diff --git a/sage/.run.term-0.term b/sage/.run.term-0.term
index c885a45..d659c25 100644
--- a/sage/.run.term-0.term
+++ b/sage/.run.term-0.term
@@ -26877,4 +26877,11773 @@ File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2443
 [?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l = 5[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: p = 3

 [?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp = 3[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l(C.basis_of_cohomology()[0]^p).coordinates()[?7h[?12l[?25h[?25l[?7lsage: (C.basis_of_cohomology()[0]^p).coordinates()

 [?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 1]
-[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq = 5[?7h[?12l[?25h
\ No newline at end of file
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq = 5[?7h[?12l[?25h[?25l[?7luadratic_form(parity_quadratic_form(v0, q))[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

+[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd ..
+]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ cd ..sagegit pushcommit -m "Cohomology of structure sheaf of superelliptic"
add -u
+]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -ucd ..sagegit pushsagecd ..git add -ugit add -ucd ..sagegit pushcommit -m "Cohomology of structure sheaf of superelliptic"
add -ucommit -m "Cohomology of structure sheaf of superelliptic"""""""""""""""""""""""""""""""""""""""""""""""c"o"h"o"m"o"l"o"g"y" "o"f" "s"t"r" "s"h"e"a"f" "d"o"d"a"n"y";" "z"m"i"""a"c"z"y"n"a"m"y" "z"m"i"e"n"i"a"c" "w"s"p"o"l"r"z"e"d"n"e" "w" "s"u"p"e"r"e"l"l"i"p"t"i"c" "h"o"l"o"
+[master f683017] cohomology of str sheaf dodany; zaczynamy zmieniac wspolrzedne w superelliptic holo
+ 5 files changed, 194 insertions(+), 4 deletions(-)
+]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git push
+Username for 'https://git.wmi.amu.edu.pl': jgarnek
+Password for 'https://jgarnek@git.wmi.amu.edu.pl': 
+Enumerating objects: 16, done.
+Counting objects:   6% (1/16)
Counting objects:  12% (2/16)
Counting objects:  18% (3/16)
Counting objects:  25% (4/16)
Counting objects:  31% (5/16)
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Counting objects:  81% (13/16)
Counting objects:  87% (14/16)
Counting objects:  93% (15/16)
Counting objects: 100% (16/16)
Counting objects: 100% (16/16), done.
+Delta compression using up to 8 threads
+Compressing objects:  11% (1/9)
Compressing objects:  22% (2/9)
Compressing objects:  33% (3/9)
Compressing objects:  44% (4/9)
Compressing objects:  55% (5/9)
Compressing objects:  66% (6/9)
Compressing objects:  77% (7/9)
Compressing objects:  88% (8/9)
Compressing objects: 100% (9/9)
Compressing objects: 100% (9/9), done.
+Writing objects:  11% (1/9)
Writing objects:  22% (2/9)
Writing objects:  33% (3/9)
Writing objects:  44% (4/9)
Writing objects:  55% (5/9)
Writing objects:  66% (6/9)
Writing objects:  77% (7/9)
Writing objects:  88% (8/9)
Writing objects: 100% (9/9)
Writing objects: 100% (9/9), 4.68 KiB | 4.68 MiB/s, done.
+Total 9 (delta 7), reused 0 (delta 0)
+remote: . Processing 1 references
+remote: Processed 1 references in total
+To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git
+   be66e7b..f683017  master -> master
+]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ cd sage
+]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd drafty/sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.basis_of_cohomology()[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7llomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis()

+[?7h[?12l[?25h[?2004l[?7h[(1/y) dx, (1/y^2) dx, (x/y^2) dx, (1/y^3) dx, (x/y^3) dx, (x^2/y^3) dx]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbC.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7lbC.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7lbC.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7l C.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7l C.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7lC.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7l=C.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7l C.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: bbb = C.holomorphic_differentials_basis()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3b[1][?7h[?12l[?25h[?25l[?7l*b[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la3*b[1][?7h[?12l[?25h[?25l[?7l 3*b[1][?7h[?12l[?25h[?25l[?7l=3*b[1][?7h[?12l[?25h[?25l[?7l 3*b[1][?7h[?12l[?25h[?25l[?7l3*b[1][?7h[?12l[?25h[?25l[?7l3*b[1][?7h[?12l[?25h[?25l[?7l3*b[1][?7h[?12l[?25h[?25l[?7la3*b[1][?7h[?12l[?25h[?25l[?7la3*b[1][?7h[?12l[?25h[?25l[?7la3*b[1][?7h[?12l[?25h[?25l[?7l 3*b[1][?7h[?12l[?25h[?25l[?7l=3*b[1][?7h[?12l[?25h[?25l[?7l 3*b[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = 3*b[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l ][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*b[1] -[?7h[?12l[?25h[?25l[?7l2*b[1] -[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: aaa = 2*bbb[1] + 2*bbb[2] + bbb[5]

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa = 2*bbb[1] + 2*bbb[2] + bbb[5][?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aaa.coordinates()

+[?7h[?12l[?25h[?2004l[?7h(0, 2, 2, 0, 0, 1)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa.coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l2()[?7h[?12l[?25h[?25l[?7lsage: aaa.coordinates2()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [6], in <cell line: 1>()
+----> 1 aaa.coordinates2()
+
+File <string>:101, in coordinates2(self, basis)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
+    786     return self._call_with_args(x, args, kwds)
+    787 
+--> 788 cpdef Element _call_(self, x):
+    789     """
+    790     Call method with a single argument, not implemented in the base class.
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
+   1249     return num
+   1250 if check and not den.is_unit():
+   1251     # This should probably be a ValueError.
+   1252     # However, too much existing code is expecting this to throw a
+   1253     # TypeError, so we decided to keep it for the time being.
+-> 1254     raise TypeError("fraction must have unit denominator")
+   1255 return num * den.inverse_of_unit()
+
+TypeError: fraction must have unit denominator
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa.coordinates2()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l = 2*bbb[1] + 2*bbb[2] + bbb[5][?7h[?12l[?25h[?25l[?7lbbbC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa.coordinates2()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcoordinates2()[?7h[?12l[?25h[?25l[?7lsage: aaa.coordinates2()

+[?7h[?12l[?25h[?2004lbasis [((x^5 + x)/y^2) dx, ((x^5 + x)/y^3) dx, ((x^6 + x^2)/y^3) dx, 1 dx, x dx, (x^2) dx]
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [8], in <cell line: 1>()
+----> 1 aaa.coordinates2()
+
+File <string>:102, in coordinates2(self, basis)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
+    786     return self._call_with_args(x, args, kwds)
+    787 
+--> 788 cpdef Element _call_(self, x):
+    789     """
+    790     Call method with a single argument, not implemented in the base class.
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
+   1249     return num
+   1250 if check and not den.is_unit():
+   1251     # This should probably be a ValueError.
+   1252     # However, too much existing code is expecting this to throw a
+   1253     # TypeError, so we decided to keep it for the time being.
+-> 1254     raise TypeError("fraction must have unit denominator")
+   1255 return num * den.inverse_of_unit()
+
+TypeError: fraction must have unit denominator
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7laa.coordinates2()[?7h[?12l[?25h[?25l[?7lsage: aaa.coordinates2()

+[?7h[?12l[?25h[?2004lbasis [((x^5 + x)/y^2) dx, ((x^5 + x)/y^3) dx, ((x^6 + x^2)/y^3) dx, 1 dx, x dx, (x^2) dx]
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [10], in <cell line: 1>()
+----> 1 aaa.coordinates2()
+
+File <string>:102, in coordinates2(self, basis)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
+    786     return self._call_with_args(x, args, kwds)
+    787 
+--> 788 cpdef Element _call_(self, x):
+    789     """
+    790     Call method with a single argument, not implemented in the base class.
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
+   1249     return num
+   1250 if check and not den.is_unit():
+   1251     # This should probably be a ValueError.
+   1252     # However, too much existing code is expecting this to throw a
+   1253     # TypeError, so we decided to keep it for the time being.
+-> 1254     raise TypeError("fraction must have unit denominator")
+   1255 return num * den.inverse_of_unit()
+
+TypeError: fraction must have unit denominator
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lsage: bbb

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

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lbbb[?7h[?12l[?25h[?25l[?7laaa.coordinates2()[?7h[?12l[?25h[?25l[?7lsage: aaa.coordinates2()

+[?7h[?12l[?25h[?2004l[(1/y) dx, (1/y^2) dx, (x/y^2) dx, (1/y^3) dx, (x/y^3) dx, (x^2/y^3) dx] [y, y^2, y^2, y^3, y^3, y^3]
+basis [((x^5 + x)/y^2) dx, ((x^5 + x)/y^3) dx, ((x^6 + x^2)/y^3) dx, 1 dx, x dx, (x^2) dx]
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [13], in <cell line: 1>()
+----> 1 aaa.coordinates2()
+
+File <string>:103, in coordinates2(self, basis)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
+    786     return self._call_with_args(x, args, kwds)
+    787 
+--> 788 cpdef Element _call_(self, x):
+    789     """
+    790     Call method with a single argument, not implemented in the base class.
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
+   1249     return num
+   1250 if check and not den.is_unit():
+   1251     # This should probably be a ValueError.
+   1252     # However, too much existing code is expecting this to throw a
+   1253     # TypeError, so we decided to keep it for the time being.
+-> 1254     raise TypeError("fraction must have unit denominator")
+   1255 return num * den.inverse_of_unit()
+
+TypeError: fraction must have unit denominator
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(0, 2, 2, 0, 0, 1)
+[(1/y) dx, (1/y^2) dx, (x/y^2) dx, (1/y^3) dx, (x/y^3) dx, (x^2/y^3) dx] [y, y^2, y^2, y^3, y^3, y^3] y^3
+basis [((x^5 + x)/y^2) dx, ((x^5 + x)/y^3) dx, ((x^6 + x^2)/y^3) dx, 1 dx, x dx, (x^2) dx]
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [14], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:22, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:12, in <module>
+
+File <string>:103, in coordinates2(self, basis)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
+    786     return self._call_with_args(x, args, kwds)
+    787 
+--> 788 cpdef Element _call_(self, x):
+    789     """
+    790     Call method with a single argument, not implemented in the base class.
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
+   1249     return num
+   1250 if check and not den.is_unit():
+   1251     # This should probably be a ValueError.
+   1252     # However, too much existing code is expecting this to throw a
+   1253     # TypeError, so we decided to keep it for the time being.
+-> 1254     raise TypeError("fraction must have unit denominator")
+   1255 return num * den.inverse_of_unit()
+
+TypeError: fraction must have unit denominator
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lsage: bbb

+[?7h[?12l[?25h[?2004l[?7h[(1/y) dx, (1/y^2) dx, (x/y^2) dx, (1/y^3) dx, (x/y^3) dx, (x^2/y^3) dx]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(0, 2, 2, 0, 0, 1)
+[(1/y) dx, (1/y^2) dx, (x/y^2) dx, (1/y^3) dx, (x/y^3) dx, (x^2/y^3) dx] [y, y^2, y^2, y^3, y^3, y^3] y^3
+basis [y^2, y, x*y, 1, x, x^2]
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [16], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:22, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:12, in <module>
+
+File <string>:103, in coordinates2(self, basis)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
+    786     return self._call_with_args(x, args, kwds)
+    787 
+--> 788 cpdef Element _call_(self, x):
+    789     """
+    790     Call method with a single argument, not implemented in the base class.
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
+   1249     return num
+   1250 if check and not den.is_unit():
+   1251     # This should probably be a ValueError.
+   1252     # However, too much existing code is expecting this to throw a
+   1253     # TypeError, so we decided to keep it for the time being.
+-> 1254     raise TypeError("fraction must have unit denominator")
+   1255 return num * den.inverse_of_unit()
+
+TypeError: fraction must have unit denominator
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(0, 2, 2, 0, 0, 1)
+[(1/y) dx, (1/y^2) dx, (x/y^2) dx, (1/y^3) dx, (x/y^3) dx, (x^2/y^3) dx] [y, y^2, y^2, y^3, y^3, y^3] y^3
+basis [y^2, y, x*y, 1, x, x^2]
+[0, 2, 2, 0, 0, 1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(0, 2, 2, 0, 0, 1)
+[(1/y) dx, (1/y^2) dx, (x/y^2) dx, (1/y^3) dx, (x/y^3) dx, (x^2/y^3) dx] [y, y^2, y^2, y^3, y^3, y^3] y^3
+basis [y^2, y, x*y, 1, x, x^2]
+[0, 2, 2, 0, 0, 1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7lt.sage')[?7h[?12l[?25h[?25l[?7le.sage')[?7h[?12l[?25h[?25l[?7ls.sage')[?7h[?12l[?25h[?25l[?7lt.sage')[?7h[?12l[?25h[?25l[?7ls.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

+[?7h[?12l[?25h[?2004lsuperelliptic form coordinates test:
+[(1/y) dx, (1/y^2) dx, (x/y^2) dx, (1/y^3) dx, (x/y^3) dx, (x^2/y^3) dx] [y, y^2, y^2, y^3, y^3, y^3] y^3
+basis [y^2, y, x*y, 1, x, x^2]
+False
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

+[?7h[?12l[?25h[?2004lsuperelliptic form coordinates test:
+[(1/y) dx, (1/y^2) dx, (x/y^2) dx, (1/y^3) dx, (x/y^3) dx, (x^2/y^3) dx] [y, y^2, y^2, y^3, y^3, y^3] y^3
+basis [y^2, y, x*y, 1, x, x^2]
+False
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

+[?7h[?12l[?25h[?2004lsuperelliptic form coordinates test:
+[(1/y) dx, (1/y^2) dx, (x/y^2) dx, (1/y^3) dx, (x/y^3) dx, (x^2/y^3) dx] [y, y^2, y^2, y^3, y^3, y^3] y^3
+basis [y^2, y, x*y, 1, x, x^2]
+True
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('tests.sage')[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7li.sage')[?7h[?12l[?25h[?25l[?7ln.sage')[?7h[?12l[?25h[?25l[?7li.sage')[?7h[?12l[?25h[?25l[?7lt.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[0, 2, 2, 0, 0, 1]
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [22], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:22, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:12, in <module>
+
+AttributeError: 'superelliptic_form' object has no attribute 'coordinates2'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7lt.sage')[?7h[?12l[?25h[?25l[?7le.sage')[?7h[?12l[?25h[?25l[?7ls.sage')[?7h[?12l[?25h[?25l[?7lt.sage')[?7h[?12l[?25h[?25l[?7ls.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

+[?7h[?12l[?25h[?2004lsuperelliptic form coordinates test:
+True
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^4 = x^5 + x over Finite Field of size 7
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7ldx.cartier()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxC.dx[?7h[?12l[?25h[?25l[?7l^C.dx[?7h[?12l[?25h[?25l[?7l(C.dx[?7h[?12l[?25h[?25l[?7l()C.dx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)C.dx[?7h[?12l[?25h[?25l[?7l-)C.dx[?7h[?12l[?25h[?25l[?7l1)C.dx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()*C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^(p-1)*C.dx[?7h[?12l[?25h[?25l[?7l.x^(p-1)*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfC.x^(p-1)*C.dx[?7h[?12l[?25h[?25l[?7lfC.x^(p-1)*C.dx[?7h[?12l[?25h[?25l[?7lfC.x^(p-1)*C.dx[?7h[?12l[?25h[?25l[?7lfC.x^(p-1)*C.dx[?7h[?12l[?25h[?25l[?7l C.x^(p-1)*C.dx[?7h[?12l[?25h[?25l[?7l=C.x^(p-1)*C.dx[?7h[?12l[?25h[?25l[?7l C.x^(p-1)*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ffff = C.x^(p-1)*C.dx

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lffff = C.x^(p-1)*C.dx[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: ffff

+[?7h[?12l[?25h[?2004l[?7h(x^6) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lffff[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ffff.cartier()

+[?7h[?12l[?25h[?2004l[?7h0 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lffff.cartier()[?7h[?12l[?25h[?25l[?7lor om in C.holomorphic_differentials_basis():[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li,x in enumerate(lista):[?7h[?12l[?25h[?25l[?7l inrange(0, p):[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7linr[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l range(0, p):[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lrange[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: for i in range(0, p^2):

+....: [?7h[?12l[?25h[?25l[?7lfor B in range(-10, 30):[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l....:     ffff = (C.x)^i*C.dx

+....: [?7h[?12l[?25h[?25l[?7lprint(om.cartier())[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:     print(ffff.cartier())

+....: [?7h[?12l[?25h[?25l[?7lsage: for i in range(0, p^2):

+....:     ffff = (C.x)^i*C.dx

+....:     print(ffff.cartier())

+....: 

+[?7h[?12l[?25h[?2004l0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+0 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7li.sage')[?7h[?12l[?25h[?25l[?7ln.sage')[?7h[?12l[?25h[?25l[?7li.sage')[?7h[?12l[?25h[?25l[?7lt.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lTraceback (most recent call last):
+
+  File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
+    exec(code_obj, self.user_global_ns, self.user_ns)
+
+  Input In [29] in <cell line: 1>
+    load('init.sage')
+
+  File sage/misc/persist.pyx:175 in sage.misc.persist.load
+    sage.repl.load.load(filename, globals())
+
+  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
+    exec(preparse_file(f.read()) + "\n", globals)
+
+  File <string>:22 in <module>
+
+  File sage/misc/persist.pyx:175 in sage.misc.persist.load
+    sage.repl.load.load(filename, globals())
+
+  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
+    exec(preparse_file(f.read()) + "\n", globals)
+
+  File <string>:9
+    a = C.x**(p-_sage_const_1 )C.dx
+                               ^
+SyntaxError: invalid syntax
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0 0
+0 0
+0 0
+0 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lx^2 1
+0 0
+0 0
+0 0
+1 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa.coordinates2()[?7h[?12l[?25h[?25l[?7l.prod(C.holomorphic_differentials_basis()[3])[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a.cartier()

+[?7h[?12l[?25h[?2004lx^2 1
+0 0
+0 0
+0 0
+[?7h1 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.cartier()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l1 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la.cartier()[?7h[?12l[?25h[?25l[?7lsage: a.cartier()

+[?7h[?12l[?25h[?2004l[?7h1 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.cartier()[?7h[?12l[?25h[?25l[?7l = basis_of_cohomology(C)[0][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.cartier()[?7h[?12l[?25h[?25l[?7l = basis_of_cohomology(C)[0][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: a = C.dx

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = C.dx[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: a/C.x

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [36], in <cell line: 1>()
+----> 1 a/C.x
+
+TypeError: unsupported operand type(s) for /: 'superelliptic_form' and 'superelliptic_function'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la/C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in range(0, p^2):[?7h[?12l[?25h[?25l[?7l =d/(e*g)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l1.[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f = superelliptic_function(C, 1/x)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = superelliptic_function(C, 1/x)[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: f*C.dx

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

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [39], in <cell line: 1>()
+----> 1 (f*C.dx).cartier()
+
+File <string>:52, in cartier(self)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1331, in sage.rings.fraction_field_FpT.FpT_Polyring_section._call_()
+   1329     normalize(x._numer, x._denom, self.p)
+   1330     if nmod_poly_degree(x._denom) != 0:
+-> 1331         raise ValueError("not integral")
+   1332 ans = Polynomial_zmod_flint.__new__(Polynomial_zmod_flint)
+   1333 if nmod_poly_get_coeff_ui(x._denom, 0) != 1:
+
+ValueError: not integral
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l1 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(f*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lf*C.dx[?7h[?12l[?25h[?25l[?7l = superelliptic_function(C, 1/x)[?7h[?12l[?25h[?25l[?7la/C.x[?7h[?12l[?25h[?25l[?7lf = superelliptic_function(C, 1/x)[?7h[?12l[?25h[?25l[?7lsage: f = superelliptic_function(C, 1/x)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = superelliptic_function(C, 1/x)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(f*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lsage: (f*C.dx).cartier()

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

+[?7h[?12l[?25h[?2004l0 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0 dx
+1 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(1/x) dx
+1 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llist_of_m = [m for m in list_of_m if m%p != 0][?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(1/x) dx
+1 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^4 = x^5 + x over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix(prec=50)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [3], in <cell line: 1>()
+----> 1 C.frobenius_matrix(prec=Integer(50))
+
+File <string>:164, in frobenius_matrix(self, prec)
+
+File <string>:90, in coordinates(self, basis, basis_holo, prec)
+
+NameError: name 'basis_of_cohomology' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lbasis_of_cohomology()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lis_of_cohomology()[?7h[?12l[?25h[?25l[?7lsage: C.basis_of_cohomology()

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

+[?7h[?12l[?25h[?2004l(1/x) dx
+1 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.basis_of_cohomology()[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix(prec=50)

+[?7h[?12l[?25h[?2004l[?7h[0 0 0 1 0 0]
+[0 0 1 0 0 0]
+[0 1 0 0 0 0]
+[0 0 0 0 0 0]
+[0 0 0 0 0 0]
+[1 0 0 0 0 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lj[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lkronecker_symbol(7, 8)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = superelliptic_function(C, 1/x)[?7h[?12l[?25h[?25l[?7lrobenius_kernel(C, prec=50)[0][?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lenius_kernel(C, prec=50)[0][?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)[0]

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [7], in <cell line: 1>()
+----> 1 frobenius_kernel(C, prec=Integer(50))[Integer(0)]
+
+File <string>:3, in frobenius_kernel(C, prec)
+
+NameError: name 'frobenius_matrix' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(1/x) dx
+1 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[0][?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)[0]

+[?7h[?12l[?25h[?2004l[?7h1/x*y^3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)

