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis
genus ith_ramificaton_gpnb_o_pts_atinftyramification_jumps 
groupjumpsprec uniformizer 
heigh lift_to_de_rham pseudo_magical_elementx>
holomorphic_differentials_basismagical_elementquotientx  [?7h[?12l[?25h[?25l[?7leight
 C.height 
 C.holomorphic_differentials_basis [?7h[?12l[?25h[?25l[?7lgroup
 C.group 
 C.height [?7h[?12l[?25h[?25l[?7lens
 C.genus 
 C.group [?7h[?12l[?25h[?25l[?7lexponent_of_different
exponent_of_differentgenus ith_ramificaton_gpnb_o_pts_atinfty
exponent_of_different_primgroupjumpsprec 
fct_fieldheigh lift_to_de_rham pseudo_magical_element
functions holomorphic_differentials_basismagical_elementquotient[?7h[?12l[?25h[?25l[?7l_prim
 C.exponent_of_different 
 C.exponent_of_different_prim [?7h[?12l[?25h[?25l[?7lfct_field
 C.exponent_of_different_prim 
 C.fct_field [?7h[?12l[?25h[?25l[?7lunctons
 C.fct_field 
 C.functions [?7h[?12l[?25h[?25l[?7ldx_serie
cohmology_of_structure_sheaf_basisexponent_of_differentgenus ith_ramificaton_gp
de_rham_basis exponent_of_different_primgroupjumps
dx fct_fieldheigh lift_to_de_rham 
dx_seriefunctions holomorphic_differentials_basismagical_element[?7h[?12l[?25h[?25l[?7lcharactristic
 at_most_poles cohmology_of_structure_sheaf_basisexponent_of_differentgenus 
 atmostpole_formsde_rham_basis exponent_of_different_primgroup
 base_ringdx fct_fieldheigh 
 charactristicdx_seriefunctions holomorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l




[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[[1 2]
[0 1]]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 
 [?7h[?12l[?25h[?25l[?7lIntegers(9)(-7/2)[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l9)(-7/2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l/2)[?7h[?12l[?25h[?25l[?7l/2)[?7h[?12l[?25h[?25l[?7l5/2)[?7h[?12l[?25h[?25l[?7lsage: Integers(9)(5/2)
[?7h[?12l[?25h[?2004l[?7h7
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l%[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: 7%3
[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sa
bash: sa: command not found
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ gesage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llista2 = [][?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[[1 2]
[0 1]]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C
[?7h[?12l[?25h[?2004l[?7h(Z/p)-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equation:
z^3 - z = x^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.dx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: C.x
[?7h[?12l[?25h[?2004l[?7hx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion_at_infty[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty()
[?7h[?12l[?25h[?2004l[?7ht^-3 + t + t^5 + O(t^7)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty()[-3]
[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty()[-3][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l2][?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty()[-2]
[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty()[-2][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l1][?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty()[-1]
[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty()[-1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l1][?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty()[1]
[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004lTraceback (most recent call last):
File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
exec(code_obj, self.user_global_ns, self.user_ns)
Input In [9] in <cell line: 1>
load('init.sage')
File sage/misc/persist.pyx:175 in sage.misc.persist.load
sage.repl.load.load(filename, globals())
File /ext/sage/9.7/src/sage/repl/load.py:272 in load
exec(preparse_file(f.read()) + "\n", globals)
File <string>:21 in <module>
File sage/misc/persist.pyx:175 in sage.misc.persist.load
sage.repl.load.load(filename, globals())
 File /ext/sage/9.7/src/sage/repl/load.py:272 in load
 exec(preparse_file(f.read()) + "\n", globals)
 File <string>:32
 basis += [superelliptic_cohomology(C, Fxy(m*y**(m-j)/x**i)))]
 ^
SyntaxError: closing parenthesis ')' does not match opening parenthesis '['
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[[1 2]
[0 1]]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: basis
 basis 
 basis_of_cohomology
 [?7h[?12l[?25h[?25l[?7l
 basis 
 <unknown> [?7h[?12l[?25h[?25l[?7l_of_cohomology
 basis 
 basis_of_cohomology[?7h[?12l[?25h[?25l[?7l


[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: basis_of_cohomology(C)
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [11], in <cell line: 1>()
----> 1 basis_of_cohomology(C)
File <string>:18, in basis_of_cohomology(C)
AttributeError: 'as_cover' object has no attribute 'exponent'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty()[1][?7h[?12l[?25h[?25l[?7lsage: C
[?7h[?12l[?25h[?2004l[?7h(Z/p)-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equation:
z^3 - z = x^2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lbasis_of_cohomology(C)[?7h[?12l[?25h[?25l[?7lsage: basis_of_cohomology(C)
[?7h[?12l[?25h[?2004l[?7h[<__main__.superelliptic_cohomology object at 0x7f4110fc8a60>]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbasis_of_cohomology(C)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lbasis_of_cohomology(C)[?7h[?12l[?25h[?25l[?7lsage: basis_of_cohomology(C)
[?7h[?12l[?25h[?2004l[?7h[[(-y)/x]]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.x.expansion_at_infty()[1][?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: C.bas
 C.base_ring 
 C.basis_de_rham_degrees 
 C.basis_holomorphic_differentials_degree
 [?7h[?12l[?25h[?25l[?7l


[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis()
[?7h[?12l[?25h[?2004l[?7h[(1/y) dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 
 [?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lbasis_of_cohomology(C)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004lTraceback (most recent call last):
File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
exec(code_obj, self.user_global_ns, self.user_ns)
Input In [18] in <cell line: 1>
load('init.sage')
File sage/misc/persist.pyx:175 in sage.misc.persist.load
sage.repl.load.load(filename, globals())
File /ext/sage/9.7/src/sage/repl/load.py:272 in load
exec(preparse_file(f.read()) + "\n", globals)
File <string>:22 in <module>
File sage/misc/persist.pyx:175 in sage.misc.persist.load
sage.repl.load.load(filename, globals())
 File /ext/sage/9.7/src/sage/repl/load.py:272 in load
 exec(preparse_file(f.read()) + "\n", globals)
 File <string>:10
 print f.prod(omega)
 ^
SyntaxError: Missing parentheses in call to 'print'. Did you mean print(...)?
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [19], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:22, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:9, in <module>
NameError: name 'basis_cohomology' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbasis_of_cohomology(C)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [20], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:22, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:10, in <module>
File <string>:13, in prod(self, form)
TypeError: unsupported operand type(s) for *: 'superelliptic_form' and 'superelliptic_cohomology'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [21], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:22, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:10, in <module>
File <string>:14, in prod(self, form)
File <string>:59, in __rmul__(self, constant)
TypeError: unsupported operand type(s) for *: 'superelliptic_form' and 'PolynomialRing_field_with_category.element_class'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [22], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:22, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:10, in <module>
File <string>:14, in prod(self, form)
TypeError: superelliptic_form.expansion_at_infty() got an unexpected keyword argument 'place'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
IndexError Traceback (most recent call last)
Input In [24], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:22, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:10, in <module>
File <string>:14, in prod(self, form)
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__()
 542 return type(self)(self._parent, f, self.__n)
 543
--> 544 return self.__u[i - self.__n]
 545
 546 def __iter__(self):
File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__()
 451 return self.base_ring().zero()