+[?7h[?12l[?25h[?2004l[?7h[1/x*y^3, 1/x^2*y^3]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: bbb = C.holomorphic_differentials_basis()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: bbb[0].cartier()

+[?7h[?12l[?25h[?2004l[?7h(1/y^3) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcartier_matrix()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrtier_matrix()[?7h[?12l[?25h[?25l[?7lsage: C.cartier_matrix()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+IndexError                                Traceback (most recent call last)
+Input In [13], in <cell line: 1>()
+----> 1 C.cartier_matrix()
+
+File <string>:155, in cartier_matrix(self)
+
+File /ext/sage/9.7/src/sage/matrix/matrix0.pyx:1507, in sage.matrix.matrix0.Matrix.__setitem__()
+   1505 else:
+   1506     if row_list_len != len(value_list):
+-> 1507         raise IndexError("value does not have the right number of rows")
+   1508     for value_row in value_list:
+   1509         if col_list_len != len(value_row):
+
+IndexError: value does not have the right number of rows
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cartier_matrix()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(1/x) dx
+1 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cartier_matrix()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrtier_matrix()[?7h[?12l[?25h[?25l[?7lsage: C.cartier_matrix()

+[?7h[?12l[?25h[?2004l[?7h[0 0 0 1 0 0]
+[0 0 1 0 0 0]
+[0 1 0 0 0 0]
+[0 0 0 0 0 0]
+[0 0 0 0 0 0]
+[1 0 0 0 0 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[0].cartier()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: bbb = C.holomorphic_differentials_basis()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[0].cartier()[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l].cartier()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l(*)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: bbb[0].cartier().coordinates()

+[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 1, 0, 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(1/x) dx
+1 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cartier_matrix()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcartier_matrix()[?7h[?12l[?25h[?25l[?7lsage: C.cartier_matrix()

+[?7h[?12l[?25h[?2004l[?7h[0 0 0 0 0 1]
+[0 0 1 0 0 0]
+[0 1 0 0 0 0]
+[1 0 0 0 0 0]
+[0 0 0 0 0 0]
+[0 0 0 0 0 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cartier_matrix()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lbbb[0].cartier().coordinates()[?7h[?12l[?25h[?25l[?7l = C.holomorphic_differntials_basis()[?7h[?12l[?25h[?25l[?7lsage: bbb = C.holomorphic_differentials_basis()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb = C.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lC.cartier_matrix()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lbbb[0].cartier().coordinates()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: bbb[0].cartier().coordinates()

+[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 1, 0, 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[0].cartier().coordinates()[?7h[?12l[?25h[?25l[?7l = C.holomorphic_differntials_basis()[?7h[?12l[?25h[?25l[?7l[0].cartier().coordinats()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l].cartier().cordinates()[?7h[?12l[?25h[?25l[?7l1].cartier().cordinates()[?7h[?12l[?25h[?25l[?7lsage: bbb[1].cartier().coordinates()

+[?7h[?12l[?25h[?2004l[?7h[0, 0, 1, 0, 0, 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[1].cartier().coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l].cartier().cordinates()[?7h[?12l[?25h[?25l[?7l5].cartier().cordinates()[?7h[?12l[?25h[?25l[?7lsage: bbb[5].cartier().coordinates()

+[?7h[?12l[?25h[?2004l[?7h[1, 0, 0, 0, 0, 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [24], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:23, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:10, in <module>
+
+File <string>:137, in pth_root(self)
+
+AttributeError: 'superelliptic_form' object has no attribute 'function'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l2*x^2*y^3 + x^5*y^2
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l2*x^2*y^3 + x^5*y^2 2*x^2*y^3 + x^5*y^2
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cartier_matrix()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)^p[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.x).pth_root()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [27], in <cell line: 1>()
+----> 1 (C.x).pth_root()
+
+File <string>:132, in pth_root(self)
+
+ValueError: Function is not a p-th power.
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lFalse
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [28], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:23, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:12, in <module>
+
+File <string>:134, in pth_root(self)
+
+ValueError: Function is not a p-th power.
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lTrue
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [29], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:23, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:12, in <module>
+
+File <string>:139, in pth_root(self)
+
+ValueError: Function is not a p-th power.
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ltess.sage')[?7h[?12l[?25h[?25l[?7l(ests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

+[?7h[?12l[?25h[?2004lp-th root test:
+True
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [30], in <cell line: 1>()
+----> 1 load('tests.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:4, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:12, in <module>
+
+File <string>:139, in pth_root(self)
+
+ValueError: Function is not a p-th power.
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cartier_matrix()[?7h[?12l[?25h[?25l[?7lsage: C

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^4 = x^5 + x over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.cartier_matrix()[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lkronecker_symbol(7, 8)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lnel[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lobenius_kernel(C, prec=50)[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)

+[?7h[?12l[?25h[?2004l[?7h[1/x*y^3, 1/x^2*y^3]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[?7h[?12l[?25h[?25l[?7l()[0][?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)[0]

+[?7h[?12l[?25h[?2004l[?7h1/x*y^3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la/C.x[?7h[?12l[?25h[?25l[?7laacoordinates2()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = 2*bbb[1] + 2*bbb[2] + bbb[5][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lnius_kernel[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: aaa = frobenius_kernel(C)[0]

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa = frobenius_kernel(C)[0][?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lsage: aaa^p

+[?7h[?12l[?25h[?2004l[?7h((x^8 + 2*x^4 + 1)/x)*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[5].cartier().coordinates()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l = C.holomorphic_differntials_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l%[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lsage: bbb = aaa^p

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb = aaa^p[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsage: bbb.function

+[?7h[?12l[?25h[?2004l[?7h((x^8 + 2*x^4 + 1)/x)*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb.function[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcb.function[?7h[?12l[?25h[?25l[?7lcb.function[?7h[?12l[?25h[?25l[?7lcb.function[?7h[?12l[?25h[?25l[?7l b.function[?7h[?12l[?25h[?25l[?7l-b.function[?7h[?12l[?25h[?25l[?7l b.function[?7h[?12l[?25h[?25l[?7lsage: ccc - bbb.function

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [38], in <cell line: 1>()
+----> 1 ccc - bbb.function
+
+NameError: name 'ccc' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lccc - bbb.function[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l b.function[?7h[?12l[?25h[?25l[?7l= b.function[?7h[?12l[?25h[?25l[?7lsage: ccc = bbb.function

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lccc = bbb.function[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lnc[?7h[?12l[?25h[?25l[?7luc[?7h[?12l[?25h[?25l[?7lmc[?7h[?12l[?25h[?25l[?7lec[?7h[?12l[?25h[?25l[?7lrc[?7h[?12l[?25h[?25l[?7lac[?7h[?12l[?25h[?25l[?7ltc[?7h[?12l[?25h[?25l[?7loc[?7h[?12l[?25h[?25l[?7lrc[?7h[?12l[?25h[?25l[?7l(c[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: numerator(ccc)

+[?7h[?12l[?25h[?2004l[?7h(x^8 + 2*x^4 + 1)*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmm.f[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: monomials(ccc)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [41], in <cell line: 1>()
+----> 1 monomials(ccc)
+
+TypeError: monomials() missing 1 required positional argument: 'n'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmonomials(ccc)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcmonomials()[?7h[?12l[?25h[?25l[?7lcmonomials()[?7h[?12l[?25h[?25l[?7lcmonomials()[?7h[?12l[?25h[?25l[?7l.monomials()[?7h[?12l[?25h[?25l[?7lsage: ccc.monomials()

+[?7h[?12l[?25h[?2004l[?7h[y]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lccc.monomials()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpc[?7h[?12l[?25h[?25l[?7lac[?7h[?12l[?25h[?25l[?7lrc[?7h[?12l[?25h[?25l[?7lec[?7h[?12l[?25h[?25l[?7lnc[?7h[?12l[?25h[?25l[?7ltc[?7h[?12l[?25h[?25l[?7l(c[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: parent(ccc)

+[?7h[?12l[?25h[?2004l[?7hUnivariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFF = FractionField(F)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: Fxy

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [44], in <cell line: 1>()
+----> 1 Fxy
+
+NameError: name 'Fxy' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y = self.fct_field[?7h[?12l[?25h[?25l[?7lsage: Fxy, Rxy, x, y = self.fct_field

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [45], in <cell line: 1>()
+----> 1 Fxy, Rxy, x, y = self.fct_field
+
+NameError: name 'self' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y = self.fct_field[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsel.fct_field[?7h[?12l[?25h[?25l[?7l.fct_field[?7h[?12l[?25h[?25l[?7l.fct_field[?7h[?12l[?25h[?25l[?7l.fct_field[?7h[?12l[?25h[?25l[?7lC.fct_field[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: Fxy, Rxy, x, y = C.fct_field

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y = C.fct_field[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: Fxy

+[?7h[?12l[?25h[?2004l[?7hFraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7lini.sage')[?7h[?12l[?25h[?25l[?7l(nit.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [48], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:23, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:30, in <module>
+
+File <string>:13, in decomposition_g0_g8(fct)
+
+AttributeError: 'list' object has no attribute 'curve'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[((x^8 + 2*x^4 + 1)/x)*y, ((x^8 + 2*x^4 + 1)/x^4)*y]
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [49], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:23, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:31, in <module>
+
+File <string>:14, in decomposition_g0_g8(fct)
+
+AttributeError: 'list' object has no attribute 'curve'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lkronecker_symbol(7, 8)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lsage: ker

+[?7h[?12l[?25h[?2004l[?7h[1/x*y^3, 1/x^2*y^3]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa^p[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: aaa

+[?7h[?12l[?25h[?2004l[?7h[((x^8 + 2*x^4 + 1)/x)*y, ((x^8 + 2*x^4 + 1)/x^4)*y]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: aaa

+[?7h[?12l[?25h[?2004l[?7h[((x^8 + 2*x^4 + 1)/x)*y, ((x^8 + 2*x^4 + 1)/x^4)*y]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lker[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]^[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lsage: ker[0]^p

+[?7h[?12l[?25h[?2004l[?7h((x^8 + 2*x^4 + 1)/x)*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l((x^8 + 2*x^4 + 1)/x)*y
+---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [54], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:23, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:31, in <module>
+
+File <string>:15, in decomposition_g0_g8(fct)
+
+NameError: name 'self' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l((x^8 + 2*x^4 + 1)/x)*y
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce)
+    705 try:
+--> 706     x, y = resolve_fractions(x0, y0)
+    707 except (AttributeError, TypeError):
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:683, in FractionField_generic._element_constructor_.<locals>.resolve_fractions(x, y)
+    682 def resolve_fractions(x, y):
+--> 683     xn = x.numerator()
+    684     xd = x.denominator()
+
+AttributeError: 'function' object has no attribute 'numerator'
+
+During handling of the above exception, another exception occurred:
+
+TypeError                                 Traceback (most recent call last)
+Input In [55], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:23, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:31, in <module>
+
+File <string>:19, in decomposition_g0_g8(fct)
+
+File <string>:14, in __init__(self, C, g)
+
+File <string>:209, in reduction(C, g)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    159             print(type(C), C)
+    160             print(type(C._element_constructor), C._element_constructor)
+--> 161         raise
+    162 
+    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:708, in FractionField_generic._element_constructor_(self, x, y, coerce)
+    706     x, y = resolve_fractions(x0, y0)
+    707 except (AttributeError, TypeError):
+--> 708     raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
+    709                     x0, y0, self))
+    710 try:
+    711     return self._element_class(self, x, y, coerce=coerce)
+
+TypeError: cannot convert <function denominator at 0x7f0bd4ee8820>/1 to an element of Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l! (x^8*y - x^4*y + y)/x
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce)
+    705 try:
+--> 706     x, y = resolve_fractions(x0, y0)
+    707 except (AttributeError, TypeError):
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:683, in FractionField_generic._element_constructor_.<locals>.resolve_fractions(x, y)
+    682 def resolve_fractions(x, y):
+--> 683     xn = x.numerator()
+    684     xd = x.denominator()
+
+AttributeError: 'function' object has no attribute 'numerator'
+
+During handling of the above exception, another exception occurred:
+
+TypeError                                 Traceback (most recent call last)
+Input In [56], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:23, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:31, in <module>
+
+File <string>:19, in decomposition_g0_g8(fct)
+
+File <string>:14, in __init__(self, C, g)
+
+File <string>:209, in reduction(C, g)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    159             print(type(C), C)
+    160             print(type(C._element_constructor), C._element_constructor)
+--> 161         raise
+    162 
+    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:708, in FractionField_generic._element_constructor_(self, x, y, coerce)
+    706     x, y = resolve_fractions(x0, y0)
+    707 except (AttributeError, TypeError):
+--> 708     raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
+    709                     x0, y0, self))
+    710 try:
+    711     return self._element_class(self, x, y, coerce=coerce)
+
+TypeError: cannot convert <function denominator at 0x7f0bd4ee8820>/1 to an element of Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: aaa

+[?7h[?12l[?25h[?2004l[?7h[((x^8 + 2*x^4 + 1)/x)*y, ((x^8 + 2*x^4 + 1)/x^4)*y]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsage: aaa[0].function

+[?7h[?12l[?25h[?2004l[?7h((x^8 + 2*x^4 + 1)/x)*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[0].function[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lna[0].function[?7h[?12l[?25h[?25l[?7lua[0].function[?7h[?12l[?25h[?25l[?7lma[0].function[?7h[?12l[?25h[?25l[?7lea[0].function[?7h[?12l[?25h[?25l[?7lra[0].function[?7h[?12l[?25h[?25l[?7la[0].function[?7h[?12l[?25h[?25l[?7lta[0].function[?7h[?12l[?25h[?25l[?7loa[0].function[?7h[?12l[?25h[?25l[?7lra[0].function[?7h[?12l[?25h[?25l[?7l(a[0].function[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: numerator(aaa[0].function)

+[?7h[?12l[?25h[?2004l[?7h(x^8 + 2*x^4 + 1)*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[0].function[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpa[0][?7h[?12l[?25h[?25l[?7la[0][?7h[?12l[?25h[?25l[?7lra[0][?7h[?12l[?25h[?25l[?7lea[0][?7h[?12l[?25h[?25l[?7lna[0][?7h[?12l[?25h[?25l[?7lta[0][?7h[?12l[?25h[?25l[?7l(a[0][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: parent(aaa[0])

+[?7h[?12l[?25h[?2004l[?7h<class '__main__.superelliptic_function'>
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(aaa[0])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7lsage: parent(aaa[0].function)

+[?7h[?12l[?25h[?2004l[?7hUnivariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[0].function[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0].function[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lna[0][?7h[?12l[?25h[?25l[?7lua[0][?7h[?12l[?25h[?25l[?7lma[0][?7h[?12l[?25h[?25l[?7lea[0][?7h[?12l[?25h[?25l[?7lra[0][?7h[?12l[?25h[?25l[?7la[0][?7h[?12l[?25h[?25l[?7lta[0][?7h[?12l[?25h[?25l[?7loa[0][?7h[?12l[?25h[?25l[?7lra[0][?7h[?12l[?25h[?25l[?7l(a[0][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a[0][?7h[?12l[?25h[?25l[?7l(a[0][?7h[?12l[?25h[?25l[?7l(a[0][?7h[?12l[?25h[?25l[?7l(a[0][?7h[?12l[?25h[?25l[?7l(a[0][?7h[?12l[?25h[?25l[?7l(a[0][?7h[?12l[?25h[?25l[?7l(a[0][?7h[?12l[?25h[?25l[?7l(a[0][?7h[?12l[?25h[?25l[?7l(a[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lF(a[0][?7h[?12l[?25h[?25l[?7lx(a[0][?7h[?12l[?25h[?25l[?7ly(a[0][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: Fxy(aaa[0])

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce)
+    705 try:
+--> 706     x, y = resolve_fractions(x0, y0)
+    707 except (AttributeError, TypeError):
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:683, in FractionField_generic._element_constructor_.<locals>.resolve_fractions(x, y)
+    682 def resolve_fractions(x, y):
+--> 683     xn = x.numerator()
+    684     xd = x.denominator()
+
+AttributeError: 'superelliptic_function' object has no attribute 'numerator'
+
+During handling of the above exception, another exception occurred:
+
+TypeError                                 Traceback (most recent call last)
+Input In [62], in <cell line: 1>()
+----> 1 Fxy(aaa[Integer(0)])
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    159             print(type(C), C)
+    160             print(type(C._element_constructor), C._element_constructor)
+--> 161         raise
+    162 
+    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:708, in FractionField_generic._element_constructor_(self, x, y, coerce)
+    706     x, y = resolve_fractions(x0, y0)
+    707 except (AttributeError, TypeError):
+--> 708     raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
+    709                     x0, y0, self))
+    710 try:
+    711     return self._element_class(self, x, y, coerce=coerce)
+
+TypeError: cannot convert ((x^8 + 2*x^4 + 1)/x)*y/1 to an element of Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy(aaa[0])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7lsage: Fxy(aaa[0].function)

+[?7h[?12l[?25h[?2004l[?7h(x^8*y - x^4*y + y)/x
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy(aaa[0].function)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: Fxy(aaa[0].function).denominator()

+[?7h[?12l[?25h[?2004l[?7hx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy(aaa[0].function).denominator()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l! (x^8*y - x^4*y + y)/x
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce)
+    705 try:
+--> 706     x, y = resolve_fractions(x0, y0)
+    707 except (AttributeError, TypeError):
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:683, in FractionField_generic._element_constructor_.<locals>.resolve_fractions(x, y)
+    682 def resolve_fractions(x, y):
+--> 683     xn = x.numerator()
+    684     xd = x.denominator()
+
+AttributeError: 'function' object has no attribute 'numerator'
+
+During handling of the above exception, another exception occurred:
+
+TypeError                                 Traceback (most recent call last)
+Input In [65], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:23, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:31, in <module>
+
+File <string>:19, in decomposition_g0_g8(fct)
+
+File <string>:14, in __init__(self, C, g)
+
+File <string>:209, in reduction(C, g)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    159             print(type(C), C)
+    160             print(type(C._element_constructor), C._element_constructor)
+--> 161         raise
+    162 
+    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:708, in FractionField_generic._element_constructor_(self, x, y, coerce)
+    706     x, y = resolve_fractions(x0, y0)
+    707 except (AttributeError, TypeError):
+--> 708     raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
+    709                     x0, y0, self))
+    710 try:
+    711     return self._element_class(self, x, y, coerce=coerce)
+
+TypeError: cannot convert <function denominator at 0x7f0bd4ee8820>/1 to an element of Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l! (x^8*y - x^4*y + y)/x
+x^8*y - x^4*y + y x
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce)
+    705 try:
+--> 706     x, y = resolve_fractions(x0, y0)
+    707 except (AttributeError, TypeError):
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:683, in FractionField_generic._element_constructor_.<locals>.resolve_fractions(x, y)
+    682 def resolve_fractions(x, y):
+--> 683     xn = x.numerator()
+    684     xd = x.denominator()
+
+AttributeError: 'function' object has no attribute 'numerator'
+
+During handling of the above exception, another exception occurred:
+
+TypeError                                 Traceback (most recent call last)
+Input In [66], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:23, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:32, in <module>
+
+File <string>:20, in decomposition_g0_g8(fct)
+
+File <string>:14, in __init__(self, C, g)
+
+File <string>:209, in reduction(C, g)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    159             print(type(C), C)
+    160             print(type(C._element_constructor), C._element_constructor)
+--> 161         raise
+    162 
+    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:708, in FractionField_generic._element_constructor_(self, x, y, coerce)
+    706     x, y = resolve_fractions(x0, y0)
+    707 except (AttributeError, TypeError):
+--> 708     raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
+    709                     x0, y0, self))
+    710 try:
+    711     return self._element_class(self, x, y, coerce=coerce)
+
+TypeError: cannot convert <function denominator at 0x7f0bd4ee8820>/1 to an element of Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l! (x^8*y - x^4*y + y)/x
+x^8*y - x^4*y + y x
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1009, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
+   1008 # now try calling the base ring's __call__ methods
+-> 1009 element = self.base_ring()(element)
+   1010 _p = p_NSet(sa2si(element,_ring), _ring)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    896 if no_extra_args:
+--> 897     return mor._call_(x)
+    898 else:
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    160     print(type(C._element_constructor), C._element_constructor)
+--> 161 raise
+    162 
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+
+File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x)
+   1184 try:
+-> 1185     return integer_mod.IntegerMod(self, x)
+   1186 except (NotImplementedError, PariError):
+
+File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod()
+    200 t = modulus.element_class()
+--> 201 return t(parent, value)
+    202 
+
+File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:391, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
+    390         else:
+--> 391             raise
+    392 self.set_from_mpz(z.value)
+
+File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:380, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
+    379 try:
+--> 380     z = integer_ring.Z(value)
+    381 except (TypeError, ValueError):
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    896 if no_extra_args:
+--> 897     return mor._call_(x)
+    898 else:
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    160     print(type(C._element_constructor), C._element_constructor)
+--> 161 raise
+    162 
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+
+File /ext/sage/9.7/src/sage/rings/integer.pyx:717, in sage.rings.integer.Integer.__init__()
+    716 
+--> 717                 raise TypeError("unable to coerce %s to an integer" % type(x))
+    718 
+
+TypeError: unable to coerce <class 'function'> to an integer
+
+During handling of the above exception, another exception occurred:
+
+TypeError                                 Traceback (most recent call last)
+Input In [67], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:23, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:32, in <module>
+
+File <string>:20, in decomposition_g0_g8(fct)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    159             print(type(C), C)
+    160             print(type(C._element_constructor), C._element_constructor)
+--> 161         raise
+    162 
+    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1013, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
+   1011         return new_MP(self,_p)
+   1012     except (TypeError, ValueError):
+-> 1013         raise TypeError("Could not find a mapping of the passed element to this ring.")
+   1014 
+   1015 def _repr_(self):
+
+TypeError: Could not find a mapping of the passed element to this ring.
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l! (x^8*y - x^4*y + y)/x
+x^8*y - x^4*y + y x
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1009, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
+   1008 # now try calling the base ring's __call__ methods
+-> 1009 element = self.base_ring()(element)
+   1010 _p = p_NSet(sa2si(element,_ring), _ring)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    896 if no_extra_args:
+--> 897     return mor._call_(x)
+    898 else:
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    160     print(type(C._element_constructor), C._element_constructor)
+--> 161 raise
+    162 
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+
+File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x)
+   1184 try:
+-> 1185     return integer_mod.IntegerMod(self, x)
+   1186 except (NotImplementedError, PariError):
+
+File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod()
+    200 t = modulus.element_class()
+--> 201 return t(parent, value)
+    202 
+
+File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:391, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
+    390         else:
+--> 391             raise
+    392 self.set_from_mpz(z.value)
+
+File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:380, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
+    379 try:
+--> 380     z = integer_ring.Z(value)
+    381 except (TypeError, ValueError):
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    896 if no_extra_args:
+--> 897     return mor._call_(x)
+    898 else:
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    160     print(type(C._element_constructor), C._element_constructor)
+--> 161 raise
+    162 
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+
+File /ext/sage/9.7/src/sage/rings/integer.pyx:717, in sage.rings.integer.Integer.__init__()
+    716 
+--> 717                 raise TypeError("unable to coerce %s to an integer" % type(x))
+    718 
+
+TypeError: unable to coerce <class 'function'> to an integer
+
+During handling of the above exception, another exception occurred:
+
+TypeError                                 Traceback (most recent call last)
+Input In [68], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:23, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:33, in <module>
+
+File <string>:20, in decomposition_g0_g8(fct)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    159             print(type(C), C)
+    160             print(type(C._element_constructor), C._element_constructor)
+--> 161         raise
+    162 
+    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1013, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
+   1011         return new_MP(self,_p)
+   1012     except (TypeError, ValueError):
+-> 1013         raise TypeError("Could not find a mapping of the passed element to this ring.")
+   1014 
+   1015 def _repr_(self):
+
+TypeError: Could not find a mapping of the passed element to this ring.
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l! (x^8*y - x^4*y + y)/x
+x^8*y - x^4*y + y x Multivariate Polynomial Ring in x, y over Finite Field of size 3 <class 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular'>
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1009, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
+   1008 # now try calling the base ring's __call__ methods
+-> 1009 element = self.base_ring()(element)
+   1010 _p = p_NSet(sa2si(element,_ring), _ring)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    896 if no_extra_args:
+--> 897     return mor._call_(x)
+    898 else:
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    160     print(type(C._element_constructor), C._element_constructor)
+--> 161 raise
+    162 
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+
+File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x)
+   1184 try:
+-> 1185     return integer_mod.IntegerMod(self, x)
+   1186 except (NotImplementedError, PariError):
+
+File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod()
+    200 t = modulus.element_class()
+--> 201 return t(parent, value)
+    202 
+
+File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:391, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
+    390         else:
+--> 391             raise
+    392 self.set_from_mpz(z.value)
+
+File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:380, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
+    379 try:
+--> 380     z = integer_ring.Z(value)
+    381 except (TypeError, ValueError):
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    896 if no_extra_args:
+--> 897     return mor._call_(x)
+    898 else:
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    160     print(type(C._element_constructor), C._element_constructor)
+--> 161 raise
+    162 
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+
+File /ext/sage/9.7/src/sage/rings/integer.pyx:717, in sage.rings.integer.Integer.__init__()
+    716 
+--> 717                 raise TypeError("unable to coerce %s to an integer" % type(x))
+    718 
+
+TypeError: unable to coerce <class 'function'> to an integer
+
+During handling of the above exception, another exception occurred:
+
+TypeError                                 Traceback (most recent call last)
+Input In [69], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:23, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:33, in <module>
+
+File <string>:20, in decomposition_g0_g8(fct)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    159             print(type(C), C)
+    160             print(type(C._element_constructor), C._element_constructor)
+--> 161         raise
+    162 
+    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1013, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
+   1011         return new_MP(self,_p)
+   1012     except (TypeError, ValueError):
+-> 1013         raise TypeError("Could not find a mapping of the passed element to this ring.")
+   1014 
+   1015 def _repr_(self):
+
+TypeError: Could not find a mapping of the passed element to this ring.
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l((x^8 + 2*x^4 + 1)*y, 0)
+((x^8 + 2*x^4)*y, y)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(((x^8 + 2*x^4 + 1)/x)*y, 0)
+((x^4 + 2)*y, 1/x^4*y)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.cartier_matrix()[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lX[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.y/C.x).coordinates()

+[?7h[?12l[?25h[?2004l[?7h[1, 0, 0, 0, 0, 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[0].function[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: aaa

+[?7h[?12l[?25h[?2004l[?7h[((x^8 + 2*x^4 + 1)/x)*y, ((x^8 + 2*x^4 + 1)/x^4)*y]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[0].function[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].function[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7linates()[?7h[?12l[?25h[?25l[?7lsage: aaa[0].coordinates()

+[?7h[?12l[?25h[?2004l[?7h[1, 0, 0, 0, 0, 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lker[0]^p[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lsage: ker

+[?7h[?12l[?25h[?2004l[?7h[1/x*y^3, 1/x^2*y^3]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lker[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[0]^p[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]^[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^4 = x^5 + x over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(aaa[0].function)[?7h[?12l[?25h[?25l[?7lsage: p

+[?7h[?12l[?25h[?2004l[?7h3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lker[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[0]^p[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]^p[?7h[?12l[?25h[?25l[?7lsage: ker[0]^p

+[?7h[?12l[?25h[?2004l[?7h((x^8 + 2*x^4 + 1)/x)*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lker[0]^p[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(ker[0]^p)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (ker[0]^p).coordinates()

+[?7h[?12l[?25h[?2004l[?7h[1, 0, 0, 0, 0, 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^4 = x^5 + x over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.cartier_matrix()[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lbenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix(prec=50)

+[?7h[?12l[?25h[?2004l[?7h[0 0 0 1 0 0]
+[0 0 1 0 0 0]
+[0 1 0 0 0 0]
+[0 0 0 0 0 0]
+[0 0 0 0 0 0]
+[1 0 0 0 0 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[0].coordinates()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = frbenus_kernel(C)[0][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCbasis_of[?7h[?12l[?25h[?25l[?7l.basis_of[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_cohomology[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aaa = C.basis_of_cohomology()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa = C.basis_of_cohomology()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[0].coordinates()[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: aaa[0]

+[?7h[?12l[?25h[?2004l[?7h1/x*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[0][?7h[?12l[?25h[?25l[?7l[].coordinates()[?7h[?12l[?25h[?25l[?7lfuncton[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aaa[0].frobenius()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [84], in <cell line: 1>()
+----> 1 aaa[Integer(0)].frobenius()
+
+AttributeError: 'superelliptic_function' object has no attribute 'frobenius'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[0].frobenius()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]^[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aaa[0]^p.coordinates()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [85], in <cell line: 1>()
+----> 1 aaa[Integer(0)]**p.coordinates()
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
+    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
+    493     """
+--> 494     return self.getattr_from_category(name)
+    495 
+    496 cdef getattr_from_category(self, name):
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
+    505     else:
+    506         cls = P._abstract_element_class
+--> 507     return getattr_from_other_class(self, cls, name)
+    508 
+    509 def __dir__(self):
+
+File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
+    359     dummy_error_message.cls = type(self)
+    360     dummy_error_message.name = name
+--> 361     raise AttributeError(dummy_error_message)
+    362 attribute = <object>attr
+    363 # Check for a descriptor (__get__ in Python)
+
+AttributeError: 'sage.rings.integer.Integer' object has no attribute 'coordinates'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[0]^p.coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a[0]^p.cordinates()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().cordinates()[?7h[?12l[?25h[?25l[?7lsage: (aaa[0]^p).coordinates()

+[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[0]^p.coordinates()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: aaa[4]

+[?7h[?12l[?25h[?2004l[?7h1/x^2*y^3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[4][?7h[?12l[?25h[?25l[?7l[]^[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aaa[4]^p.coordinates()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [88], in <cell line: 1>()
+----> 1 aaa[Integer(4)]**p.coordinates()
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
+    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
+    493     """
+--> 494     return self.getattr_from_category(name)
+    495 
+    496 cdef getattr_from_category(self, name):
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
+    505     else:
+    506         cls = P._abstract_element_class
+--> 507     return getattr_from_other_class(self, cls, name)
+    508 
+    509 def __dir__(self):
+
+File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
+    359     dummy_error_message.cls = type(self)
+    360     dummy_error_message.name = name
+--> 361     raise AttributeError(dummy_error_message)
+    362 attribute = <object>attr
+    363 # Check for a descriptor (__get__ in Python)
+
+AttributeError: 'sage.rings.integer.Integer' object has no attribute 'coordinates'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[4]^p.coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l).cordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a[4]^p).cordinates()[?7h[?12l[?25h[?25l[?7lsage: (aaa[4]^p).coordinates()

+[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(aaa[4]^p).coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]^p).cordinates()[?7h[?12l[?25h[?25l[?7l5]^p).cordinates()[?7h[?12l[?25h[?25l[?7lsage: (aaa[5]^p).coordinates()

+[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[4]^p.coordinates()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: aaa[4]

+[?7h[?12l[?25h[?2004l[?7h1/x^2*y^3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[4][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l5][?7h[?12l[?25h[?25l[?7lsage: aaa[5]

+[?7h[?12l[?25h[?2004l[?7h1/x^3*y^3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[0][?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lbenius_kernel(C, prec=50)[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)

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

+[?7h[?12l[?25h[?2004l[
+(0, 0, 0, 1, 0, 0),
+(0, 0, 0, 0, 1, 0)
+]
+(((x^8 + 2*x^4 + 1)/x)*y, 0)
+((x^4 + 2)*y, 1/x^4*y)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lbenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix(prec=50).kernel().basis()

+[?7h[?12l[?25h[?2004l[?7h[
+(0, 0, 0, 1, 0, 0),
+(0, 0, 0, 0, 1, 0)
+]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50).kernel().basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.frobenius_matrix(prec=50).kernel().basis()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lrkernel().basis()[?7h[?12l[?25h[?25l[?7lkernel().basis()[?7h[?12l[?25h[?25l[?7ltkernel().basis()[?7h[?12l[?25h[?25l[?7lrkernel().basis()[?7h[?12l[?25h[?25l[?7lakernel().basis()[?7h[?12l[?25h[?25l[?7lnkernel().basis()[?7h[?12l[?25h[?25l[?7lskernel().basis()[?7h[?12l[?25h[?25l[?7lpkernel().basis()[?7h[?12l[?25h[?25l[?7lokernel().basis()[?7h[?12l[?25h[?25l[?7lskernel().basis()[?7h[?12l[?25h[?25l[?7lekernel().basis()[?7h[?12l[?25h[?25l[?7l(kernel().basis()[?7h[?12l[?25h[?25l[?7l()kernel().basis()[?7h[?12l[?25h[?25l[?7l().kernel().basis()[?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix(prec=50).transpose().kernel().basis()

+[?7h[?12l[?25h[?2004l[?7h[
+(0, 0, 0, 0, 1, 0),
+(0, 0, 0, 0, 0, 1)
+]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldimension_of_RHS = p*gY + (len(list_of_m) - 1)*(p-1) + sum(sum(i*alpha(i, m, p) for i in range(1, p)) for m in list_of_m)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[
+(0, 0, 0, 0, 1, 0),
+(0, 0, 0, 0, 0, 1)
+]
+((x^4 + 2)*y, 1/x^4*y)
+(x*y, ((2*x^4 + 1)/x^7)*y)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[
+(0, 0, 0, 0, 1, 0),
+(0, 0, 0, 0, 0, 1)
+]
+((x^4 + 2)*y, 1/x^4*y)
+(x*y, ((2*x^4 + 1)/x^7)*y)
+((x/(x^4 + 1))*y^3, (1/(x^7 + x^3))*y^3)
+(0, 0)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[
+(0, 0, 0, 0, 1, 0),
+(0, 0, 0, 0, 0, 1)
+]
+((x^4 + 2)*y, 1/x^4*y)
+(x*y, ((2*x^4 + 1)/x^7)*y)
+!
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [99], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:23, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:52, in <module>
+
+File <string>:47, in decomposition_omega0_omega8(omega, prec)
+
+File <string>:38, in __add__(self, other)
+
+AttributeError: 'superelliptic_form' object has no attribute 'function'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[
+(0, 0, 0, 0, 1, 0),
+(0, 0, 0, 0, 0, 1)
+]
+((x^4 + 2)*y, 1/x^4*y)
+(x*y, ((2*x^4 + 1)/x^7)*y)
+!
+((x^2/y) dx, (1/(x^2*y)) dx)
+(0 dx, 0 dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lker[0]^p[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lsage: ker

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

+[?7h[?12l[?25h[?2004l[
+(0, 0, 0, 0, 1, 0),
+(0, 0, 0, 0, 0, 1)
+]
+((x^4 + 2)*y, 1/x^4*y)
+(x*y, ((2*x^4 + 1)/x^7)*y)
+!
+1
+1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[
+(0, 0, 0, 0, 1, 0),
+(0, 0, 0, 0, 0, 1)
+]
+((x^4 + 2)*y, 1/x^4*y)
+(x*y, ((2*x^4 + 1)/x^7)*y)
+!
+1
+1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50).transpose().kernel().basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basi()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7llomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [104], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:23, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:8, in <module>
+
+NameError: name 'basis_W2Omega' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[<__main__.superelliptic_drw_form object at 0x7f0b7df25930>, <__main__.superelliptic_drw_form object at 0x7f0b7df26050>, <__main__.superelliptic_drw_form object at 0x7f0b7df256f0>, <__main__.superelliptic_drw_form object at 0x7f0b7df25330>, <__main__.superelliptic_drw_form object at 0x7f0b7df265f0>, <__main__.superelliptic_drw_form object at 0x7f0b7df263e0>]
+!
+1
+1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[[0] d[x] + V((x^2/y^3) dx) + dV([0]), [0] d[x] + V((x/(x^4*y^2 + y^2)) dx) + dV([0]), [0] d[x] + V((x^4/(x^4*y^2 + y^2)) dx) + dV([0]), [0] d[x] + V((1/(x^8*y - x^4*y + y)) dx) + dV([0]), [0] d[x] + V((x^3/(x^8*y - x^4*y + y)) dx) + dV([0]), [0] d[x] + V((x^6/(x^8*y - x^4*y + y)) dx) + dV([0])]
+!
+1
+1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: V = GF(p)^3

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV = GF(p)^3[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[],[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: V.subspace([1, 2, 2], [1, 1, 1])

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/modules/free_module.py:6394, in FreeModule_submodule_with_basis_pid.__init__(self, ambient, basis, check, echelonize, echelonized_basis, already_echelonized)
+   6393 try:
+-> 6394     basis = [ambient(x) for x in basis]
+   6395 except TypeError:
+   6396     # That failed, try the ambient vector space instead
+
+File /ext/sage/9.7/src/sage/modules/free_module.py:6394, in <listcomp>(.0)
+   6393 try:
+-> 6394     basis = [ambient(x) for x in basis]
+   6395 except TypeError:
+   6396     # That failed, try the ambient vector space instead
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    896 if no_extra_args:
+--> 897     return mor._call_(x)
+    898 else:
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    160     print(type(C._element_constructor), C._element_constructor)
+--> 161 raise
+    162 
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+
+File /ext/sage/9.7/src/sage/modules/free_module.py:6281, in FreeModule_ambient_field._element_constructor_(self, e, *args, **kwds)
+   6280     pass
+-> 6281 return FreeModule_generic_field._element_constructor_(self, e, *args, **kwds)
+
+File /ext/sage/9.7/src/sage/modules/free_module.py:2096, in FreeModule_generic._element_constructor_(self, x, coerce, copy, check)
+   2095 if isinstance(self, FreeModule_ambient):
+-> 2096     return self.element_class(self, x, coerce, copy)
+   2097 try:
+
+File /ext/sage/9.7/src/sage/modules/vector_modn_dense.pyx:188, in sage.modules.vector_modn_dense.Vector_modn_dense.__init__()
+    187 if x != 0:
+--> 188     raise TypeError("can't initialize vector from nonzero non-list")
+    189 else:
+
+TypeError: can't initialize vector from nonzero non-list
+
+During handling of the above exception, another exception occurred:
+
+TypeError                                 Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/modules/free_module.py:6400, in FreeModule_submodule_with_basis_pid.__init__(self, ambient, basis, check, echelonize, echelonized_basis, already_echelonized)
+   6399 try:
+-> 6400     basis = [V(x) for x in basis]
+   6401 except TypeError:
+
+File /ext/sage/9.7/src/sage/modules/free_module.py:6400, in <listcomp>(.0)
+   6399 try:
+-> 6400     basis = [V(x) for x in basis]
+   6401 except TypeError:
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    896 if no_extra_args:
+--> 897     return mor._call_(x)
+    898 else:
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    160     print(type(C._element_constructor), C._element_constructor)
+--> 161 raise
+    162 
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+
+File /ext/sage/9.7/src/sage/modules/free_module.py:6281, in FreeModule_ambient_field._element_constructor_(self, e, *args, **kwds)
+   6280     pass
+-> 6281 return FreeModule_generic_field._element_constructor_(self, e, *args, **kwds)
+
+File /ext/sage/9.7/src/sage/modules/free_module.py:2096, in FreeModule_generic._element_constructor_(self, x, coerce, copy, check)
+   2095 if isinstance(self, FreeModule_ambient):
+-> 2096     return self.element_class(self, x, coerce, copy)
+   2097 try:
+
+File /ext/sage/9.7/src/sage/modules/vector_modn_dense.pyx:188, in sage.modules.vector_modn_dense.Vector_modn_dense.__init__()
+    187 if x != 0:
+--> 188     raise TypeError("can't initialize vector from nonzero non-list")
+    189 else:
+
+TypeError: can't initialize vector from nonzero non-list
+
+During handling of the above exception, another exception occurred:
+
+TypeError                                 Traceback (most recent call last)
+Input In [108], in <cell line: 1>()
+----> 1 V.subspace([Integer(1), Integer(2), Integer(2)], [Integer(1), Integer(1), Integer(1)])
+
+File /ext/sage/9.7/src/sage/modules/free_module.py:4598, in FreeModule_generic_field.subspace(self, gens, check, already_echelonized)
+   4555 def subspace(self, gens, check=True, already_echelonized=False):
+   4556     """
+   4557     Return the subspace of ``self`` spanned by the elements of gens.
+   4558 
+   (...)
+   4596         ArithmeticError: argument gens (= [[1, 1, 0]]) does not generate a submodule of self
+   4597     """
+-> 4598     return self.submodule(gens, check=check, already_echelonized=already_echelonized)
+
+File /ext/sage/9.7/src/sage/modules/free_module.py:1744, in Module_free_ambient.submodule(self, gens, check, already_echelonized)
+   1742 if isinstance(gens, Module_free_ambient):
+   1743     gens = gens.gens()
+-> 1744 V = self.span(gens, check=check, already_echelonized=already_echelonized)
+   1745 if check:
+   1746     if not V.is_submodule(self):
+
+File /ext/sage/9.7/src/sage/modules/free_module.py:1659, in Module_free_ambient.span(self, gens, base_ring, check, already_echelonized)
+   1657     gens = gens.gens()
+   1658 if base_ring is None or base_ring is self.base_ring():
+-> 1659     return self._submodule_class(self.ambient_module(), gens, check=check, already_echelonized=already_echelonized)
+   1661 # The base ring has changed
+   1662 try:
+
+File /ext/sage/9.7/src/sage/modules/free_module.py:7690, in FreeModule_submodule_field.__init__(self, ambient, gens, check, already_echelonized)
+   7688 if is_FreeModule(gens):
+   7689     gens = gens.gens()
+-> 7690 FreeModule_submodule_with_basis_field.__init__(self, ambient, basis=gens, check=check,
+   7691     echelonize=not already_echelonized, already_echelonized=already_echelonized)
+
+File /ext/sage/9.7/src/sage/modules/free_module.py:7491, in FreeModule_submodule_with_basis_field.__init__(self, ambient, basis, check, echelonize, echelonized_basis, already_echelonized)
+   7476 def __init__(self, ambient, basis, check=True,
+   7477     echelonize=False, echelonized_basis=None, already_echelonized=False):
+   7478     """
+   7479     Create a vector space with given basis.
+   7480 
+   (...)
+   7489         [4 5 6]
+   7490     """
+-> 7491     FreeModule_submodule_with_basis_pid.__init__(
+   7492         self, ambient, basis=basis, check=check, echelonize=echelonize,
+   7493         echelonized_basis=echelonized_basis, already_echelonized=already_echelonized)
+
+File /ext/sage/9.7/src/sage/modules/free_module.py:6402, in FreeModule_submodule_with_basis_pid.__init__(self, ambient, basis, check, echelonize, echelonized_basis, already_echelonized)
+   6400         basis = [V(x) for x in basis]
+   6401     except TypeError:
+-> 6402         raise TypeError("each element of basis must be in "
+   6403                         "the ambient vector space")
+   6405 if echelonize and not already_echelonized:
+   6406     basis = self._echelonized_basis(ambient, basis)
+
+TypeError: each element of basis must be in the ambient vector space
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV.subspace([1, 2, 2], [1, 1, 1])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lv[1, 2, 2], [1, 1, 1])[?7h[?12l[?25h[?25l[?7le[1, 2, 2], [1, 1, 1])[?7h[?12l[?25h[?25l[?7lc[1, 2, 2], [1, 1, 1])[?7h[?12l[?25h[?25l[?7lt[1, 2, 2], [1, 1, 1])[?7h[?12l[?25h[?25l[?7lo[1, 2, 2], [1, 1, 1])[?7h[?12l[?25h[?25l[?7lr[1, 2, 2], [1, 1, 1])[?7h[?12l[?25h[?25l[?7l([1, 2, 2], [1, 1, 1])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l([]), [1, 1, 1])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lv[1, 1, 1])[?7h[?12l[?25h[?25l[?7le[1, 1, 1])[?7h[?12l[?25h[?25l[?7lc[1, 1, 1])[?7h[?12l[?25h[?25l[?7lt[1, 1, 1])[?7h[?12l[?25h[?25l[?7lo[1, 1, 1])[?7h[?12l[?25h[?25l[?7lr[1, 1, 1])[?7h[?12l[?25h[?25l[?7l([1, 1, 1])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: V.subspace(vector([1, 2, 2]), vector([1, 1, 1]))