 452 else:
--> 453 raise IndexError("coefficient not known")
 454 return self.__f[n]
 455
IndexError: coefficient not known
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l2*t^-11 + O(t^-1)
---------------------------------------------------------------------------
IndexError Traceback (most recent call last)
Input In [25], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:22, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:10, in <module>
File <string>:15, in prod(self, form)
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__()
 542 return type(self)(self._parent, f, self.__n)
 543
--> 544 return self.__u[i - self.__n]
 545
 546 def __iter__(self):
File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__()
 451 return self.base_ring().zero()
 452 else:
--> 453 raise IndexError("coefficient not known")
 454 return self.__f[n]
 455
IndexError: coefficient not known
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l2*t^-11 + 2*t^5 + O(t^9)
0
2*t^-7 + 2*t^9 + O(t^13)
0
2*t^-3 + 2*t^13 + O(t^17)
0
2*t^-6 + t^10 + O(t^14)
0
2*t^-2 + t^14 + O(t^18)
0
2*t^-1 + O(t^19)
2
2*t^-6 + t^10 + O(t^14)
0
2*t^-2 + t^14 + O(t^18)
0
2*t^2 + t^18 + O(t^22)
0
2*t^-1 + O(t^19)
2
2*t^3 + O(t^23)
0
2*t^4 + t^20 + O(t^24)
0
2*t^-10 + t^6 + O(t^10)
0
2*t^-6 + t^10 + O(t^14)
0
2*t^-2 + t^14 + O(t^18)
0
2*t^-5 + O(t^15)
0
2*t^-1 + O(t^19)
2
2 + t^16 + O(t^20)
0
2*t^-1 + O(t^19)
2
2*t^3 + O(t^23)
0
2*t^7 + O(t^27)
0
2*t^4 + t^20 + O(t^24)
0
2*t^8 + t^24 + O(t^28)
0
2*t^9 + O(t^29)
0
2*t^-5 + O(t^15)
0
2*t^-1 + O(t^19)
2
2*t^3 + O(t^23)
0
2 + t^16 + O(t^20)
0
2*t^4 + t^20 + O(t^24)
0
2*t^5 + O(t^25)
0
2*t^-9 + O(t^11)
0
2*t^-5 + O(t^15)
0
2*t^-1 + O(t^19)
2
2*t^-4 + t^12 + O(t^16)
0
2 + t^16 + O(t^20)
0
2*t + O(t^21)
0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C
[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^4 = x^5 + x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis()
[?7h[?12l[?25h[?2004l[?7h[(1/y) dx, (1/y^2) dx, (x/y^2) dx, (1/y^3) dx, (x/y^3) dx, (x^2/y^3) dx]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l_of_pts_at_infty[?7h[?12l[?25h[?25l[?7lsage: C.nb_of_pts_at_infty
[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.nb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_smooth[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.is_smooth()
[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbasis_of_cohomology(C)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls_of_cohomology(C)[?7h[?12l[?25h[?25l[?7lsage: basis_of_cohomology(C)
[?7h[?12l[?25h[?2004l[?7h[[y^3/x], [y^3/x^2], [y^3/x^3], [y^2/x], [y^2/x^2], [y/x]]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbasis_of_cohomology(C)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7labasis_of_cohomology(C)[0][?7h[?12l[?25h[?25l[?7l basis_of_cohomology(C)[0][?7h[?12l[?25h[?25l[?7l=basis_of_cohomology(C)[0][?7h[?12l[?25h[?25l[?7l basis_of_cohomology(C)[0][?7h[?12l[?25h[?25l[?7lsage: a = basis_of_cohomology(C)[0]
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = basis_of_cohomology(C)[0][?7h[?12l[?25h[?25l[?7l.squre_rot()[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: a.prod(C.holomorphic_differentials_basis()[0])
[?7h[?12l[?25h[?2004l2*t^-11 + 2*t^5 + O(t^9)
[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.prod(C.holomorphic_differentials_basis()[0])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l1])[?7h[?12l[?25h[?25l[?7lsage: a.prod(C.holomorphic_differentials_basis()[1])
[?7h[?12l[?25h[?2004l2*t^-6 + t^10 + O(t^14)
[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.prod(C.holomorphic_differentials_basis()[1])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l2])[?7h[?12l[?25h[?25l[?7lsage: a.prod(C.holomorphic_differentials_basis()[2])
[?7h[?12l[?25h[?2004l2*t^-10 + t^6 + O(t^10)
[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.prod(C.holomorphic_differentials_basis()[2])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l3])[?7h[?12l[?25h[?25l[?7lsage: a.prod(C.holomorphic_differentials_basis()[3])
[?7h[?12l[?25h[?2004l2*t^-1 + O(t^19)
[?7h2
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.is_smooth()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.genus()
[?7h[?12l[?25h[?2004l[?7h6
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lista2 = [][?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7llist[?7h[?12l[?25h[?25l[?7llista[?7h[?12l[?25h[?25l[?7l = [][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: lista = ['a', 'b', 'c']
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in lista2:[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lirange(0, p):[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, f in enumerate(AS.cohomology_of_structure_sheaf_basis()):[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: for i, x in enum
 enum_affine_finite_field enumerate_totallyreal_fields_all 
 enum_affine_rational_field enumerate_totallyreal_fields_prim
 enumerate enumerate_totallyreal_fields_rel 
 [?7h[?12l[?25h[?25l[?7le


[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lenumerate[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7llist[?7h[?12l[?25h[?25l[?7llista[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7l
....: [?7h[?12l[?25h[?25l[?7lprint(a, lista.count(a))[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()
....: [?7h[?12l[?25h[?25l[?7lsage: for i, x in enumerate(lista):
....:  print(i, x)
....: 
[?7h[?12l[?25h[?2004l0 a
1 b
2 c
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llista = ['a', 'b', 'c'][?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[0, 0, 0, 1, 0, 0]
[0, 0, 0, 0, 1, 0]
[0, 0, 0, 0, 0, 1]
[0, 1, 0, 0, 0, 0]
[0, 0, 1, 0, 0, 0]
[1, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[1, 0, 0, 0, 0, 0]
[0, 1, 0, 0, 0, 0]
[0, 0, 1, 0, 0, 0]
[0, 0, 0, 1, 0, 0]
[0, 0, 0, 0, 1, 0]
[0, 0, 0, 0, 0, 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[1, 0, 0, 0, 0, 0]
[0, 1, 0, 0, 0, 0]
[0, 0, 1, 0, 0, 0]
[0, 0, 0, 1, 0, 0]
[0, 0, 0, 0, 1, 0]
[0, 0, 0, 0, 0, 1]
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [44], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:22, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:10, in <module>
File <string>:59, in frobenius_matrix(C)
File <string>:35, in frobenius(self)
AttributeError: 'superelliptic_cohomology' object has no attribute 'base_ring'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[1, 0, 0, 0, 0, 0]
[0, 1, 0, 0, 0, 0]
[0, 0, 1, 0, 0, 0]
[0, 0, 0, 1, 0, 0]
[0, 0, 0, 0, 1, 0]
[0, 0, 0, 0, 0, 1]
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [45], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:22, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:10, in <module>
File <string>:59, in frobenius_matrix(C)
File /ext/sage/9.7/src/sage/matrix/matrix0.pyx:1509, in sage.matrix.matrix0.Matrix.__setitem__()
 1507 raise IndexError("value does not have the right number of rows")
 1508 for value_row in value_list:
-> 1509 if col_list_len != len(value_row):
 1510 raise IndexError("value does not have the right number of columns")
 1511
TypeError: object of type 'sage.rings.finite_rings.integer_mod.IntegerMod_int' has no len()
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[1, 0, 0, 0, 0, 0]
[0, 1, 0, 0, 0, 0]
[0, 0, 1, 0, 0, 0]
[0, 0, 0, 1, 0, 0]
[0, 0, 0, 0, 1, 0]
[0, 0, 0, 0, 0, 1]
---------------------------------------------------------------------------
IndexError Traceback (most recent call last)
Input In [46], in <cell line: 1>()
----> 1 load('init.sage')
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:22, in <module>
File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
 173
 174 if sage.repl.load.is_loadable_filename(filename):
--> 175 sage.repl.load.load(filename, globals())
 176 return
 177
File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
 270 add_attached_file(fpath)
 271 with open(fpath) as f:
--> 272 exec(preparse_file(f.read()) + "\n", globals)
 273 elif ext == '.spyx' or ext == '.pyx':
 274 if attach:
File <string>:10, in <module>
File <string>:59, in frobenius_matrix(C)
File <string>:29, in coordinates(self, basis, basis_holo)
File <string>:14, in prod(self, form, prec)
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__()
 542 return type(self)(self._parent, f, self.__n)
 543
--> 544 return self.__u[i - self.__n]
 545
 546 def __iter__(self):
File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__()
 451 return self.base_ring().zero()
 452 else:
--> 453 raise IndexError("coefficient not known")
 454 return self.__f[n]
 455
IndexError: coefficient not known