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/modules/free_module.py:6394, in FreeModule_submodule_with_basis_pid.__init__(self, ambient, basis, check, echelonize, echelonized_basis, already_echelonized)
+   6393 try:
+-> 6394     basis = [ambient(x) for x in basis]
+   6395 except TypeError:
+   6396     # That failed, try the ambient vector space instead
+
+File /ext/sage/9.7/src/sage/modules/free_module.py:6394, in <listcomp>(.0)
+   6393 try:
+-> 6394     basis = [ambient(x) for x in basis]
+   6395 except TypeError:
+   6396     # That failed, try the ambient vector space instead
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    896 if no_extra_args:
+--> 897     return mor._call_(x)
+    898 else:
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    160     print(type(C._element_constructor), C._element_constructor)
+--> 161 raise
+    162 
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+
+File /ext/sage/9.7/src/sage/modules/free_module.py:6281, in FreeModule_ambient_field._element_constructor_(self, e, *args, **kwds)
+   6280     pass
+-> 6281 return FreeModule_generic_field._element_constructor_(self, e, *args, **kwds)
+
+File /ext/sage/9.7/src/sage/modules/free_module.py:2096, in FreeModule_generic._element_constructor_(self, x, coerce, copy, check)
+   2095 if isinstance(self, FreeModule_ambient):
+-> 2096     return self.element_class(self, x, coerce, copy)
+   2097 try:
+
+File /ext/sage/9.7/src/sage/modules/vector_modn_dense.pyx:188, in sage.modules.vector_modn_dense.Vector_modn_dense.__init__()
+    187 if x != 0:
+--> 188     raise TypeError("can't initialize vector from nonzero non-list")
+    189 else:
+
+TypeError: can't initialize vector from nonzero non-list
+
+During handling of the above exception, another exception occurred:
+
+TypeError                                 Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/modules/free_module.py:6400, in FreeModule_submodule_with_basis_pid.__init__(self, ambient, basis, check, echelonize, echelonized_basis, already_echelonized)
+   6399 try:
+-> 6400     basis = [V(x) for x in basis]
+   6401 except TypeError:
+
+File /ext/sage/9.7/src/sage/modules/free_module.py:6400, in <listcomp>(.0)
+   6399 try:
+-> 6400     basis = [V(x) for x in basis]
+   6401 except TypeError:
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    896 if no_extra_args:
+--> 897     return mor._call_(x)
+    898 else:
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    160     print(type(C._element_constructor), C._element_constructor)
+--> 161 raise
+    162 
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+
+File /ext/sage/9.7/src/sage/modules/free_module.py:6281, in FreeModule_ambient_field._element_constructor_(self, e, *args, **kwds)
+   6280     pass
+-> 6281 return FreeModule_generic_field._element_constructor_(self, e, *args, **kwds)
+
+File /ext/sage/9.7/src/sage/modules/free_module.py:2096, in FreeModule_generic._element_constructor_(self, x, coerce, copy, check)
+   2095 if isinstance(self, FreeModule_ambient):
+-> 2096     return self.element_class(self, x, coerce, copy)
+   2097 try:
+
+File /ext/sage/9.7/src/sage/modules/vector_modn_dense.pyx:188, in sage.modules.vector_modn_dense.Vector_modn_dense.__init__()
+    187 if x != 0:
+--> 188     raise TypeError("can't initialize vector from nonzero non-list")
+    189 else:
+
+TypeError: can't initialize vector from nonzero non-list
+
+During handling of the above exception, another exception occurred:
+
+TypeError                                 Traceback (most recent call last)
+Input In [109], in <cell line: 1>()
+----> 1 V.subspace(vector([Integer(1), Integer(2), Integer(2)]), vector([Integer(1), Integer(1), Integer(1)]))
+
+File /ext/sage/9.7/src/sage/modules/free_module.py:4598, in FreeModule_generic_field.subspace(self, gens, check, already_echelonized)
+   4555 def subspace(self, gens, check=True, already_echelonized=False):
+   4556     """
+   4557     Return the subspace of ``self`` spanned by the elements of gens.
+   4558 
+   (...)
+   4596         ArithmeticError: argument gens (= [[1, 1, 0]]) does not generate a submodule of self
+   4597     """
+-> 4598     return self.submodule(gens, check=check, already_echelonized=already_echelonized)
+
+File /ext/sage/9.7/src/sage/modules/free_module.py:1744, in Module_free_ambient.submodule(self, gens, check, already_echelonized)
+   1742 if isinstance(gens, Module_free_ambient):
+   1743     gens = gens.gens()
+-> 1744 V = self.span(gens, check=check, already_echelonized=already_echelonized)
+   1745 if check:
+   1746     if not V.is_submodule(self):
+
+File /ext/sage/9.7/src/sage/modules/free_module.py:1659, in Module_free_ambient.span(self, gens, base_ring, check, already_echelonized)
+   1657     gens = gens.gens()
+   1658 if base_ring is None or base_ring is self.base_ring():
+-> 1659     return self._submodule_class(self.ambient_module(), gens, check=check, already_echelonized=already_echelonized)
+   1661 # The base ring has changed
+   1662 try:
+
+File /ext/sage/9.7/src/sage/modules/free_module.py:7690, in FreeModule_submodule_field.__init__(self, ambient, gens, check, already_echelonized)
+   7688 if is_FreeModule(gens):
+   7689     gens = gens.gens()
+-> 7690 FreeModule_submodule_with_basis_field.__init__(self, ambient, basis=gens, check=check,
+   7691     echelonize=not already_echelonized, already_echelonized=already_echelonized)
+
+File /ext/sage/9.7/src/sage/modules/free_module.py:7491, in FreeModule_submodule_with_basis_field.__init__(self, ambient, basis, check, echelonize, echelonized_basis, already_echelonized)
+   7476 def __init__(self, ambient, basis, check=True,
+   7477     echelonize=False, echelonized_basis=None, already_echelonized=False):
+   7478     """
+   7479     Create a vector space with given basis.
+   7480 
+   (...)
+   7489         [4 5 6]
+   7490     """
+-> 7491     FreeModule_submodule_with_basis_pid.__init__(
+   7492         self, ambient, basis=basis, check=check, echelonize=echelonize,
+   7493         echelonized_basis=echelonized_basis, already_echelonized=already_echelonized)
+
+File /ext/sage/9.7/src/sage/modules/free_module.py:6402, in FreeModule_submodule_with_basis_pid.__init__(self, ambient, basis, check, echelonize, echelonized_basis, already_echelonized)
+   6400         basis = [V(x) for x in basis]
+   6401     except TypeError:
+-> 6402         raise TypeError("each element of basis must be in "
+   6403                         "the ambient vector space")
+   6405 if echelonize and not already_echelonized:
+   6406     basis = self._echelonized_basis(ambient, basis)
+
+TypeError: each element of basis must be in the ambient vector space
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV.subspace(vector([1, 2, 2]), vector([1, 1, 1]))[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50).transpose().kernel().basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(prec=50).transpose().kernel().basis()[?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix(prec=50).transpose().kernel().basis()

+[?7h[?12l[?25h[?2004l[?7h[
+(0, 0, 0, 0, 1, 0),
+(0, 0, 0, 0, 0, 1)
+]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50).transpose().kernel().basis()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix(prec=50).transpose().kernel().basis()[0]

+[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, 0, 1, 0)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50).transpose().kernel().basis()[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lj[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lker[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lbenius_kernel(C, prec=50)[?7h[?12l[?25h[?25l[?7l()[0][?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]^[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l).cordinates[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(frobenius_kernel(C, prec=50)[0]^p).cordinates[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: (frobenius_kernel(C, prec=50)[0]^p).coordinates() == vector(6*[0])

+[?7h[?12l[?25h[?2004l[
+(0, 0, 0, 0, 1, 0),
+(0, 0, 0, 0, 0, 1)
+]
+[?7hFalse
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(frobenius_kernel(C, prec=50)[0]^p).coordinates() == vector(6*[0])[?7h[?12l[?25h[?25l[?7l([][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (frobenius_kernel(C, prec=50)[0]^p).coordinates()

+[?7h[?12l[?25h[?2004l[
+(0, 0, 0, 0, 1, 0),
+(0, 0, 0, 0, 0, 1)
+]
+[?7h[0, 0, 0, 0, 0, 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(frobenius_kernel(C, prec=50)[0]^p).coordinates()[?7h[?12l[?25h[?25l[?7l() == vector(6*[0])[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: (frobenius_kernel(C, prec=50)[0]^p).coordinates() = 6*[0]

+[?7h[?12l[?25h[?2004l  Input In [114]
+    (frobenius_kernel(C, prec=Integer(50))[Integer(0)]**p).coordinates() = Integer(6)*[Integer(0)]
+    ^
+SyntaxError: cannot assign to function call here. Maybe you meant '==' instead of '='?
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(frobenius_kernel(C, prec=50)[0]^p).coordinates() = 6*[0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l= 6*[0][?7h[?12l[?25h[?25l[?7lsage: (frobenius_kernel(C, prec=50)[0]^p).coordinates() == 6*[0]

+[?7h[?12l[?25h[?2004l[
+(0, 0, 0, 0, 1, 0),
+(0, 0, 0, 0, 0, 1)
+]
+[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(frobenius_kernel(C, prec=50)[0]^p).coordinates() == 6*[0][?7h[?12l[?25h[?25l[?7lsage: (frobenius_kernel(C, prec=50)[0]^p).coordinates() == 6*[0]

+[?7h[?12l[?25h[?2004l[
+(0, 0, 0, 0, 1, 0),
+(0, 0, 0, 0, 0, 1)
+]
+[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [117], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:25, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:13, in <module>
+
+File <string>:36, in __init__(self, C, list_of_fcts, prec)
+
+TypeError: superelliptic_function.expansion_at_infty() got an unexpected keyword argument 'i'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq = 5[?7h[?12l[?25h[?25l[?7luadratic_form(parity_quadratic_form(v0, q))[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

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

+[?7h[?12l[?25h[?2004lsuperelliptic form coordinates test:
+True
+p-th root test:
+True
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [1], in <cell line: 1>()
+----> 1 load('tests.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:5, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:12, in <module>
+
+File <string>:139, in pth_root(self)
+
+ValueError: Function is not a p-th power.
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

+[?7h[?12l[?25h[?2004las_cover_test:
+True
+True
+group_action_matrices_test:
+True
+True
+True
+dual_element_test:
+True
+True
+True
+True
+True
+True
+True
+True
+True
+True
+True
+True
+True
+True
+True
+True
+True
+True
+True
+True
+True
+True
+True
+True
+True
+ith_component_test:
+True
+ith ramification group test:
+^Csage/rings/polynomial/polynomial_zmod_flint.pyx:7: DeprecationWarning: invalid escape sequence '\Z'
+  """
+sage/rings/polynomial/polynomial_zmod_flint.pyx:7: DeprecationWarning: invalid escape sequence '\Z'
+  """
+^C
+KeyboardInterrupt
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7lini.sage')[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l(t.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/rings/infinity.py:1201, in InfinityRing_class._element_constructor_(self, x)
+   1199 try:
+   1200     # For example, RealField() implements this
+-> 1201     if x.is_positive_infinity():
+   1202         return self.gen(0)
+
+AttributeError: 'int' object has no attribute 'is_positive_infinity'
+
+During handling of the above exception, another exception occurred:
+
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [3], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:25, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:13, in <module>
+
+File <string>:44, in __init__(self, C, list_of_fcts, prec)
+
+File <string>:134, in artin_schreier_transform(power_series, prec)
+
+File <string>:17, in new_reverse(power_series, prec)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1356, in sage.structure.element.Element.__sub__()
+   1354 cdef int cl = classify_elements(left, right)
+   1355 if HAVE_SAME_PARENT(cl):
+-> 1356     return (<Element>left)._sub_(right)
+   1357 if BOTH_ARE_ELEMENT(cl):
+   1358     return coercion_model.bin_op(left, right, sub)
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:792, in sage.rings.laurent_series_ring_element.LaurentSeries._sub_()
+    790 # 1. Special case when one or the other is 0.
+    791 if not right:
+--> 792     return self.add_bigoh(right.prec())
+    793 if not self:
+    794     return -right.add_bigoh(self.prec())
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1334, in sage.rings.laurent_series_ring_element.LaurentSeries.prec()
+   1332         8
+   1333     """
+-> 1334     return self.__u.prec() + self.__n
+   1335 
+   1336 def precision_absolute(self):
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1241, in sage.structure.element.Element.__add__()
+   1239 integer_check_long_py(right, &value, &err)
+   1240 if not err:
+-> 1241     return (<Element>left)._add_long(value)
+   1242 integer_check_long_py(left, &value, &err)
+   1243 if not err:
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:2388, in sage.structure.element.ModuleElement._add_long()
+   2386     if n == 0:
+   2387         return self
+-> 2388     return coercion_model.bin_op(self, n, add)
+   2389 
+   2390 cpdef _sub_(self, other):
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1200, in sage.structure.coerce.CoercionModel.bin_op()
+   1198 # Now coerce to a common parent and do the operation there
+   1199 try:
+-> 1200     xy = self.canonical_coercion(x, y)
+   1201 except TypeError:
+   1202     self._record_exception()
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1315, in sage.structure.coerce.CoercionModel.canonical_coercion()
+   1313     x_elt = x
+   1314 if y_map is not None:
+-> 1315     y_elt = (<Map>y_map)._call_(y)
+   1316 else:
+   1317     y_elt = y
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/infinity.py:1201, in InfinityRing_class._element_constructor_(self, x)
+   1198 else:
+   1199     try:
+   1200         # For example, RealField() implements this
+-> 1201         if x.is_positive_infinity():
+   1202             return self.gen(0)
+   1203         if x.is_negative_infinity():
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[-1].f.function[?7h[?12l[?25h[?25l[?7lS.genus()[?7h[?12l[?25h[?25l[?7lsage: AS

+[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 5 with the equations:
+z0^5 - z0 = x^3 + x
+z1^5 - z1 = x^2
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.genus()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS.

+  AS.at_most_poles                       AS.cohomology_of_structure_sheaf_basis AS.exponent_of_different               AS.genus                               
 

+  AS.at_most_poles_forms                 AS.de_rham_basis                       AS.exponent_of_different_prim          AS.group                               
 

+  AS.base_ring                           AS.dx                                  AS.fct_field                           AS.height                              
>

+  AS.characteristic                      AS.dx_series                           AS.functions                           AS.holomorphic_differentials_basis     
 

+ [?7h[?12l[?25h[?25l[?7lat_most_poles

+ AS.at_most_poles                      

+

+

+

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

+ AS.at_most_poles                       AS.cohomology_of_structure_sheaf_basis[?7h[?12l[?25h[?25l[?7lexpnent_of_different

+ AS.cohomology_of_structure_sheaf_basis AS.exponent_of_different              [?7h[?12l[?25h[?25l[?7lgenus

+ AS.exponent_of_different               AS.genus                              [?7h[?12l[?25h[?25l[?7lith_ramification_gp

+ cohomology_of_structure_sheaf_basisexpnent_of_different              genus                ith_ramification_gp

+ derhambasi      exponent_of_different_primgroup                     jumps

+<dx       fct_fieldheight   lift_o_de_rham

+ dx_seris     functionholomorphic_differentials_basismagical_element                [?7h[?12l[?25h[?25l[?7lgenus

+ AS.genus                               AS.ith_ramification_gp                [?7h[?12l[?25h[?25l[?7lrop

+ AS.genus                              

+ AS.group                              [?7h[?12l[?25h[?25l[?7lheight

+

+ AS.group                              

+ AS.height                             [?7h[?12l[?25h[?25l[?7lolomorphic_differentials_basis

+

+

+ AS.height                             

+ AS.holomorphic_differentials_basis    [?7h[?12l[?25h[?25l[?7l()

+

+

+

+

+[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis()

+[?7h[?12l[?25h[?2004l[?7h[(1) * dx,
+ (z1) * dx,
+ (z1^2) * dx,
+ (z1^3) * dx,
+ (z1^4) * dx,
+ (z0) * dx,
+ (z0*z1) * dx,
+ (z0*z1^2) * dx,
+ (z0*z1^3 - x*z1^2) * dx,
+ (z0*z1^4 + 2*x*z1^3 + 2*x*z0^2) * dx,
+ (z0^2) * dx,
+ (z0^2*z1) * dx,
+ (z0^2*z1^2 - x^2) * dx,
+ (z0^2*z1^3 - z0^4 + 2*x*z0*z1^2 - 2*x^2*z1) * dx,
+ (z0^2*z1^4 + z0^4*z1 + x*z0*z1^3 + x*z0^3 + x^2*z1^2) * dx,
+ (z0^3 - x*z1^2) * dx,
+ (z0^3*z1 - 2*x*z1^3 + x*z0^2) * dx,
+ (z0^3*z1^2 - x*z1^4 + 2*x*z0^2*z1 - 2*x^2*z0) * dx,
+ (x) * dx,
+ (x*z1) * dx,
+ (x*z0) * dx,
+ (x*z0*z1 - x^2) * dx]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb.function[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbAS.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7lbAS.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7lbAS.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7l AS.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7l=AS.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7l AS.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7lsage: bbb = AS.holomorphic_differentials_basis()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb = AS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[5].cartier().coornates()[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7lsage: bbb[9[

+....: [?7h[?12l[?25h[?25l[?7l....: 

+....: [?7h[?12l[?25h[?25l[?7l

+ 

+ [?7h[?12l[?25h[?25l[?7lbbb = AS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[5].cartier().coornates()[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: bbb[9]

+[?7h[?12l[?25h[?2004l[?7h(z0*z1^4 + 2*x*z1^3 + 2*x*z0^2) * dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[9][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: bbb[9].monomials()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [9], in <cell line: 1>()
+----> 1 bbb[Integer(9)].monomials()
+
+AttributeError: 'as_form' object has no attribute 'monomials'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[9].monomials()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lfmonomials()[?7h[?12l[?25h[?25l[?7lomonomials()[?7h[?12l[?25h[?25l[?7lrmonomials()[?7h[?12l[?25h[?25l[?7lmonomials()[?7h[?12l[?25h[?25l[?7l.monomials()[?7h[?12l[?25h[?25l[?7lsage: bbb[9].form.monomials()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [10], in <cell line: 1>()
+----> 1 bbb[Integer(9)].form.monomials()
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
+    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
+    493     """
+--> 494     return self.getattr_from_category(name)
+    495 
+    496 cdef getattr_from_category(self, name):
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
+    505     else:
+    506         cls = P._abstract_element_class
+--> 507     return getattr_from_other_class(self, cls, name)
+    508 
+    509 def __dir__(self):
+
+File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
+    359     dummy_error_message.cls = type(self)
+    360     dummy_error_message.name = name
+--> 361     raise AttributeError(dummy_error_message)
+    362 attribute = <object>attr
+    363 # Check for a descriptor (__get__ in Python)
+
+AttributeError: 'sage.rings.fraction_field_element.FractionFieldElement' object has no attribute 'monomials'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[9].form.monomials()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(RxyzQ, Rxyz, x, y, z)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lsage: (RxyzQ, Rxyz, x, y, z) = AS.fct_field

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(RxyzQ, Rxyz, x, y, z) = AS.fct_field[?7h[?12l[?25h[?25l[?7lbbb[9].form.monomials()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRb[9].form.monomials()[?7h[?12l[?25h[?25l[?7lxb[9].form.monomials()[?7h[?12l[?25h[?25l[?7lyb[9].form.monomials()[?7h[?12l[?25h[?25l[?7lzb[9].form.monomials()[?7h[?12l[?25h[?25l[?7l(b[9].form.monomials()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().monomials()[?7h[?12l[?25h[?25l[?7lsage: Rxyz(bbb[9].form).monomials()

+[?7h[?12l[?25h[?2004l[?7h[z0*z1^4, x*z1^3, x*z0^2]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxyz(bbb[9].form).monomials()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmonomials(ccc)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxyz(bbb[9].form).monomials()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmRxyz(b[9].form).monomials()[0][?7h[?12l[?25h[?25l[?7l Rxyz(b[9].form).monomials()[0][?7h[?12l[?25h[?25l[?7l=Rxyz(b[9].form).monomials()[0][?7h[?12l[?25h[?25l[?7l Rxyz(b[9].form).monomials()[0][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: m = Rxyz(bbb[9].form).monomials()[0]

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm = Rxyz(bbb[9].form).monomials()[0][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lsage: m.