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[1, 0, 0, 0, 0, 0]
[0, 1, 0, 0, 0, 0]
[0, 0, 1, 0, 0, 0]
[0, 0, 0, 1, 0, 0]
[0, 0, 0, 0, 1, 0]
[0, 0, 0, 0, 0, 1]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM.jordan_form()[?7h[?12l[?25h[?25l[?7lsage: M
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [48], in <cell line: 1>()
----> 1 M
NameError: name 'M' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i, x in enumerate(lista):[?7h[?12l[?25h[?25l[?7lrom itertools import product[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: frobenius_matrix(C)
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
IndexError Traceback (most recent call last)
Input In [49], in <cell line: 1>()
----> 1 frobenius_matrix(C)
File <string>:59, in frobenius_matrix(C, prec)
File <string>:29, in coordinates(self, basis, basis_holo, prec)
File <string>:14, in prod(self, form, prec)
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__()
 542 return type(self)(self._parent, f, self.__n)
 543
--> 544 return self.__u[i - self.__n]
 545
 546 def __iter__(self):
File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__()
 451 return self.base_ring().zero()
 452 else:
--> 453 raise IndexError("coefficient not known")
 454 return self.__f[n]
 455
IndexError: coefficient not known
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(C)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l5)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7lsage: frobenius_matrix(C, prec=50)
[?7h[?12l[?25h[?2004l[?7h[0 0 0 1 0 0]
[0 0 1 0 0 0]
[0 1 0 0 0 0]
[0 0 0 0 0 0]
[0 0 0 0 0 0]
[1 0 0 0 0 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(C, prec=50)[?7h[?12l[?25h[?25l[?7l(),[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic_curve(2, x^3 - x)
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [51], in <cell line: 1>()
----> 1 C = superelliptic_curve(Integer(2), x**Integer(3) - x)
NameError: name 'superelliptic_curve' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic_curve(2, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(2, x^3 - x)[?7h[?12l[?25h[?25l[?7l(2, x^3 - x)[?7h[?12l[?25h[?25l[?7l(2, x^3 - x)[?7h[?12l[?25h[?25l[?7l(2, x^3 - x)[?7h[?12l[?25h[?25l[?7l(2, x^3 - x)[?7h[?12l[?25h[?25l[?7l(2, x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(2, x^3 - x)
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2441, in sage.rings.polynomial.polynomial_element.Polynomial.__pow__()
 2440 try:
-> 2441 right = Integer(right)
 2442 except TypeError:
File /ext/sage/9.7/src/sage/rings/integer.pyx:658, in sage.rings.integer.Integer.__init__()
 657 if otmp is not None:
--> 658 set_from_Integer(self, otmp(the_integer_ring))
 659 return
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:1390, in sage.rings.polynomial.polynomial_element.Polynomial._scalar_conversion()
 1389 if self.degree() > 0:
-> 1390 raise TypeError("cannot convert nonconstant polynomial")
 1391 return R(self.get_coeff_c(0))
TypeError: cannot convert nonconstant polynomial
During handling of the above exception, another exception occurred:
TypeError Traceback (most recent call last)
Input In [52], in <cell line: 1>()
----> 1 C = superelliptic(Integer(2), x**Integer(3) - x)
File <string>:19, in __init__(self, f, m)
File <string>:13, in __init__(self, C, g)
File <string>:188, in reduction(C, g)
File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2443, in sage.rings.polynomial.polynomial_element.Polynomial.__pow__()
 2441 right = Integer(right)
 2442 except TypeError:
-> 2443 raise TypeError("non-integral exponents not supported")
 2444
 2445 d = self.degree()
TypeError: non-integral exponents not supported
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(2, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx^3 - x)[?7h[?12l[?25h[?25l[?7lx^3 - x)[?7h[?12l[?25h[?25l[?7lx^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 - x, 2)
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.gens()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(C, prec=50)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lus_matrix(C, prec=50)[?7h[?12l[?25h[?25l[?7lsage: frobenius_matrix(C, prec=50)
[?7h[?12l[?25h[?2004l[?7h[0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(C, prec=50)[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l+, 2)[?7h[?12l[?25h[?25l[?7l , 2)[?7h[?12l[?25h[?25l[?7l1, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 + 1, 2)