+  m.abs                    m.base_extend            m.change_ring            m.content                m.denominator            m.divides                 

+  m.add_m_mul_q            m.base_ring              m.coefficient            m.content_ideal          m.derivative             m.dump                    

+  m.additive_order         m.cartesian_product      m.coefficients           m.degree                 m.dict                   m.dumps                  >

+  m.args                   m.category               m.constant_coefficient   m.degrees                m.discriminant           m.exponents               

+ [?7h[?12l[?25h[?25l[?7labs

+ m.abs                   

+

+

+

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

+ m.abs                    m.base_extend           [?7h[?12l[?25h[?25l[?7lchang_rig

+ m.base_extend            m.change_ring           [?7h[?12l[?25h[?25l[?7lontent

+ m.change_ring            m.content               [?7h[?12l[?25h[?25l[?7ldeominator

+ m.content                m.denominator           [?7h[?12l[?25h[?25l[?7lcotent

+ m.content                m.denominator           [?7h[?12l[?25h[?25l[?7lhange_ring

+ m.change_ring            m.content               [?7h[?12l[?25h[?25l[?7lontent

+ m.change_ring            m.content               [?7h[?12l[?25h[?25l[?7l_ideal

+ m.content               

+ m.content_ideal         [?7h[?12l[?25h[?25l[?7ldegre

+

+ m.content_ideal         

+ m.degree                [?7h[?12l[?25h[?25l[?7l(

+

+

+

+

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

+  std_grading=                                 AA                                           AbelianGroup                                  

+  x=                                           AS                                           AbelianGroupMorphism                          

+  %%!                                          AS1                                          AbelianGroupWithValues                       >

+  A                                            AS2                                          AbelianVariety                                [?7h[?12l[?25h[?25l[?7lz

+

+

+

+[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: m.degree(z0)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [14], in <cell line: 1>()
+----> 1 m.degree(z0)
+
+NameError: name 'z0' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm.degree(z0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[0)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: m.degree(z[0])

+[?7h[?12l[?25h[?2004l[?7h1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm.degree(z[0])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l1])[?7h[?12l[?25h[?25l[?7lsage: m.degree(z[1])

+[?7h[?12l[?25h[?2004l[?7h4
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [17], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:25, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:15, in <module>
+
+NameError: name 'cartier' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [18], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:26, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:15, in <module>
+
+File <string>:16, in cartier(omega)
+
+NameError: name 'Fxy' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [19], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:26, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:15, in <module>
+
+File <string>:17, in cartier(omega)
+
+File <string>:17, in <dictcomp>(.0)
+
+TypeError: unsupported operand type(s) for -: 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular' and 'superelliptic_function'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: z[0]

+[?7h[?12l[?25h[?2004l[?7hz0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[0][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltz[0][?7h[?12l[?25h[?25l[?7lyz[0][?7h[?12l[?25h[?25l[?7lpz[0][?7h[?12l[?25h[?25l[?7lez[0][?7h[?12l[?25h[?25l[?7ltype(z[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: type(z[0])

+[?7h[?12l[?25h[?2004l[?7h<class 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular'>
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [22], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:26, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:15, in <module>
+
+File <string>:18, in cartier(omega)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute()
+    941         5
+    942      """
+--> 943     return self.subs(in_dict,**kwds)
+    944 
+    945 cpdef _act_on_(self, x, bint self_on_left):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs()
+   3537     id_Delete(&to_id, _ring)
+   3538     p_Delete(&_p, _ring)
+-> 3539     raise TypeError("keys do not match self's parent")
+   3540 try:
+   3541     v = parent.coerce(v)
+
+TypeError: keys do not match self's parent
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lMultivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [23], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:26, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:15, in <module>
+
+File <string>:19, in cartier(omega)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute()
+    941         5
+    942      """
+--> 943     return self.subs(in_dict,**kwds)
+    944 
+    945 cpdef _act_on_(self, x, bint self_on_left):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs()
+   3537     id_Delete(&to_id, _ring)
+   3538     p_Delete(&_p, _ring)
+-> 3539     raise TypeError("keys do not match self's parent")
+   3540 try:
+   3541     v = parent.coerce(v)
+
+TypeError: keys do not match self's parent
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l!!! Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [24], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:26, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:15, in <module>
+
+File <string>:19, in cartier(omega)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute()
+    941         5
+    942      """
+--> 943     return self.subs(in_dict,**kwds)
+    944 
+    945 cpdef _act_on_(self, x, bint self_on_left):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs()
+   3537     id_Delete(&to_id, _ring)
+   3538     p_Delete(&_p, _ring)
+-> 3539     raise TypeError("keys do not match self's parent")
+   3540 try:
+   3541     v = parent.coerce(v)
+
+TypeError: keys do not match self's parent
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l!!! Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [25], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:26, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:15, in <module>
+
+File <string>:19, in cartier(omega)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute()
+    941         5
+    942      """
+--> 943     return self.subs(in_dict,**kwds)
+    944 
+    945 cpdef _act_on_(self, x, bint self_on_left):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs()
+   3537     id_Delete(&to_id, _ring)
+   3538     p_Delete(&_p, _ring)
+-> 3539     raise TypeError("keys do not match self's parent")
+   3540 try:
+   3541     v = parent.coerce(v)
+
+TypeError: keys do not match self's parent
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50).transpose().kernel().basis()[0][?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basi()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lsage: C.height

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [26], in <cell line: 1>()
+----> 1 C.height
+
+AttributeError: 'superelliptic' object has no attribute 'height'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.height[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq = 5[?7h[?12l[?25h[?25l[?7luadratic_form(parity_quadratic_form(v0, q))[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

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

+[?7h[?12l[?25h[?2004l!!! Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [1], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:26, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:15, in <module>
+
+File <string>:19, in cartier(omega)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute()
+    941         5
+    942      """
+--> 943     return self.subs(in_dict,**kwds)
+    944 
+    945 cpdef _act_on_(self, x, bint self_on_left):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs()
+   3537     id_Delete(&to_id, _ring)
+   3538     p_Delete(&_p, _ring)
+-> 3539     raise TypeError("keys do not match self's parent")
+   3540 try:
+   3541     v = parent.coerce(v)
+
+TypeError: keys do not match self's parent
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l!!! Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [2], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:26, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:15, in <module>
+
+File <string>:20, in cartier(omega)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute()
+    941         5
+    942      """
+--> 943     return self.subs(in_dict,**kwds)
+    944 
+    945 cpdef _act_on_(self, x, bint self_on_left):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs()
+   3537     id_Delete(&to_id, _ring)
+   3538     p_Delete(&_p, _ring)
+-> 3539     raise TypeError("keys do not match self's parent")
+   3540 try:
+   3541     v = parent.coerce(v)
+
+TypeError: keys do not match self's parent
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
+!!! Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [3], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:26, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:15, in <module>
+
+File <string>:21, in cartier(omega)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute()
+    941         5
+    942      """
+--> 943     return self.subs(in_dict,**kwds)
+    944 
+    945 cpdef _act_on_(self, x, bint self_on_left):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs()
+   3537     id_Delete(&to_id, _ring)
+   3538     p_Delete(&_p, _ring)
+-> 3539     raise TypeError("keys do not match self's parent")
+   3540 try:
+   3541     v = parent.coerce(v)
+
+TypeError: keys do not match self's parent
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq = 5[?7h[?12l[?25h[?25l[?7luadratic_form(parity_quadratic_form(v0, q))[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

+[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
+^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[17;1R^[[18;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;2R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[19;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[18;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[18;1R^[[20;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[20;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[19;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[18;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[18;1R^[[20;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R^[[21;1R
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

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

+[?7h[?12l[?25h[?2004l{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
+!!! Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [1], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:26, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:15, in <module>
+
+File <string>:21, in cartier(omega)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute()
+    941         5
+    942      """
+--> 943     return self.subs(in_dict,**kwds)
+    944 
+    945 cpdef _act_on_(self, x, bint self_on_left):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs()
+   3537     id_Delete(&to_id, _ring)
+   3538     p_Delete(&_p, _ring)
+-> 3539     raise TypeError("keys do not match self's parent")
+   3540 try:
+   3541     v = parent.coerce(v)
+
+TypeError: keys do not match self's parent
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.height[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfC.x[?7h[?12l[?25h[?25l[?7l C.x[?7h[?12l[?25h[?25l[?7l=C.x[?7h[?12l[?25h[?25l[?7l C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()x[?7h[?12l[?25h[?25l[?7l(x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: f = (C.x)*(C.z[1])

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [2], in <cell line: 1>()
+----> 1 f = (C.x)*(C.z[Integer(1)])
+
+NameError: name 'C' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = (C.x)*(C.z[1])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.x)*(C.z[1])[?7h[?12l[?25h[?25l[?7lA.x)*(C.z[1])[?7h[?12l[?25h[?25l[?7lS.x)*(C.z[1])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.z[1])[?7h[?12l[?25h[?25l[?7lA.z[1])[?7h[?12l[?25h[?25l[?7lS.z[1])[?7h[?12l[?25h[?25l[?7lsage: f = (AS.x)*(AS.z[1])

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = (AS.x)*(AS.z[1])[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l{[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]:[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]:[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l{}[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7lsage: f.substitute({x:x^2, y:x, z[0]:x, z[1]:x})

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [4], in <cell line: 1>()
+----> 1 f.substitute({x:x**Integer(2), y:x, z[Integer(0)]:x, z[Integer(1)]:x})
+
+AttributeError: 'as_function' object has no attribute 'substitute'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.substitute({x:x^2, y:x, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.substitute({x:x^2, y:x, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l = (AS.x)*(AS.z[1])[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsage: f = f.function

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l'bad' in str(E.local_data(3))[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = f.function[?7h[?12l[?25h[?25l[?7l.substitue({x:x^2, y:x, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7lsage: f.substitute({x:x^2, y:x, z[0]:x, z[1]:x})

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [6], in <cell line: 1>()
+----> 1 f.substitute({x:x**Integer(2), y:x, z[Integer(0)]:x, z[Integer(1)]:x})
+
+NameError: name 'z' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(RxyzQ, Rxyz, x, y, z) = C.fct_field[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.fct_field[?7h[?12l[?25h[?25l[?7lA.fct_field[?7h[?12l[?25h[?25l[?7lS.fct_field[?7h[?12l[?25h[?25l[?7lsage: (RxyzQ, Rxyz, x, y, z) = AS.fct_field

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(RxyzQ, Rxyz, x, y, z) = AS.fct_field[?7h[?12l[?25h[?25l[?7lf.substitute({:x^2, y:x, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7lsage: f.substitute({x:x^2, y:x, z[0]:x, z[1]:x})

+[?7h[?12l[?25h[?2004l[?7hx^3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lTraceback (most recent call last):
+
+  File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
+    exec(code_obj, self.user_global_ns, self.user_ns)
+
+  Input In [9] in <cell line: 1>
+    load('init.sage')
+
+  File sage/misc/persist.pyx:175 in sage.misc.persist.load
+    sage.repl.load.load(filename, globals())
+
+  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
+    exec(preparse_file(f.read()) + "\n", globals)
+
+  File <string>:26 in <module>
+
+  File sage/misc/persist.pyx:175 in sage.misc.persist.load
+    sage.repl.load.load(filename, globals())
+
+  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
+    exec(preparse_file(f.read()) + "\n", globals)
+
+  File <string>:14
+    omega = AS.holomorphic_differentials_basis()[_sage_const_0 ]:
+                                                                ^
+SyntaxError: invalid syntax
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lnumerator(aaa[0].function)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: num

+[?7h[?12l[?25h[?2004l[?7h1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxyz(bbb[9].form).monomials()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lnu[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: Rxyz(num)

+[?7h[?12l[?25h[?2004l[?7h1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxyz(num)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l{)[?7h[?12l[?25h[?25l[?7l})[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7lx})[?7h[?12l[?25h[?25l[?7l:})[?7h[?12l[?25h[?25l[?7lx})[?7h[?12l[?25h[?25l[?7l^})[?7h[?12l[?25h[?25l[?7l2})[?7h[?12l[?25h[?25l[?7l,})[?7h[?12l[?25h[?25l[?7l })[?7h[?12l[?25h[?25l[?7ly})[?7h[?12l[?25h[?25l[?7l:})[?7h[?12l[?25h[?25l[?7ly})[?7h[?12l[?25h[?25l[?7l,})[?7h[?12l[?25h[?25l[?7l })[?7h[?12l[?25h[?25l[?7lz})[?7h[?12l[?25h[?25l[?7l:})[?7h[?12l[?25h[?25l[?7l})[?7h[?12l[?25h[?25l[?7l[})[?7h[?12l[?25h[?25l[?7l0})[?7h[?12l[?25h[?25l[?7l]})[?7h[?12l[?25h[?25l[?7l:})[?7h[?12l[?25h[?25l[?7lx})[?7h[?12l[?25h[?25l[?7l,})[?7h[?12l[?25h[?25l[?7l })[?7h[?12l[?25h[?25l[?7lz})[?7h[?12l[?25h[?25l[?7l[})[?7h[?12l[?25h[?25l[?7l1})[?7h[?12l[?25h[?25l[?7l]})[?7h[?12l[?25h[?25l[?7l:})[?7h[?12l[?25h[?25l[?7lx})[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: Rxyz(num).substitute({x:x^2, y:y, z[0]:x, z[1]:x})

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [13], in <cell line: 1>()
+----> 1 Rxyz(num).substitute({x:x**Integer(2), y:y, z[Integer(0)]:x, z[Integer(1)]:x})
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute()
+    941         5
+    942      """
+--> 943     return self.subs(in_dict,**kwds)
+    944 
+    945 cpdef _act_on_(self, x, bint self_on_left):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs()
+   3537     id_Delete(&to_id, _ring)
+   3538     p_Delete(&_p, _ring)
+-> 3539     raise TypeError("keys do not match self's parent")
+   3540 try:
+   3541     v = parent.coerce(v)
+
+TypeError: keys do not match self's parent
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa[5][?7h[?12l[?25h[?25l[?7l = C.dx[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a = Rxyz(1)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = Rxyz(1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7larent(aaa[0].function)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: parent(a)

+[?7h[?12l[?25h[?2004l[?7hMultivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(a)[?7h[?12l[?25h[?25l[?7la = Rxyz(1)[?7h[?12l[?25h[?25l[?7lRxyz(num).substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7l{}[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l{}[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7lsage: a.substitute({x:x^2, y:y, z[0]:x, z[1]:x})

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [16], in <cell line: 1>()
+----> 1 a.substitute({x:x**Integer(2), y:y, z[Integer(0)]:x, z[Integer(1)]:x})
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute()
+    941         5
+    942      """
+--> 943     return self.subs(in_dict,**kwds)
+    944 
+    945 cpdef _act_on_(self, x, bint self_on_left):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs()
+   3537     id_Delete(&to_id, _ring)
+   3538     p_Delete(&_p, _ring)
+-> 3539     raise TypeError("keys do not match self's parent")
+   3540 try:
+   3541     v = parent.coerce(v)
+
+TypeError: keys do not match self's parent
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(a)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: parent(a)

+[?7h[?12l[?25h[?2004l[?7hMultivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(a)[?7h[?12l[?25h[?25l[?7la.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7l{}[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l{}[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l({}[?7h[?12l[?25h[?25l[?7l{[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: z = parent(a).gens()[2:]

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz = parent(a).gens()[2:][?7h[?12l[?25h[?25l[?7lparent(a)[?7h[?12l[?25h[?25l[?7la.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7lsage: a.substitute({x:x^2, y:y, z[0]:x, z[1]:x})

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [19], in <cell line: 1>()
+----> 1 a.substitute({x:x**Integer(2), y:y, z[Integer(0)]:x, z[Integer(1)]:x})
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute()
+    941         5
+    942      """
+--> 943     return self.subs(in_dict,**kwds)
+    944 
+    945 cpdef _act_on_(self, x, bint self_on_left):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs()
+   3537     id_Delete(&to_id, _ring)
+   3538     p_Delete(&_p, _ring)
+-> 3539     raise TypeError("keys do not match self's parent")
+   3540 try:
+   3541     v = parent.coerce(v)
+
+TypeError: keys do not match self's parent
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lstr(E.local_data(2))[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lP1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l<[?7h[?12l[?25h[?25l[?7l>[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lX>[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lP[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: P.<X> = PolynomialRing(GF(p))

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lP.<X> = PolynomialRing(GF(p))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: P.<X> = PolynomialRing(GF(p), 1)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l = C_super.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lP[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A = P(1)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = P(1)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l{)[?7h[?12l[?25h[?25l[?7l})[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7lx})[?7h[?12l[?25h[?25l[?7l:})[?7h[?12l[?25h[?25l[?7lx})[?7h[?12l[?25h[?25l[?7l^})[?7h[?12l[?25h[?25l[?7l2})[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A.substitute({x:x^2})

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [23], in <cell line: 1>()
+----> 1 A.substitute({x:x**Integer(2)})
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:943, in sage.structure.element.Element.substitute()
+    941         5
+    942      """
+--> 943     return self.subs(in_dict,**kwds)
+    944 
+    945 cpdef _act_on_(self, x, bint self_on_left):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:3539, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs()
+   3537     id_Delete(&to_id, _ring)
+   3538     p_Delete(&_p, _ring)
+-> 3539     raise TypeError("keys do not match self's parent")
+   3540 try:
+   3541     v = parent.coerce(v)
+
+TypeError: keys do not match self's parent
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(a)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA.base_ring().order()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: parent(A)

+[?7h[?12l[?25h[?2004l[?7hMultivariate Polynomial Ring in X over Finite Field of size 5
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(A)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lA.substitute({x:x^2})[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7l{}[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^2})[?7h[?12l[?25h[?25l[?7lX^2})[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l:X^2})[?7h[?12l[?25h[?25l[?7lX:X^2})[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l{}[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A.substitute({X:X^2})

+[?7h[?12l[?25h[?2004l[?7h1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.substitute({X:X^2})[?7h[?12l[?25h[?25l[?7lparent(A)[?7h[?12l[?25h[?25l[?7lA.substitute({x:x^2})[?7h[?12l[?25h[?25l[?7l = P(1)[?7h[?12l[?25h[?25l[?7lP.<X> = PolynomialRing(GF(p), 1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lasubstitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7lz = parent(a).gens()[2][?7h[?12l[?25h[?25l[?7la.substitute({x:x^2, yy, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lz = parent(a).gens()[2][?7h[?12l[?25h[?25l[?7la.substitute({x:x^2, yy, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7lP<X> = PolynomialRing(GF(p))[?7h[?12l[?25h[?25l[?7l, 1)[?7h[?12l[?25h[?25l[?7lA = P(1)[?7h[?12l[?25h[?25l[?7l.substitute({x:x^2})[?7h[?12l[?25h[?25l[?7lparent(A)[?7h[?12l[?25h[?25l[?7lA.substitute({X:X^2})[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y = C_super.x, C_super.y[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly = C_super.x, C_super.y[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: x, y = parent(a).gens[0:1]

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [26], in <cell line: 1>()
+----> 1 x, y = parent(a).gens[Integer(0):Integer(1)]
+
+TypeError: 'builtin_function_or_method' object is not subscriptable
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y = parent(a).gens[0:1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: x, y = parent(a).gens[0:2]

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [27], in <cell line: 1>()
+----> 1 x, y = parent(a).gens[Integer(0):Integer(2)]
+
+TypeError: 'builtin_function_or_method' object is not subscriptable
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y = parent(a).gens[0:2][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[],[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: x, y = parent(a).gens[0], parent(a).gens(1)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [28], in <cell line: 1>()
+----> 1 x, y = parent(a).gens[Integer(0)], parent(a).gens(Integer(1))
+
+TypeError: 'builtin_function_or_method' object is not subscriptable
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y = parent(a).gens[0], parent(a).gens(1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([0], parent(a).gens(1)[?7h[?12l[?25h[?25l[?7l)[0], parent(a).gens(1)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: x, y = parent(a).gens()[0], parent(a).gens()[1]

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y = parent(a).gens()[0], parent(a).gens()[1][?7h[?12l[?25h[?25l[?7l[0], parent(a).gens(1)[?7h[?12l[?25h[?25l[?7l[:2][?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lA.substitute({X:X^2})[?7h[?12l[?25h[?25l[?7lparent(A)[?7h[?12l[?25h[?25l[?7lA.substitute({x:x^2})[?7h[?12l[?25h[?25l[?7l = P(1)[?7h[?12l[?25h[?25l[?7lP.<X> = PolynomialRing(GF(p), 1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lasubstitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7lsage: a.substitute({x:x^2, y:y, z[0]:x, z[1]:x})

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

+[?7h[?12l[?25h[?2004l{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
+!!! Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [31], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:26, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:15, in <module>
+
+File <string>:31, in cartier(omega)
+
+File <string>:44, in __add__(self, other)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
+    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
+    493     """
+--> 494     return self.getattr_from_category(name)
+    495 
+    496 cdef getattr_from_category(self, name):
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
+    505     else:
+    506         cls = P._abstract_element_class
+--> 507     return getattr_from_other_class(self, cls, name)
+    508 
+    509 def __dir__(self):
+
+File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
+    359     dummy_error_message.cls = type(self)
+    360     dummy_error_message.name = name
+--> 361     raise AttributeError(dummy_error_message)
+    362 attribute = <object>attr
+    363 # Check for a descriptor (__get__ in Python)
+
+AttributeError: 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular' object has no attribute 'form'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
+!!! Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [32], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:26, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:15, in <module>
+
+TypeError: cannot unpack non-iterable as_form object
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
+!!! Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+(0) * dx
+{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
+!!! Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [33], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:26, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:15, in <module>
+
+File <string>:24, in cartier(omega)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    159             print(type(C), C)
+    160             print(type(C._element_constructor), C._element_constructor)
+--> 161         raise
+    162 
+    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:842, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
+    840 if check:
+    841     try:
+--> 842         c = base_ring(c)
+    843     except TypeError:
+    844         p_Delete(&_p, _ring)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1654, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
+   1652         raise ValueError("not integral")
+   1653     if nmod_poly_degree(x._numer) > 0:
+-> 1654         raise ValueError("not constant")
+   1655 ans = IntegerMod_int.__new__(IntegerMod_int)
+   1656 ans._parent = self.codomain()
+
+ValueError: not constant
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
+num 1
+monomial 1
+(0) * dx
+{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
+num z1
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [34], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:26, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:15, in <module>
+
+File <string>:24, in cartier(omega)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    159             print(type(C), C)
+    160             print(type(C._element_constructor), C._element_constructor)
+--> 161         raise
+    162 
+    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:842, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
+    840 if check:
+    841     try:
+--> 842         c = base_ring(c)
+    843     except TypeError:
+    844         p_Delete(&_p, _ring)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1654, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
+   1652         raise ValueError("not integral")
+   1653     if nmod_poly_degree(x._numer) > 0:
+-> 1654         raise ValueError("not constant")
+   1655 ans = IntegerMod_int.__new__(IntegerMod_int)
+   1656 ans._parent = self.codomain()
+
+ValueError: not constant
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
+num 1
+monomials: [1]
+monomial 1
+(0) * dx
+{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
+num z1
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [35], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:26, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:15, in <module>
+
+File <string>:24, in cartier(omega)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    159             print(type(C), C)
+    160             print(type(C._element_constructor), C._element_constructor)
+--> 161         raise
+    162 
+    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:842, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
+    840 if check:
+    841     try:
+--> 842         c = base_ring(c)
+    843     except TypeError:
+    844         p_Delete(&_p, _ring)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1654, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
+   1652         raise ValueError("not integral")
+   1653     if nmod_poly_degree(x._numer) > 0:
+-> 1654         raise ValueError("not constant")
+   1655 ans = IntegerMod_int.__new__(IntegerMod_int)
+   1656 ans._parent = self.codomain()
+
+ValueError: not constant
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm.degree(z[1])[?7h[?12l[?25h[?25l[?7lonomials(ccc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz = parent(a).gens()[2:][?7h[?12l[?25h[?25l[?7l[0][?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: z[1]

+[?7h[?12l[?25h[?2004l[?7hz1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[1][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: z[1].monomials()

+[?7h[?12l[?25h[?2004l[?7h[z1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxyz(num).substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxyz(num).substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: Rxyz(z[1])

+[?7h[?12l[?25h[?2004l[?7hz1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
+num 1
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [39], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:26, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:15, in <module>
+
+File <string>:24, in cartier(omega)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
+    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
+    493     """
+--> 494     return self.getattr_from_category(name)
+    495 
+    496 cdef getattr_from_category(self, name):
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
+    505     else:
+    506         cls = P._abstract_element_class
+--> 507     return getattr_from_other_class(self, cls, name)
+    508 
+    509 def __dir__(self):
+
+File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
+    359     dummy_error_message.cls = type(self)
+    360     dummy_error_message.name = name
+--> 361     raise AttributeError(dummy_error_message)
+    362 attribute = <object>attr
+    363 # Check for a descriptor (__get__ in Python)
+
+AttributeError: 'sage.rings.finite_rings.integer_mod.IntegerMod_int' object has no attribute 'monomials'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
+num 1
+monomials: 1
+monomial 1
+(0) * dx
+{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
+num z1
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [40], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:26, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:15, in <module>
+
+File <string>:24, in cartier(omega)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    159             print(type(C), C)
+    160             print(type(C._element_constructor), C._element_constructor)
+--> 161         raise
+    162 
+    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:842, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
+    840 if check:
+    841     try:
+--> 842         c = base_ring(c)
+    843     except TypeError:
+    844         p_Delete(&_p, _ring)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1654, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
+   1652         raise ValueError("not integral")
+   1653     if nmod_poly_degree(x._numer) > 0:
+-> 1654         raise ValueError("not constant")
+   1655 ans = IntegerMod_int.__new__(IntegerMod_int)
+   1656 ans._parent = self.codomain()
+
+ValueError: not constant
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
+num, den 1 1
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [41], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:26, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:15, in <module>
+
+File <string>:24, in cartier(omega)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
+    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
+    493     """
+--> 494     return self.getattr_from_category(name)
+    495 
+    496 cdef getattr_from_category(self, name):
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
+    505     else:
+    506         cls = P._abstract_element_class
+--> 507     return getattr_from_other_class(self, cls, name)
+    508 
+    509 def __dir__(self):
+
+File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
+    359     dummy_error_message.cls = type(self)
+    360     dummy_error_message.name = name
+--> 361     raise AttributeError(dummy_error_message)
+    362 attribute = <object>attr
+    363 # Check for a descriptor (__get__ in Python)
+
+AttributeError: 'sage.rings.finite_rings.integer_mod.IntegerMod_int' object has no attribute 'monomials'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
+num, den 1 1
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [42], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:26, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:15, in <module>
+
+File <string>:25, in cartier(omega)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
+    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
+    493     """
+--> 494     return self.getattr_from_category(name)
+    495 
+    496 cdef getattr_from_category(self, name):
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
+    505     else:
+    506         cls = P._abstract_element_class
+--> 507     return getattr_from_other_class(self, cls, name)
+    508 
+    509 def __dir__(self):
+
+File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
+    359     dummy_error_message.cls = type(self)
+    360     dummy_error_message.name = name
+--> 361     raise AttributeError(dummy_error_message)
+    362 attribute = <object>attr
+    363 # Check for a descriptor (__get__ in Python)
+
+AttributeError: 'sage.rings.finite_rings.integer_mod.IntegerMod_int' object has no attribute 'monomials'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
+num, den 1 1
+monomials: [1]
+monomial 1
+(0) * dx
+z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
+num, den z1 1
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [43], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:26, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:15, in <module>
+
+File <string>:24, in cartier(omega)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    159             print(type(C), C)
+    160             print(type(C._element_constructor), C._element_constructor)
+--> 161         raise
+    162 
+    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:842, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
+    840 if check:
+    841     try:
+--> 842         c = base_ring(c)
+    843     except TypeError:
+    844         p_Delete(&_p, _ring)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1654, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
+   1652         raise ValueError("not integral")
+   1653     if nmod_poly_degree(x._numer) > 0:
+-> 1654         raise ValueError("not constant")
+   1655 ans = IntegerMod_int.__new__(IntegerMod_int)
+   1656 ans._parent = self.codomain()
+
+ValueError: not constant
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
+num, den 1 1
+monomials: [1]
+monomial 1
+(0) * dx
+z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
+num, den z1 1
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [44], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:26, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:15, in <module>
+
+File <string>:25, in cartier(omega)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    159             print(type(C), C)
+    160             print(type(C._element_constructor), C._element_constructor)
+--> 161         raise
+    162 
+    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:842, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
+    840 if check:
+    841     try:
+--> 842         c = base_ring(c)
+    843     except TypeError:
+    844         p_Delete(&_p, _ring)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1654, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
+   1652         raise ValueError("not integral")
+   1653     if nmod_poly_degree(x._numer) > 0:
+-> 1654         raise ValueError("not constant")
+   1655 ans = IntegerMod_int.__new__(IntegerMod_int)
+   1656 ans._parent = self.codomain()
+
+ValueError: not constant
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
+num, den 1 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+monomials: [1]
+monomial 1
+(0) * dx
+z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
+num, den z1 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [45], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:26, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:15, in <module>
+
+File <string>:25, in cartier(omega)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    159             print(type(C), C)
+    160             print(type(C._element_constructor), C._element_constructor)
+--> 161         raise
+    162 
+    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:842, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
+    840 if check:
+    841     try:
+--> 842         c = base_ring(c)
+    843     except TypeError:
+    844         p_Delete(&_p, _ring)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1654, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
+   1652         raise ValueError("not integral")
+   1653     if nmod_poly_degree(x._numer) > 0:
+-> 1654         raise ValueError("not constant")
+   1655 ans = IntegerMod_int.__new__(IntegerMod_int)
+   1656 ans._parent = self.codomain()
+
+ValueError: not constant
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
+num, den 1 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+aaa: 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+monomials: [1]
+monomial 1
+(0) * dx
+z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+{x: x, y: y, z0: z0^5 + (-x^3 - x), z1: z1^5 + (-x^2)}
+num, den z1 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [46], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:26, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:15, in <module>
+
+File <string>:25, in cartier(omega)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    159             print(type(C), C)
+    160             print(type(C._element_constructor), C._element_constructor)
+--> 161         raise
+    162 
+    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:842, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
+    840 if check:
+    841     try:
+--> 842         c = base_ring(c)
+    843     except TypeError:
+    844         p_Delete(&_p, _ring)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1654, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
+   1652         raise ValueError("not integral")
+   1653     if nmod_poly_degree(x._numer) > 0:
+-> 1654         raise ValueError("not constant")
+   1655 ans = IntegerMod_int.__new__(IntegerMod_int)
+   1656 ans._parent = self.codomain()
+
+ValueError: not constant
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
+num, den 1 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+aaa: 1 Fraction Field of Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [47], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:26, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:15, in <module>
+
+File <string>:27, in cartier(omega)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
+    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
+    493     """
+--> 494     return self.getattr_from_category(name)
+    495 
+    496 cdef getattr_from_category(self, name):
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
+    505     else:
+    506         cls = P._abstract_element_class
+--> 507     return getattr_from_other_class(self, cls, name)
+    508 
+    509 def __dir__(self):
+
+File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
+    359     dummy_error_message.cls = type(self)
+    360     dummy_error_message.name = name
+--> 361     raise AttributeError(dummy_error_message)
+    362 attribute = <object>attr
+    363 # Check for a descriptor (__get__ in Python)
+
+AttributeError: 'sage.rings.fraction_field_element.FractionFieldElement' object has no attribute 'monomials'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
+num, den 1 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+aaa: 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+monomials: [1]
+monomial 1
+(0) * dx
+z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
+num, den z1 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+aaa: z1^5 - x^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+monomials: [z1^5, x^2]
+monomial z1^5
+monomial x^2
+(0) * dx
+z1^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
+num, den z1^2 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+aaa: z1^10 - 2*x^2*z1^5 + x^4 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+monomials: [z1^10, x^2*z1^5, x^4]
+monomial z1^10
+monomial x^2*z1^5
+monomial x^4
+(1) * dx
+z1^3 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
+num, den z1^3 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+aaa: z1^15 + 2*x^2*z1^10 - 2*x^4*z1^5 - x^6 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+monomials: [z1^15, x^2*z1^10, x^4*z1^5, x^6]
+monomial z1^15
+monomial x^2*z1^10
+monomial x^4*z1^5
+monomial x^6
+(-2*z1) * dx
+z1^4 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
+num, den z1^4 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+aaa: z1^20 + x^2*z1^15 + x^4*z1^10 + x^6*z1^5 + x^8 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+monomials: [z1^20, x^2*z1^15, x^4*z1^10, x^6*z1^5, x^8]
+monomial z1^20
+monomial x^2*z1^15
+monomial x^4*z1^10
+monomial x^6*z1^5
+monomial x^8
+(z1^2) * dx
+z0 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
+num, den z0 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+aaa: z0^5 - x^3 - x Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+monomials: [z0^5, x^3, x]
+monomial z0^5
+monomial x^3
+monomial x
+(0) * dx
+z0*z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
+num, den z0*z1 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+aaa: z0^5*z1^5 - x^3*z1^5 - x^2*z0^5 - x*z1^5 + x^5 + x^3 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+monomials: [z0^5*z1^5, x^3*z1^5, x^2*z0^5, x*z1^5, x^5, x^3]
+monomial z0^5*z1^5
+monomial x^3*z1^5
+monomial x^2*z0^5
+monomial x*z1^5
+monomial x^5
+monomial x^3
+(0) * dx
+z0*z1^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
+num, den z0*z1^2 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+aaa: z0^5*z1^10 - x^3*z1^10 - 2*x^2*z0^5*z1^5 - x*z1^10 + 2*x^5*z1^5 + x^4*z0^5 + 2*x^3*z1^5 - x^7 - x^5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+monomials: [z0^5*z1^10, x^3*z1^10, x^2*z0^5*z1^5, x*z1^10, x^5*z1^5, x^4*z0^5, x^3*z1^5, x^7, x^5]
+monomial z0^5*z1^10
+monomial x^3*z1^10
+monomial x^2*z0^5*z1^5
+monomial x*z1^10
+monomial x^5*z1^5
+monomial x^4*z0^5
+monomial x^3*z1^5
+monomial x^7
+monomial x^5
+(z0) * dx
+z0*z1^3 - x*z1^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
+num, den z0*z1^3 - x*z1^2 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+aaa: z0^5*z1^15 - x^3*z1^15 + 2*x^2*z0^5*z1^10 - x*z1^15 - 2*x^5*z1^10 - 2*x^4*z0^5*z1^5 - 2*x^3*z1^10 + 2*x^7*z1^5 - x^6*z0^5 - x*z1^10 + 2*x^5*z1^5 + x^9 + 2*x^3*z1^5 + x^7 - x^5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+monomials: [z0^5*z1^15, x^3*z1^15, x^2*z0^5*z1^10, x*z1^15, x^5*z1^10, x^4*z0^5*z1^5, x^3*z1^10, x^7*z1^5, x^6*z0^5, x*z1^10, x^5*z1^5, x^9, x^3*z1^5, x^7, x^5]
+monomial z0^5*z1^15
+monomial x^3*z1^15
+monomial x^2*z0^5*z1^10
+monomial x*z1^15
+monomial x^5*z1^10
+monomial x^4*z0^5*z1^5
+monomial x^3*z1^10
+monomial x^7*z1^5
+monomial x^6*z0^5
+monomial x*z1^10
+monomial x^5*z1^5
+monomial x^9
+monomial x^3*z1^5
+monomial x^7
+monomial x^5
+(-2*z0*z1 + x) * dx
+z0*z1^4 + 2*x*z1^3 + 2*x*z0^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
+num, den z0*z1^4 + 2*x*z1^3 + 2*x*z0^2 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+aaa: z0^5*z1^20 - x^3*z1^20 + x^2*z0^5*z1^15 - x*z1^20 - x^5*z1^15 + x^4*z0^5*z1^10 - x^3*z1^15 - x^7*z1^10 + x^6*z0^5*z1^5 + 2*x*z1^15 - x^5*z1^10 - x^9*z1^5 + x^8*z0^5 - x^3*z1^10 - x^7*z1^5 - x^11 + 2*x*z0^10 + x^5*z1^5 - x^9 + x^4*z0^5 + x^2*z0^5 - x^5 + 2*x^3 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+monomials: [z0^5*z1^20, x^3*z1^20, x^2*z0^5*z1^15, x*z1^20, x^5*z1^15, x^4*z0^5*z1^10, x^3*z1^15, x^7*z1^10, x^6*z0^5*z1^5, x*z1^15, x^5*z1^10, x^9*z1^5, x^8*z0^5, x^3*z1^10, x^7*z1^5, x^11, x*z0^10, x^5*z1^5, x^9, x^4*z0^5, x^2*z0^5, x^5, x^3]
+monomial z0^5*z1^20
+monomial x^3*z1^20
+monomial x^2*z0^5*z1^15
+monomial x*z1^20
+monomial x^5*z1^15
+monomial x^4*z0^5*z1^10
+monomial x^3*z1^15
+monomial x^7*z1^10
+monomial x^6*z0^5*z1^5
+monomial x*z1^15
+monomial x^5*z1^10
+monomial x^9*z1^5
+monomial x^8*z0^5
+monomial x^3*z1^10
+monomial x^7*z1^5
+monomial x^11
+monomial x*z0^10
+monomial x^5*z1^5
+monomial x^9
+monomial x^4*z0^5
+monomial x^2*z0^5
+monomial x^5
+monomial x^3
+(z0*z1^2 - x*z1 - x + z0) * dx
+z0^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
+num, den z0^2 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+aaa: z0^10 - 2*x^3*z0^5 + x^6 - 2*x*z0^5 + 2*x^4 + x^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+monomials: [z0^10, x^3*z0^5, x^6, x*z0^5, x^4, x^2]
+monomial z0^10
+monomial x^3*z0^5
+monomial x^6
+monomial x*z0^5
+monomial x^4
+monomial x^2
+(2) * dx
+z0^2*z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
+num, den z0^2*z1 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+aaa: z0^10*z1^5 - 2*x^3*z0^5*z1^5 - x^2*z0^10 + x^6*z1^5 - 2*x*z0^5*z1^5 + 2*x^5*z0^5 + 2*x^4*z1^5 - x^8 + 2*x^3*z0^5 + x^2*z1^5 - 2*x^6 - x^4 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+monomials: [z0^10*z1^5, x^3*z0^5*z1^5, x^2*z0^10, x^6*z1^5, x*z0^5*z1^5, x^5*z0^5, x^4*z1^5, x^8, x^3*z0^5, x^2*z1^5, x^6, x^4]
+monomial z0^10*z1^5
+monomial x^3*z0^5*z1^5
+monomial x^2*z0^10
+monomial x^6*z1^5
+monomial x*z0^5*z1^5
+monomial x^5*z0^5
+monomial x^4*z1^5
+monomial x^8
+monomial x^3*z0^5
+monomial x^2*z1^5
+monomial x^6
+monomial x^4
+(2*z1 - 1) * dx
+z0^2*z1^2 - x^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
+num, den z0^2*z1^2 - x^2 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+aaa: z0^10*z1^10 - 2*x^3*z0^5*z1^10 - 2*x^2*z0^10*z1^5 + x^6*z1^10 - 2*x*z0^5*z1^10 - x^5*z0^5*z1^5 + x^4*z0^10 + 2*x^4*z1^10 - 2*x^8*z1^5 - x^3*z0^5*z1^5 - 2*x^7*z0^5 + x^2*z1^10 + x^6*z1^5 + x^10 - 2*x^5*z0^5 - 2*x^4*z1^5 + 2*x^8 + x^6 - x^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+monomials: [z0^10*z1^10, x^3*z0^5*z1^10, x^2*z0^10*z1^5, x^6*z1^10, x*z0^5*z1^10, x^5*z0^5*z1^5, x^4*z0^10, x^4*z1^10, x^8*z1^5, x^3*z0^5*z1^5, x^7*z0^5, x^2*z1^10, x^6*z1^5, x^10, x^5*z0^5, x^4*z1^5, x^8, x^6, x^2]
+monomial z0^10*z1^10
+monomial x^3*z0^5*z1^10
+monomial x^2*z0^10*z1^5
+monomial x^6*z1^10
+monomial x*z0^5*z1^10
+monomial x^5*z0^5*z1^5
+monomial x^4*z0^10
+monomial x^4*z1^10
+monomial x^8*z1^5
+monomial x^3*z0^5*z1^5
+monomial x^7*z0^5
+monomial x^2*z1^10
+monomial x^6*z1^5
+monomial x^10
+monomial x^5*z0^5
+monomial x^4*z1^5
+monomial x^8
+monomial x^6
+monomial x^2
+(z0^2 + 2*z1^2 - 2*z1) * dx
+z0^2*z1^3 - z0^4 + 2*x*z0*z1^2 - 2*x^2*z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
+num, den z0^2*z1^3 - z0^4 + 2*x*z0*z1^2 - 2*x^2*z1 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+aaa: z0^10*z1^15 - 2*x^3*z0^5*z1^15 + 2*x^2*z0^10*z1^10 + x^6*z1^15 - 2*x*z0^5*z1^15 - z0^20 + x^5*z0^5*z1^10 - 2*x^4*z0^10*z1^5 + 2*x^4*z1^15 - x^3*z0^15 + 2*x^8*z1^10 + x^3*z0^5*z1^10 - x^7*z0^5*z1^5 + x^2*z1^15 - 2*x^6*z0^10 - x*z0^15 - x^6*z1^10 + 2*x*z0^5*z1^10 - 2*x^10*z1^5 - x^5*z0^5*z1^5 + x^9*z0^5 - 2*x^4*z0^10 + x^8*z1^5 + x^3*z0^5*z1^5 - 2*x^12 - x^7*z0^5 - x^2*z0^10 - 2*x^2*z1^10 + 2*x^6*z1^5 - x^10 - x^5*z0^5 - x^4*z1^5 + x^8 - x^3*z0^5 - 2*x^2*z1^5 - x^6 + x^4 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+monomials: [z0^10*z1^15, x^3*z0^5*z1^15, x^2*z0^10*z1^10, x^6*z1^15, x*z0^5*z1^15, z0^20, x^5*z0^5*z1^10, x^4*z0^10*z1^5, x^4*z1^15, x^3*z0^15, x^8*z1^10, x^3*z0^5*z1^10, x^7*z0^5*z1^5, x^2*z1^15, x^6*z0^10, x*z0^15, x^6*z1^10, x*z0^5*z1^10, x^10*z1^5, x^5*z0^5*z1^5, x^9*z0^5, x^4*z0^10, x^8*z1^5, x^3*z0^5*z1^5, x^12, x^7*z0^5, x^2*z0^10, x^2*z1^10, x^6*z1^5, x^10, x^5*z0^5, x^4*z1^5, x^8, x^3*z0^5, x^2*z1^5, x^6, x^4]
+monomial z0^10*z1^15
+monomial x^3*z0^5*z1^15
+monomial x^2*z0^10*z1^10
+monomial x^6*z1^15
+monomial x*z0^5*z1^15
+monomial z0^20
+monomial x^5*z0^5*z1^10
+monomial x^4*z0^10*z1^5
+monomial x^4*z1^15
+monomial x^3*z0^15
+monomial x^8*z1^10
+monomial x^3*z0^5*z1^10
+monomial x^7*z0^5*z1^5
+monomial x^2*z1^15
+monomial x^6*z0^10
+monomial x*z0^15
+monomial x^6*z1^10
+monomial x*z0^5*z1^10
+monomial x^10*z1^5
+monomial x^5*z0^5*z1^5
+monomial x^9*z0^5
+monomial x^4*z0^10
+monomial x^8*z1^5
+monomial x^3*z0^5*z1^5
+monomial x^12
+monomial x^7*z0^5
+monomial x^2*z0^10
+monomial x^2*z1^10
+monomial x^6*z1^5
+monomial x^10
+monomial x^5*z0^5
+monomial x^4*z1^5
+monomial x^8
+monomial x^3*z0^5
+monomial x^2*z1^5
+monomial x^6
+monomial x^4
+(-2*z0^2*z1 + 2*z1^3 + x*z0 - 2*z0^2 - z1 + 1) * dx
+z0^2*z1^4 + z0^4*z1 + x*z0*z1^3 + x*z0^3 + x^2*z1^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
+num, den z0^2*z1^4 + z0^4*z1 + x*z0*z1^3 + x*z0^3 + x^2*z1^2 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+aaa: z0^10*z1^20 - 2*x^3*z0^5*z1^20 + x^2*z0^10*z1^15 + x^6*z1^20 - 2*x*z0^5*z1^20 + z0^20*z1^5 - 2*x^5*z0^5*z1^15 + x^4*z0^10*z1^10 + 2*x^4*z1^20 + x^3*z0^15*z1^5 + x^8*z1^15 - 2*x^3*z0^5*z1^15 - x^2*z0^20 - 2*x^7*z0^5*z1^10 + x^2*z1^20 + 2*x^6*z0^10*z1^5 + x*z0^15*z1^5 + 2*x^6*z1^15 + x*z0^5*z1^15 - x^5*z0^15 + x^10*z1^10 - 2*x^5*z0^5*z1^10 - x^9*z0^5*z1^5 + 2*x^4*z0^10*z1^5 - x^3*z0^15 + 2*x^8*z1^10 + 2*x^3*z0^5*z1^10 + 2*x^12*z1^5 + x^7*z0^5*z1^5 + x^2*z0^10*z1^5 - x^2*z1^15 + 2*x^11*z0^5 - 2*x^6*z0^10 + x*z0^15 - x^6*z1^10 + x^10*z1^5 + x^5*z0^5*z1^5 + x^4*z0^10 - 2*x^4*z1^10 - x^8*z1^5 + x^3*z0^5*z1^5 - 2*x^12 - x^7*z0^5 + 2*x^2*z0^10 + x^2*z1^10 + x^6*z1^5 - x^4*z1^5 - x^8 - 2*x^3*z0^5 + 2*x^6 - x^4 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+monomials: [z0^10*z1^20, x^3*z0^5*z1^20, x^2*z0^10*z1^15, x^6*z1^20, x*z0^5*z1^20, z0^20*z1^5, x^5*z0^5*z1^15, x^4*z0^10*z1^10, x^4*z1^20, x^3*z0^15*z1^5, x^8*z1^15, x^3*z0^5*z1^15, x^2*z0^20, x^7*z0^5*z1^10, x^2*z1^20, x^6*z0^10*z1^5, x*z0^15*z1^5, x^6*z1^15, x*z0^5*z1^15, x^5*z0^15, x^10*z1^10, x^5*z0^5*z1^10, x^9*z0^5*z1^5, x^4*z0^10*z1^5, x^3*z0^15, x^8*z1^10, x^3*z0^5*z1^10, x^12*z1^5, x^7*z0^5*z1^5, x^2*z0^10*z1^5, x^2*z1^15, x^11*z0^5, x^6*z0^10, x*z0^15, x^6*z1^10, x^10*z1^5, x^5*z0^5*z1^5, x^4*z0^10, x^4*z1^10, x^8*z1^5, x^3*z0^5*z1^5, x^12, x^7*z0^5, x^2*z0^10, x^2*z1^10, x^6*z1^5, x^4*z1^5, x^8, x^3*z0^5, x^6, x^4]
+monomial z0^10*z1^20
+monomial x^3*z0^5*z1^20
+monomial x^2*z0^10*z1^15
+monomial x^6*z1^20
+monomial x*z0^5*z1^20
+monomial z0^20*z1^5
+monomial x^5*z0^5*z1^15
+monomial x^4*z0^10*z1^10
+monomial x^4*z1^20
+monomial x^3*z0^15*z1^5
+monomial x^8*z1^15
+monomial x^3*z0^5*z1^15
+monomial x^2*z0^20
+monomial x^7*z0^5*z1^10
+monomial x^2*z1^20
+monomial x^6*z0^10*z1^5
+monomial x*z0^15*z1^5
+monomial x^6*z1^15
+monomial x*z0^5*z1^15
+monomial x^5*z0^15
+monomial x^10*z1^10
+monomial x^5*z0^5*z1^10
+monomial x^9*z0^5*z1^5
+monomial x^4*z0^10*z1^5
+monomial x^3*z0^15
+monomial x^8*z1^10
+monomial x^3*z0^5*z1^10
+monomial x^12*z1^5
+monomial x^7*z0^5*z1^5
+monomial x^2*z0^10*z1^5
+monomial x^2*z1^15
+monomial x^11*z0^5
+monomial x^6*z0^10
+monomial x*z0^15
+monomial x^6*z1^10
+monomial x^10*z1^5
+monomial x^5*z0^5*z1^5
+monomial x^4*z0^10
+monomial x^4*z1^10
+monomial x^8*z1^5
+monomial x^3*z0^5*z1^5
+monomial x^12
+monomial x^7*z0^5
+monomial x^2*z0^10
+monomial x^2*z1^10
+monomial x^6*z1^5
+monomial x^4*z1^5
+monomial x^8
+monomial x^3*z0^5
+monomial x^6
+monomial x^4
+(z0^2*z1^2 + 2*z1^4 - x*z0*z1 + 2*z0^2*z1 + z0^2 - 2*z1^2 - z1 - 1) * dx
+z0^3 - x*z1^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
+num, den z0^3 - x*z1^2 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+aaa: z0^15 + 2*x^3*z0^10 - 2*x^6*z0^5 + 2*x*z0^10 - x*z1^10 - x^9 + x^4*z0^5 + 2*x^3*z1^5 + 2*x^7 - 2*x^2*z0^5 + x^5 - x^3 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+monomials: [z0^15, x^3*z0^10, x^6*z0^5, x*z0^10, x*z1^10, x^9, x^4*z0^5, x^3*z1^5, x^7, x^2*z0^5, x^5, x^3]
+monomial z0^15
+monomial x^3*z0^10
+monomial x^6*z0^5
+monomial x*z0^10
+monomial x*z1^10
+monomial x^9
+monomial x^4*z0^5
+monomial x^3*z1^5
+monomial x^7
+monomial x^2*z0^5
+monomial x^5
+monomial x^3
+(-x + z0) * dx
+z0^3*z1 - 2*x*z1^3 + x*z0^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
+num, den z0^3*z1 - 2*x*z1^3 + x*z0^2 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+aaa: z0^15*z1^5 + 2*x^3*z0^10*z1^5 - x^2*z0^15 - 2*x^6*z0^5*z1^5 + 2*x*z0^10*z1^5 - 2*x*z1^15 - 2*x^5*z0^10 - x^9*z1^5 + x^4*z0^5*z1^5 + 2*x^8*z0^5 - 2*x^3*z0^10 + x^3*z1^10 + 2*x^7*z1^5 - 2*x^2*z0^5*z1^5 + x^11 - x^6*z0^5 + x*z0^10 + x^5*z1^5 - 2*x^9 - x^3*z1^5 + x^7 - 2*x^2*z0^5 - 2*x^5 + x^3 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+monomials: [z0^15*z1^5, x^3*z0^10*z1^5, x^2*z0^15, x^6*z0^5*z1^5, x*z0^10*z1^5, x*z1^15, x^5*z0^10, x^9*z1^5, x^4*z0^5*z1^5, x^8*z0^5, x^3*z0^10, x^3*z1^10, x^7*z1^5, x^2*z0^5*z1^5, x^11, x^6*z0^5, x*z0^10, x^5*z1^5, x^9, x^3*z1^5, x^7, x^2*z0^5, x^5, x^3]
+monomial z0^15*z1^5
+monomial x^3*z0^10*z1^5
+monomial x^2*z0^15
+monomial x^6*z0^5*z1^5
+monomial x*z0^10*z1^5
+monomial x*z1^15
+monomial x^5*z0^10
+monomial x^9*z1^5
+monomial x^4*z0^5*z1^5
+monomial x^8*z0^5
+monomial x^3*z0^10
+monomial x^3*z1^10
+monomial x^7*z1^5
+monomial x^2*z0^5*z1^5
+monomial x^11
+monomial x^6*z0^5
+monomial x*z0^10
+monomial x^5*z1^5
+monomial x^9
+monomial x^3*z1^5
+monomial x^7
+monomial x^2*z0^5
+monomial x^5
+monomial x^3
+(-x*z1 + z0*z1 - 2*x) * dx
+z0^3*z1^2 - x*z1^4 + 2*x*z0^2*z1 - 2*x^2*z0 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
+num, den z0^3*z1^2 - x*z1^4 + 2*x*z0^2*z1 - 2*x^2*z0 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+aaa: z0^15*z1^10 + 2*x^3*z0^10*z1^10 - 2*x^2*z0^15*z1^5 - 2*x^6*z0^5*z1^10 + 2*x*z0^10*z1^10 - x*z1^20 + x^5*z0^10*z1^5 + x^4*z0^15 - x^9*z1^10 + x^4*z0^5*z1^10 - x^8*z0^5*z1^5 + x^3*z0^10*z1^5 - x^3*z1^15 + 2*x^7*z0^10 + 2*x^7*z1^10 - 2*x^2*z0^5*z1^10 + 2*x^11*z1^5 - 2*x^6*z0^5*z1^5 + 2*x*z0^10*z1^5 - 2*x^10*z0^5 + 2*x^5*z0^10 + x^5*z1^10 + x^9*z1^5 - x^13 + x^8*z0^5 - 2*x^3*z0^10 - x^3*z1^10 + 2*x^7*z1^5 + x^2*z0^5*z1^5 + 2*x^11 + 2*x^6*z0^5 + x^5*z1^5 - x^9 - x^4*z0^5 + 2*x^3*z1^5 - 2*x^2*z0^5 + 2*x^3 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+monomials: [z0^15*z1^10, x^3*z0^10*z1^10, x^2*z0^15*z1^5, x^6*z0^5*z1^10, x*z0^10*z1^10, x*z1^20, x^5*z0^10*z1^5, x^4*z0^15, x^9*z1^10, x^4*z0^5*z1^10, x^8*z0^5*z1^5, x^3*z0^10*z1^5, x^3*z1^15, x^7*z0^10, x^7*z1^10, x^2*z0^5*z1^10, x^11*z1^5, x^6*z0^5*z1^5, x*z0^10*z1^5, x^10*z0^5, x^5*z0^10, x^5*z1^10, x^9*z1^5, x^13, x^8*z0^5, x^3*z0^10, x^3*z1^10, x^7*z1^5, x^2*z0^5*z1^5, x^11, x^6*z0^5, x^5*z1^5, x^9, x^4*z0^5, x^3*z1^5, x^2*z0^5, x^3]
+monomial z0^15*z1^10
+monomial x^3*z0^10*z1^10
+monomial x^2*z0^15*z1^5
+monomial x^6*z0^5*z1^10
+monomial x*z0^10*z1^10
+monomial x*z1^20
+monomial x^5*z0^10*z1^5
+monomial x^4*z0^15
+monomial x^9*z1^10
+monomial x^4*z0^5*z1^10
+monomial x^8*z0^5*z1^5
+monomial x^3*z0^10*z1^5
+monomial x^3*z1^15
+monomial x^7*z0^10
+monomial x^7*z1^10
+monomial x^2*z0^5*z1^10
+monomial x^11*z1^5
+monomial x^6*z0^5*z1^5
+monomial x*z0^10*z1^5
+monomial x^10*z0^5
+monomial x^5*z0^10
+monomial x^5*z1^10
+monomial x^9*z1^5
+monomial x^13
+monomial x^8*z0^5
+monomial x^3*z0^10
+monomial x^3*z1^10
+monomial x^7*z1^5
+monomial x^2*z0^5*z1^5
+monomial x^11
+monomial x^6*z0^5
+monomial x^5*z1^5
+monomial x^9
+monomial x^4*z0^5
+monomial x^3*z1^5
+monomial x^2*z0^5
+monomial x^3
+(z0^3 - x*z1^2 + z0*z1^2 + x*z1 - x - z0) * dx
+x Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
+num, den x 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+aaa: x Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+monomials: [x]
+monomial x
+(0) * dx
+x*z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
+num, den x*z1 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+aaa: x*z1^5 - x^3 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+monomials: [x*z1^5, x^3]
+monomial x*z1^5
+monomial x^3
+(0) * dx
+x*z0 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
+num, den x*z0 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+aaa: x*z0^5 - x^4 - x^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+monomials: [x*z0^5, x^4, x^2]
+monomial x*z0^5
+monomial x^4
+monomial x^2
+(-1) * dx
+x*z0*z1 - x^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+{x: x, y: y, z0: z0^5 - x^3 - x, z1: z1^5 - x^2}
+num, den x*z0*z1 - x^2 1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+aaa: x*z0^5*z1^5 - x^4*z1^5 - x^3*z0^5 - x^2*z1^5 + x^6 + x^4 - x^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+monomials: [x*z0^5*z1^5, x^4*z1^5, x^3*z0^5, x^2*z1^5, x^6, x^4, x^2]
+monomial x*z0^5*z1^5
+monomial x^4*z1^5
+monomial x^3*z0^5
+monomial x^2*z1^5
+monomial x^6
+monomial x^4
+monomial x^2
+(-z1 + 1) * dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+(0) * dx
+z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+(0) * dx
+z1^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+(1) * dx
+z1^3 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+(-2*z1) * dx
+z1^4 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+(z1^2) * dx
+z0 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+(0) * dx
+z0*z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+(0) * dx
+z0*z1^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+(z0) * dx
+z0*z1^3 - x*z1^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+(-2*z0*z1 + x) * dx
+z0*z1^4 + 2*x*z1^3 + 2*x*z0^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+(z0*z1^2 - x*z1 - x + z0) * dx
+z0^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+(2) * dx
+z0^2*z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+(2*z1 - 1) * dx
+z0^2*z1^2 - x^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+(z0^2 + 2*z1^2 - 2*z1) * dx
+z0^2*z1^3 - z0^4 + 2*x*z0*z1^2 - 2*x^2*z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+(-2*z0^2*z1 + 2*z1^3 + x*z0 - 2*z0^2 - z1 + 1) * dx
+z0^2*z1^4 + z0^4*z1 + x*z0*z1^3 + x*z0^3 + x^2*z1^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+(z0^2*z1^2 + 2*z1^4 - x*z0*z1 + 2*z0^2*z1 + z0^2 - 2*z1^2 - z1 - 1) * dx
+z0^3 - x*z1^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+(-x + z0) * dx
+z0^3*z1 - 2*x*z1^3 + x*z0^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+(-x*z1 + z0*z1 - 2*x) * dx
+z0^3*z1^2 - x*z1^4 + 2*x*z0^2*z1 - 2*x^2*z0 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+(z0^3 - x*z1^2 + z0*z1^2 + x*z1 - x - z0) * dx
+x Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+(0) * dx
+x*z1 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+(0) * dx
+x*z0 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+(-1) * dx
+x*z0*z1 - x^2 Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 5
+(-z1 + 1) * dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(0) * dx
+(0) * dx
+(1) * dx
+(-2*z1) * dx
+(z1^2) * dx
+(0) * dx
+(0) * dx
+(z0) * dx
+(-2*z0*z1 + x) * dx
+(z0*z1^2 - x*z1 - x + z0) * dx
+(2) * dx
+(2*z1 - 1) * dx
+(z0^2 + 2*z1^2 - 2*z1) * dx
+(-2*z0^2*z1 + 2*z1^3 + x*z0 - 2*z0^2 - z1 + 1) * dx
+(z0^2*z1^2 + 2*z1^4 - x*z0*z1 + 2*z0^2*z1 + z0^2 - 2*z1^2 - z1 - 1) * dx
+(-x + z0) * dx
+(-x*z1 + z0*z1 - 2*x) * dx
+(z0^3 - x*z1^2 + z0*z1^2 + x*z1 - x - z0) * dx
+(0) * dx
+(0) * dx
+(-1) * dx
+(-z1 + 1) * dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.substitute({X:X^2})[?7h[?12l[?25h[?25l[?7lS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis()