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(C, prec=50)[?7h[?12l[?25h[?25l[?7lsage: frobenius_matrix(C, prec=50)
[?7h[?12l[?25h[?2004l[?7h[0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(C, prec=50)[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7lx, 2)[?7h[?12l[?25h[?25l[?7l , 2)[?7h[?12l[?25h[?25l[?7l+, 2)[?7h[?12l[?25h[?25l[?7l , 2)[?7h[?12l[?25h[?25l[?7l1, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 + x + 1, 2)
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 + x + 1, 2)[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(C, prec=50)[?7h[?12l[?25h[?25l[?7lsage: frobenius_matrix(C, prec=50)
[?7h[?12l[?25h[?2004l[?7h[0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE.local_data(2)[?7h[?12l[?25h[?25l[?7l = ElipticCurve([0, 16])[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lEllipticCurve([0, 16])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lG[0, 16])[?7h[?12l[?25h[?25l[?7lF[0, 16])[?7h[?12l[?25h[?25l[?7l([0, 16])[?7h[?12l[?25h[?25l[?7l)[0, 16])[?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l3)[0, 16])[?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l,[0, 16])[?7h[?12l[?25h[?25l[?7l [0, 16])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l1])[?7h[?12l[?25h[?25l[?7l,])[?7h[?12l[?25h[?25l[?7l ])[?7h[?12l[?25h[?25l[?7l1])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: E = EllipticCurve(GF(3), [1, 1])
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE = EllipticCurve(GF(3), [1, 1])[?7h[?12l[?25h[?25l[?7l.loca_data(2)[?7h[?12l[?25h[?25l[?7lis_goo(3)[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lsingular(2)[?7h[?12l[?25h[?25l[?7lupersingular(2)[?7h[?12l[?25h[?25l[?7lpersingular(2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: E.is_supersingular()
[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE.is_supersingular()[?7h[?12l[?25h[?25l[?7l = EllipticCurve(GF(3), [1, 1])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l2])[?7h[?12l[?25h[?25l[?7lsage: E = EllipticCurve(GF(3), [1, 2])
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE = EllipticCurve(GF(3), [1, 2])[?7h[?12l[?25h[?25l[?7l.is_supersingular()[?7h[?12l[?25h[?25l[?7lsage: E.is_supersingular()
[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE.is_supersingular()[?7h[?12l[?25h[?25l[?7l = EllipticCurve(GF(3), [1, 2])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l0])[?7h[?12l[?25h[?25l[?7lsage: E = EllipticCurve(GF(3), [1, 0])
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE = EllipticCurve(GF(3), [1, 0])[?7h[?12l[?25h[?25l[?7l.is_supersingular()[?7h[?12l[?25h[?25l[?7lsage: E.is_supersingular()
[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE.is_supersingular()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l = EllipticCurve(GF(3), [1, 0])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 0])[?7h[?12l[?25h[?25l[?7l2, 0])[?7h[?12l[?25h[?25l[?7lsage: E = EllipticCurve(GF(3), [2, 0])
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE = EllipticCurve(GF(3), [2, 0])[?7h[?12l[?25h[?25l[?7l.is_supersingular()[?7h[?12l[?25h[?25l[?7lsage: E.is_supersingular()
[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE.is_supersingular()[?7h[?12l[?25h[?25l[?7l = EllipticCurve(GF(3), [2, 0])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l2])[?7h[?12l[?25h[?25l[?7lsage: E = EllipticCurve(GF(3), [2, 2])
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE = EllipticCurve(GF(3), [2, 2])[?7h[?12l[?25h[?25l[?7l.is_supersingular()[?7h[?12l[?25h[?25l[?7lsage: E.is_supersingular()
[?7h[?12l[?25h[?2004l[?7hTrue
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[1, 0, 0, 0, 0, 0]
[0, 1, 0, 0, 0, 0]
[0, 0, 1, 0, 0, 0]
[0, 0, 0, 1, 0, 0]
[0, 0, 0, 0, 1, 0]
[0, 0, 0, 0, 0, 1]
[0 0 0 1 0 0]
[0 0 1 0 0 0]
[0 1 0 0 0 0]
[0 0 0 0 0 0]
[0 0 0 0 0 0]
[1 0 0 0 0 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[5]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[5]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lkronecker_symbol(7, 8)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lel[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(C, prec=50)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: frobenius_
 frobenius_kernel