+[?7h[?12l[?25h[?2004l[?7h[(1) * dx,
+ (z1) * dx,
+ (z1^2) * dx,
+ (z1^3) * dx,
+ (z1^4) * dx,
+ (z0) * dx,
+ (z0*z1) * dx,
+ (z0*z1^2) * dx,
+ (z0*z1^3 - x*z1^2) * dx,
+ (z0*z1^4 + 2*x*z1^3 + 2*x*z0^2) * dx,
+ (z0^2) * dx,
+ (z0^2*z1) * dx,
+ (z0^2*z1^2 - x^2) * dx,
+ (z0^2*z1^3 - z0^4 + 2*x*z0*z1^2 - 2*x^2*z1) * dx,
+ (z0^2*z1^4 + z0^4*z1 + x*z0*z1^3 + x*z0^3 + x^2*z1^2) * dx,
+ (z0^3 - x*z1^2) * dx,
+ (z0^3*z1 - 2*x*z1^3 + x*z0^2) * dx,
+ (z0^3*z1^2 - x*z1^4 + 2*x*z0^2*z1 - 2*x^2*z0) * dx,
+ (x) * dx,
+ (x*z1) * dx,
+ (x*z0) * dx,
+ (x*z0*z1 - x^2) * dx]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(0) * dx
+(0) * dx
+(1) * dx
+(-2*z1) * dx
+(z1^2) * dx
+(0) * dx
+(0) * dx
+(z0) * dx
+(-2*z0*z1 + x) * dx
+(z0*z1^2 - x*z1 - x + z0) * dx
+(2) * dx
+(2*z1 - 1) * dx
+(z0^2 + 2*z1^2 - 2*z1) * dx
+(-2*z0^2*z1 + 2*z1^3 + x*z0 - 2*z0^2 - z1 + 1) * dx
+(z0^2*z1^2 + 2*z1^4 - x*z0*z1 + 2*z0^2*z1 + z0^2 - 2*z1^2 - z1 - 1) * dx
+(-x + z0) * dx
+(-x*z1 + z0*z1 - 2*x) * dx
+(z0^3 - x*z1^2 + z0*z1^2 + x*z1 - x - z0) * dx
+(0) * dx
+(0) * dx
+(-1) * dx
+(-z1 + 1) * dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(0) * dx
+(0) * dx
+(1) * dx
+(-2*z1) * dx
+(z1^2) * dx
+(0) * dx
+(0) * dx
+(z0) * dx
+(-2*z0*z1 + x) * dx
+(z0*z1^2 - x*z1 - x + z0) * dx
+(2) * dx
+(2*z1 - 1) * dx
+(z0^2 + 2*z1^2 - 2*z1) * dx
+(-2*z0^2*z1 + 2*z1^3 + x*z0 - 2*z0^2 - z1 + 1) * dx
+(z0^2*z1^2 + 2*z1^4 - x*z0*z1 + 2*z0^2*z1 + z0^2 - 2*z1^2 - z1 - 1) * dx
+(-x + z0) * dx
+(-x*z1 + z0*z1 - 2*x) * dx
+(z0^3 - x*z1^2 + z0*z1^2 + x*z1 - x - z0) * dx
+(0) * dx
+(0) * dx
+(-1) * dx
+(-z1 + 1) * dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
+[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
+[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
+[0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
+[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
+[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
+[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
+[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
+[0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
+[0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 4 4 0 0]
+[2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
+[4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
+[0 3 2 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
+[1 4 0 2 0 0 0 0 0 0 3 3 0 0 0 0 0 0 0 0 1 0]
+[4 4 3 0 2 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 4]
+[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0]
+[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 3 4 0 0]
+[0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 1 0 0 4 1 0 0]
+[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
+[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
+[4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
+[1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus()

+[?7h[?12l[?25h[?2004l[?7h22
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[9].form.monomials()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lsage: bbb