 frobenius_matrix
 [?7h[?12l[?25h[?25l[?7lmatrix(C, prec=50)[?7h[?12l[?25h[?25l[?7lkernel
 frobenius_kernel
 <unknown> [?7h[?12l[?25h[?25l[?7l


[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [73], in <cell line: 1>()
----> 1 frobenius_kernel(C, prec=Integer(50))
File <string>:89, in frobenius_kernel(C, prec)
File /ext/sage/9.7/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds)
 583 return expression.sum(*args, **kwds)
 584 elif max(len(args),len(kwds)) <= 1:
--> 585 return sum(expression, *args, **kwds)
 586 else:
 587 from sage.symbolic.ring import SR
TypeError: unsupported operand type(s) for +: 'int' and 'superelliptic_function'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[5]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)
[?7h[?12l[?25h[?2004l[?7h[1/x*y^3, 1/x^2*y^3]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)[0].frobenius().coordinates()
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [76], in <cell line: 1>()
----> 1 frobenius_kernel(C, prec=Integer(50))[Integer(0)].frobenius().coordinates()
AttributeError: 'superelliptic_function' object has no attribute 'frobenius'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[5]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[0].frobenius().coordinates()[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)[0].frobenius().coordinates()
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
IndexError Traceback (most recent call last)
Input In [78], in <cell line: 1>()
----> 1 frobenius_kernel(C, prec=Integer(50))[Integer(0)].frobenius().coordinates()
File <string>:48, in coordinates(self, basis, basis_holo, prec)
File <string>:14, in prod(self, form, prec)
File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__()
 542 return type(self)(self._parent, f, self.__n)
 543
--> 544 return self.__u[i - self.__n]
 545
 546 def __iter__(self):
File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__()
 451 return self.base_ring().zero()
 452 else:
--> 453 raise IndexError("coefficient not known")
 454 return self.__f[n]
 455
IndexError: coefficient not known
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[0].frobenius().coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l5)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)[0].frobenius().coordinates(prec=50)
[?7h[?12l[?25h[?2004l[?7h[1, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[0].frobenius().coordinates(prec=50)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)[0].frobenius()
[?7h[?12l[?25h[?2004l[?7h[1/x^3*y^9]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7lsage: M
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [81], in <cell line: 1>()
----> 1 M
NameError: name 'M' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[5]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[0].frobenius()[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)[0].frobenius()
[?7h[?12l[?25h[?2004l[?7h[1/x^6*y^9]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[0].frobenius()[?7h[?12l[?25h[?25l[?7l().coordinates(prec=50)[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ltes(prec=50)[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)[0].frobenius().coordinates(prec=50)
[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq = 5[?7h[?12l[?25h[?25l[?7luadratic_form(parity_quadratic_form(v0, q))[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()
[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l[5]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[0].frobenius().coordinates(prec=50)[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)[0].frobenius().coordinates(prec=50)
[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[0].frobenius().coordinates(prec=50)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)[0]
[?7h[?12l[?25h[?2004l[?7h[1/x^2*y^3]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 + x + 1, 2)[?7h[?12l[?25h[?25l[?7l.gens()[?7h[?12l[?25h[?25l[?7ldx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: C.dx
[?7h[?12l[?25h[?2004l[?7h1 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.dx.cartier()
[?7h[?12l[?25h[?2004l[?7h0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^2+x^4)*y^2*y.diffn()[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.cartier()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty()[1][?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lD[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.x*C.dx).cartier()
[?7h[?12l[?25h[?2004l[?7h0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.dx).cartier()[?7h[?12l[?25h[?25l[?7l.dx).cartier()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lC.dx).cartier()[?7h[?12l[?25h[?25l[?7l.C.dx).cartier()[?7h[?12l[?25h[?25l[?7loC.dx).cartier()[?7h[?12l[?25h[?25l[?7lnC.dx).cartier()[?7h[?12l[?25h[?25l[?7leC.dx).cartier()[?7h[?12l[?25h[?25l[?7l.C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.dx).cartier()[?7h[?12l[?25h[?25l[?7l.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.dx).cartier()[?7h[?12l[?25h[?25l[?7leC.dx).cartier()[?7h[?12l[?25h[?25l[?7l/C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.dx).cartier()[?7h[?12l[?25h[?25l[?7l.C.dx).cartier()[?7h[?12l[?25h[?25l[?7lxC.dx).cartier()[?7h[?12l[?25h[?25l[?7l*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lsage: (C.one/C.x*C.dx).cartier()
[?7h[?12l[?25h[?2004l[?7h0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.one/C.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lrun.term-0.term[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[0][?7h[?12l[?25h[?25l[?7lor i, x in eumerate(lista:[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l i, x in enumerate(lista):[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lsage: for om in C.basis_
 C.basis_de_rham_degrees 
 C.basis_holomorphic_differentials_degree
 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7l
....: [?7h[?12l[?25h[?25l[?7lprint(i, x)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lom.serre_duality_pairing(f))[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()
....: [?7h[?12l[?25h[?25l[?7lsage: for om in C.holomorphic_differentials_basis():
....:  print(om.cartier())
....: 
[?7h[?12l[?25h[?2004l(1/y^3) dx
(x/y^2) dx
(1/y^2) dx
0 dx
0 dx
(1/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for om in C.holomorphic_differentials_basis():
....:  print(om.cartier())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(C.one/C.x*C.dx).carter()
 [?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.one/C.x*C.dx)
[?7h[?12l[?25h[?2004l[?7h(1/x) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.one/C.x*C.dx)[?7h[?12l[?25h[?25l[?7l().cartier()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrtier()[?7h[?12l[?25h[?25l[?7lsage: (C.one/C.x*C.dx).cartier()
[?7h[?12l[?25h[?2004l[?7h0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.cartier()[?7h[?12l[?25h[?25l[?7lsage: C
[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^4 = x^5 + x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.dx.cartier()[?7h[?12l[?25h[?25l[?7lis_smooth()[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_smooth()[?7h[?12l[?25h[?25l[?7lsage: C.is_smooth()
[?7h[?12l[?25h[?2004l[?7h1
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.is_smooth()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.one/C.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l(C.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l()^*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l2*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lsage: ((C.x)^2*C.dx).cartier()
[?7h[?12l[?25h[?2004l[?7h0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x)^2*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l()*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l()*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l.*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lx*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lsage: ((C.x)*C.x*C.dx).cartier()
[?7h[?12l[?25h[?2004l[?7h0 dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq = 5[?7h[?12l[?25h[?25l[?7luadratic_form(parity_quadratic_form(v0, q))[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()
[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd
]0;~~$ cd Research/2021\ De\ Rham/DEReRhamComputation/
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add draft/supsage/drafty/superelliptic_cohomology_class.sage 
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ gid add -u
bash: gid: command not found
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ gid add -u
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