+[?7h[?12l[?25h[?2004l[?7h[(1) * dx,
+ (z1) * dx,
+ (z1^2) * dx,
+ (z1^3) * dx,
+ (z1^4) * dx,
+ (z0) * dx,
+ (z0*z1) * dx,
+ (z0*z1^2) * dx,
+ (z0*z1^3 - x*z1^2) * dx,
+ (z0*z1^4 + 2*x*z1^3 + 2*x*z0^2) * dx,
+ (z0^2) * dx,
+ (z0^2*z1) * dx,
+ (z0^2*z1^2 - x^2) * dx,
+ (z0^2*z1^3 - z0^4 + 2*x*z0*z1^2 - 2*x^2*z1) * dx,
+ (z0^2*z1^4 + z0^4*z1 + x*z0*z1^3 + x*z0^3 + x^2*z1^2) * dx,
+ (z0^3 - x*z1^2) * dx,
+ (z0^3*z1 - 2*x*z1^3 + x*z0^2) * dx,
+ (z0^3*z1^2 - x*z1^4 + 2*x*z0^2*z1 - 2*x^2*z0) * dx,
+ (x) * dx,
+ (x*z1) * dx,
+ (x*z0) * dx,
+ (x*z0*z1 - x^2) * dx]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l.function[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[9].form.monomials()[?7h[?12l[?25h[?25l[?7l0catier().coordinates()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].cartier().coordinates()[?7h[?12l[?25h[?25l[?7lsage: bbb[0].cartier().coordinates()

+[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[0 0 1 0 0 0 0 0 0 0 2 4 0 1 4 0 0 0 0 0 4 1]
+[0 0 0 3 0 0 0 0 0 0 0 2 3 4 4 0 0 0 0 0 0 4]
+[0 0 0 0 1 0 0 0 0 0 0 0 2 0 3 0 0 0 0 0 0 0]
+[0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0]
+[0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0]
+[0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 4 0 0 0 0]
+[0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 1 0 0 0 0 0]
+[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0]
+[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
+[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
+[0 0 0 0 0 0 0 0 0 0 0 0 1 3 1 0 0 0 0 0 0 0]
+[0 0 0 0 0 0 0 0 0 0 0 0 0 3 2 0 0 0 0 0 0 0]
+[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
+[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
+[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
+[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
+[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
+[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
+[0 0 0 0 0 0 0 0 1 4 0 0 0 0 0 4 3 4 0 0 0 0]
+[0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 4 1 0 0 0 0]
+[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
+[0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l4
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [59], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:26, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:13, in <module>
+
+File <string>:17, in cartier_matrix(AS)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
+    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
+    493     """
+--> 494     return self.getattr_from_category(name)
+    495 
+    496 cdef getattr_from_category(self, name):
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
+    505     else:
+    506         cls = P._abstract_element_class
+--> 507     return getattr_from_other_class(self, cls, name)
+    508 
+    509 def __dir__(self):
+
+File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
+    359     dummy_error_message.cls = type(self)
+    360     dummy_error_message.name = name
+--> 361     raise AttributeError(dummy_error_message)
+    362 attribute = <object>attr
+    363 # Check for a descriptor (__get__ in Python)
+
+AttributeError: 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular' object has no attribute 'genus'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS

+[?7h[?12l[?25h[?2004l[?7h(Z/p)-cover of Superelliptic curve with the equation y^2 = x^3 + 1 over Finite Field of size 5 with the equation:
+ z^5 - z = x
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.genus()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus()

+[?7h[?12l[?25h[?2004l[?7h7
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l4
+4
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltests.sage')[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

+ tensor        tests.sage    text3d       

+ tensor_signed tetrahedron                

+ tests         text                       

+

+ [?7h[?12l[?25h[?25l[?7l(sts.sage')

+

+

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

+[?7h[?12l[?25h[?2004lCartier test:
+Increase precision.
+Increase precision.
+---------------------------------------------------------------------------
+IndexError                                Traceback (most recent call last)
+Input In [63], in <cell line: 1>()
+----> 1 load('tests.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:23, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:12, in <module>
+
+File <string>:155, in cartier_matrix(self)
+
+File /ext/sage/9.7/src/sage/matrix/matrix0.pyx:1504, in sage.matrix.matrix0.Matrix.__setitem__()
+   1502         raise IndexError("value does not have the right number of columns")
+   1503     elif single_col and row_list_len != len(value_list):
+-> 1504         raise IndexError("value does not have the right number of rows")
+   1505 else:
+   1506     if row_list_len != len(value_list):
+
+IndexError: value does not have the right number of rows
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

+[?7h[?12l[?25h[?2004lCartier test:
+Increase precision.
+Increase precision.
+---------------------------------------------------------------------------
+IndexError                                Traceback (most recent call last)
+Input In [64], in <cell line: 1>()
+----> 1 load('tests.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:23, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:12, in <module>
+
+File <string>:155, in cartier_matrix(self)
+
+File /ext/sage/9.7/src/sage/matrix/matrix0.pyx:1504, in sage.matrix.matrix0.Matrix.__setitem__()
+   1502         raise IndexError("value does not have the right number of columns")
+   1503     elif single_col and row_list_len != len(value_list):
+-> 1504         raise IndexError("value does not have the right number of rows")
+   1505 else:
+   1506     if row_list_len != len(value_list):
+
+IndexError: value does not have the right number of rows
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7load('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

+[?7h[?12l[?25h[?2004lCartier test:
+True
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l = E.frobenius_matrix_hypellfrob()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lQ[?7h[?12l[?25h[?25l[?7lQ[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[],[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: M = matrix(QQ, [[1, 1], [0, 0]])

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM = matrix(QQ, [[1, 1], [0, 0]])[?7h[?12l[?25h[?25l[?7l.jordan_form()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: M.image()

+[?7h[?12l[?25h[?2004l[?7hVector space of degree 2 and dimension 1 over Rational Field
+Basis matrix:
+[1 1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM.image()[?7h[?12l[?25h[?25l[?7lsage: M

+[?7h[?12l[?25h[?2004l[?7h[1 1]
+[0 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l.image()[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: M.kernel()

+[?7h[?12l[?25h[?2004l[?7hVector space of degree 2 and dimension 1 over Rational Field
+Basis matrix:
+[0 1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM.kernel()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7limag()[?7h[?12l[?25h[?25l[?7lmage()[?7h[?12l[?25h[?25l[?7lsage: M.image()

+[?7h[?12l[?25h[?2004l[?7hVector space of degree 2 and dimension 1 over Rational Field
+Basis matrix:
+[1 1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM.image()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltimage()[?7h[?12l[?25h[?25l[?7lrimage()[?7h[?12l[?25h[?25l[?7laimage()[?7h[?12l[?25h[?25l[?7lnimage()[?7h[?12l[?25h[?25l[?7lsimage()[?7h[?12l[?25h[?25l[?7lpimage()[?7h[?12l[?25h[?25l[?7loimage()[?7h[?12l[?25h[?25l[?7lsimage()[?7h[?12l[?25h[?25l[?7leimage()[?7h[?12l[?25h[?25l[?7l(image()[?7h[?12l[?25h[?25l[?7l()image()[?7h[?12l[?25h[?25l[?7l().image()[?7h[?12l[?25h[?25l[?7lsage: M.transpose().image()

+[?7h[?12l[?25h[?2004l[?7hVector space of degree 2 and dimension 1 over Rational Field
+Basis matrix:
+[1 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM.transpose().image()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: M.transpose().image().basis()

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

+[?7h[?12l[?25h[?2004lTrue True True
+[
+RModule M of dimension 3 over GF(2)
+]
+{
+[0 0 1]
+[1 1 1]
+[1 0 0],
+[1 1 1]
+[0 0 1]
+[0 1 0]
+}
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

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

+[?7h[?12l[?25h[?2004lTrue True True
+[
+RModule M of dimension 3 over GF(2)
+]
+{
+[0 0 1]
+[1 1 1]
+[1 0 0],
+[1 1 1]
+[0 0 1]
+[0 1 0]
+}
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.height[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 + x + 1, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x^3 + x + 1, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupe[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRax.<x> = PolynomialRing(Ra)[?7h[?12l[?25h[?25l[?7l.<x> =PolynomialRing(QQ)[?7h[?12l[?25h[?25l[?7l<[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l>[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= PolynomialRing(QQ)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lG)[?7h[?12l[?25h[?25l[?7lF)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: R.<x> = PolynomialRing(GF(3))

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR.<x> = PolynomialRing(GF(3))[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.height[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 + x + 1, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l superelliptic(x^3 + x + 1, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l-, 2)[?7h[?12l[?25h[?25l[?7lx, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l x, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 - x, 2)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.height[?7h[?12l[?25h[?25l[?7ldx.cartier()[?7h[?12l[?25h[?25l[?7le_rham_basis()[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

+[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in range(1, n):[?7h[?12l[?25h[?25l[?7l =a[n]*x^ + a[0][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic_function(C, 1/x)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in range(1, n):[?7h[?12l[?25h[?25l[?7l =a[n]*x^ + a[0][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic_function(C, 1/x)[?7h[?12l[?25h[?25l[?7luperelliptic_function(C, 1/x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7ly)[?7h[?12l[?25h[?25l[?7l/)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: f = superelliptic_function(C, y/x)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [5], in <cell line: 1>()
+----> 1 f = superelliptic_function(C, y/x)
+
+NameError: name 'y' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = superelliptic_function(C, y/x)[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lR.<x> = PoynomalRing(GF(3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l,> = PolynomialRing(GF(3)[?7h[?12l[?25h[?25l[?7l > = PolynomialRing(GF(3)[?7h[?12l[?25h[?25l[?7ly> = PolynomialRing(GF(3)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx.<x, y> = PolynomialRing(GF(3)[?7h[?12l[?25h[?25l[?7ly.<x, y> = PolynomialRing(GF(3)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: Rxy.<x, y> = PolynomialRing(GF(3), 2)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxy.<x, y> = PolynomialRing(GF(3), 2)[?7h[?12l[?25h[?25l[?7lf = superelliptic_functio(C, y/x)[?7h[?12l[?25h[?25l[?7lsage: f = superelliptic_function(C, y/x)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldimension_of_RHS = p*gY + (len(list_of_m) - 1)*(p-1) + sum(sum(i*alpha(i, m, p) for i in range(1, p)) for m in list_of_m)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = superelliptic_function(C, y/x)[?7h[?12l[?25h[?25l[?7l.substitute({x:x^2, y:x, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f.diffn()

+[?7h[?12l[?25h[?2004l[?7h((-x^2 - 1)/(x*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.expnsion_at_infty()[1][?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().pth_root()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l/*(C.dx)[?7h[?12l[?25h[?25l[?7lC*(C.dx)[?7h[?12l[?25h[?25l[?7l.*(C.dx)[?7h[?12l[?25h[?25l[?7ly*(C.dx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y*(C.dx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()*(C.dx)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.x)^2/(C.y)*(C.dx)

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

+[?7h[?12l[?25h[?2004l[?7ht^-4 + 1 + O(t^6)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

+

+

+ [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lsage: C.

+[?7h[?12l[?25h[?2004l  Input In [11]
+    C.
+      ^
+SyntaxError: invalid syntax
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l/C.x).coordinates()[?7h[?12l[?25h[?25l[?7l/C.x).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).cordinates()[?7h[?12l[?25h[?25l[?7l).cordinates()[?7h[?12l[?25h[?25l[?7l).cordinates()[?7h[?12l[?25h[?25l[?7l).cordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()^.cordinates()[?7h[?12l[?25h[?25l[?7l(.cordinates()[?7h[?12l[?25h[?25l[?7l().cordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l-).cordinates()[?7h[?12l[?25h[?25l[?7l1).cordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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.y)^(-1)

+[?7h[?12l[?25h[?2004l[?7h(1/(x^3 + 2*x))*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y)^(-1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((C.y)^(-1)).diffn()

+[?7h[?12l[?25h[?2004l[?7h((-1)/(x^3*y - x*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x[?7h[?12l[?25h[?25l[?7l1C.x[?7h[?12l[?25h[?25l[?7l/C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((1/C.x).difn()[?7h[?12l[?25h[?25l[?7l)(1/C.x).difn()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l/C.x).difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x).difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l^).difn()[?7h[?12l[?25h[?25l[?7l).difn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()^.difn()[?7h[?12l[?25h[?25l[?7l(.difn()[?7h[?12l[?25h[?25l[?7l().difn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l-).difn()[?7h[?12l[?25h[?25l[?7l1).difn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()).difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l((C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l*((C.x)^(-1)).difn()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC)*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7lx)*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7l.)*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7l)*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7l.)*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7lx)*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()^*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7l(*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7l-*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7l2*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7l()*(C.x)^(-1).difn()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.x)^(-2)*((C.x)^(-1)).diffn()

+[?7h[?12l[?25h[?2004l[?7h((-1)/x^4) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.diffn()[?7h[?12l[?25h[?25l[?7lfff.cartier()[?7h[?12l[?25h[?25l[?7l = x^3 - x + 2[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ff = superellitptic_function(C, y/x^2)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [15], in <cell line: 1>()
+----> 1 ff = superellitptic_function(C, y/x**Integer(2))
+
+NameError: name 'superellitptic_function' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = superellitptic_function(C, y/x^2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lptic_function(C, y/x^2)[?7h[?12l[?25h[?25l[?7lsage: ff = superelliptic_function(C, y/x^2)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = superelliptic_function(C, y/x^2)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.dicriminant()%8[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ff.diffn()

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

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [1], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:25, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:43, in <module>
+
+File <string>:75, in coordinates(self)
+
+File <string>:113, in degree_of_rational_fctn(f, F)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:554, in PolynomialRing(base_ring, *args, **kwds)
+     52 r"""
+     53 Return the globally unique univariate or multivariate polynomial
+     54 ring with given properties and variable name or names.
+   (...)
+    551     TypeError: unable to convert 'x' to an integer
+    552 """
+    553 if not ring.is_Ring(base_ring):
+--> 554     raise TypeError("base_ring {!r} must be a ring".format(base_ring))
+    556 n = -1  # Unknown number of variables
+    557 names = None  # Unknown variable names
+
+TypeError: base_ring 3 must be a ring
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [2], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:25, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:11, in <module>
+
+TypeError: bad operand type for unary -: 'superelliptic_function'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [3], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:25, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:11, in <module>
+
+File /ext/sage/9.7/src/sage/rings/integer.pyx:1769, in sage.rings.integer.Integer.__add__()
+   1767         return y
+   1768 
+-> 1769     return coercion_model.bin_op(left, right, operator.add)
+   1770 
+   1771 cpdef _add_(self, right):
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op()
+   1246     # We should really include the underlying error.
+   1247     # This causes so much headache.
+-> 1248     raise bin_op_exception(op, x, y)
+   1249 
+   1250 cpdef canonical_coercion(self, x, y):
+
+TypeError: unsupported operand parent(s) for +: 'Integer Ring' and '<class '__main__.superelliptic_function'>'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: C.one

+[?7h[?12l[?25h[?2004l[?7h1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.one[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: loa

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [5], in <cell line: 1>()
+----> 1 loa
+
+NameError: name 'loa' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lloa[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lloa[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx
+t^-40 + O(t^-30)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx
+t^-40 + O(t^-30)
+---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [8], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:25, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:16, in <module>
+
+NameError: name 'quo_rem' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx
+t^-40 + O(t^-30)
+(2*x^15 + 2*x^13 + x^12 + x^10 + 2*x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2, 2*x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx
+t^-40 + O(t^-30)
+(2*x^15 + 2*x^13 + x^12 + x^10 + 2*x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2, 2*x)
+(2*x^12 + x^10 + x^9 + x^8 + 2*x^7 + x^6 + x^5 + x^4 + x^2 + 2*x + 1, x^2 + x + 2)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx
+t^-40 + O(t^-30)
+[2, 1, x^2 + 2*x + 2, 2*x^2 + 2*x + 1, x^2 + 1, x^2 + x + 2, 2*x]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: omega

+[?7h[?12l[?25h[?2004l[?7h((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.one[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.xpansion_at_infty()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)^(-2)*((C.x)^(-1)).diffn()[?7h[?12l[?25h[?25l[?7l)^(-2)*((C.x)^(-1)).diffn()[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()y[?7h[?12l[?25h[?25l[?7l(y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: (C.x)^(11)/(C.y)^3*C.dx

+[?7h[?12l[?25h[?2004l[?7h(x^11/y^3) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x)^(11)/(C.y)^3*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x)^(1)/(C.y)^3*C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((C.x)^(11)/(C.y)^3*C.dx).expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7h2*t^-40 + O(t^-30)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x)^(11)/(C.y)^3*C.dx).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x)^(11)/(C.y)^3*C.dx[?7h[?12l[?25h[?25l[?7lomega[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lomega[?7h[?12l[?25h[?25l[?7l(C.x)^(11)/(C.y)^3*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x)^(11)/(C.y)^3*C.dx).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo((C.x)^(1)/(C.y)^3*C.dx)[?7h[?12l[?25h[?25l[?7lm((C.x)^(1)/(C.y)^3*C.dx)[?7h[?12l[?25h[?25l[?7l1((C.x)^(1)/(C.y)^3*C.dx)[?7h[?12l[?25h[?25l[?7l ((C.x)^(1)/(C.y)^3*C.dx)[?7h[?12l[?25h[?25l[?7l=((C.x)^(1)/(C.y)^3*C.dx)[?7h[?12l[?25h[?25l[?7l ((C.x)^(1)/(C.y)^3*C.dx)[?7h[?12l[?25h[?25l[?7lsage: om1 = ((C.x)^(11)/(C.y)^3*C.dx)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = ((C.x)^(11)/(C.y)^3*C.dx)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: om1.is_regular_on_U

+ om1.is_regular_on_U0    

+ om1.is_regular_on_Uinfty

+

+

+ [?7h[?12l[?25h[?25l[?7l0

+ om1.is_regular_on_U0    

+

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

+

+

+[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.is_regular_on_U0()

+[?7h[?12l[?25h[?2004l[?7h1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+ [?7h[?12l[?25h[?25l[?7lom1.is_regular_on_U0()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: om1

+[?7h[?12l[?25h[?2004l[?7h(x^11/y^3) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

+ [?7h[?12l[?25h[?25l[?7lom1[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.is_regular_on_U0()[?7h[?12l[?25h[?25l[?7lj[?7h[?12l[?25h[?25l[?7lth_component[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.jth_component(0)

+[?7h[?12l[?25h[?2004l[?7h0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.jth_component(0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om1.jth_component(1)

+[?7h[?12l[?25h[?2004l[?7h0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.jth_component(1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7lsage: om1.jth_component(2)

+[?7h[?12l[?25h[?2004l[?7h0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.jth_component(2)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.cartier()

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

+[?7h[?12l[?25h[?2004l[?7h(x^11/y^3) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.cartier()[?7h[?12l[?25h[?25l[?7ljth_component(2)[?7h[?12l[?25h[?25l[?7lth_component(2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7lsage: om1.jth_component(3)

+[?7h[?12l[?25h[?2004l[?7hx^11
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y = parent(a).gens()[0], parent(a).gens()[1][?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l11.[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: x^11.quo_rem(x^3 - x)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [24], in <cell line: 1>()
+----> 1 x**Integer(11).quo_rem(x**Integer(3) - x)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_template.pxi:592, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_template.__pow__()
+    590 cdef long e
+    591 try:
+--> 592     e = ee
+    593 except OverflowError:
+    594     return Polynomial.__pow__(self, ee, modulus)
+
+TypeError: an integer is required
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx^11.quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^1.quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(11).quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: (x^11).quo_rem(x^3 - x)

+[?7h[?12l[?25h[?2004l[?7h(x^8 + x^6 + x^4 + x^2 + 1, x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = Ra.gens()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc_expansion[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(x^11, x^3 - x)

+[?7h[?12l[?25h[?2004l[?7h[x^2, 0, x^2 + 1, x]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.one[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lheight[?7h[?12l[?25h[?25l[?7lolomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx
+t^-40 + O(t^-30)
+[2, 1, x^2 + 2*x + 2, 2*x^2 + 2*x + 1, x^2 + 1, x^2 + x + 2, 2*x]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

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

+[?7h[?12l[?25h[?2004l[?7h(Z/p)-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equation:
+ z^3 - z = x^4
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.genus()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.cartier_matrix()

+[?7h[?12l[?25h[?2004l[?7h[0 0 0]
+[0 0 0]
+[0 0 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cartier_matrix()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: (AS.x)^(-1)*AS.dx

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

+[?7h[?12l[?25h[?2004l[?7h(1/x) * dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.diffn()[?7h[?12l[?25h[?25l[?7lor  i range(1, n):[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: for b in AS.holomorphic_differentials_basis():

+....: [?7h[?12l[?25h[?25l[?7lprint(ffff.cartier())[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:     print(b.cartier())

+....: [?7h[?12l[?25h[?25l[?7lsage: for b in AS.holomorphic_differentials_basis():

+....:     print(b.cartier())

+....: 

+[?7h[?12l[?25h[?2004l(0) * dx
+(0) * dx
+(0) * dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cartier_matrix()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcartier_matrix()[?7h[?12l[?25h[?25l[?7lsage: AS.cartier_matrix()

+[?7h[?12l[?25h[?2004l[?7h[0 0 0 1]
+[0 0 0 0]
+[0 2 0 0]
+[0 0 0 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cartier_matrix()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lker[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lel[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lccc.monomials()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr_kernel[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: cartier_kernel(AS)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [36], in <cell line: 1>()
+----> 1 cartier_kernel(AS)
+
+File <string>:16, in cartier_kernel(C, prec)
+
+TypeError: as_cover.cartier_matrix() got an unexpected keyword argument 'prec'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cartier_matrix()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcartier_matrix()[?7h[?12l[?25h[?25l[?7lsage: AS.cartier_matrix()

+[?7h[?12l[?25h[?2004l[?7h[0 0 0 1]
+[0 0 0 0]
+[0 2 0 0]
+[0 0 0 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcartier_kernel(AS)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ltier_kernel(AS)[?7h[?12l[?25h[?25l[?7lsage: cartier_kernel(AS)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [39], in <cell line: 1>()
+----> 1 cartier_kernel(AS)
+
+File <string>:24, in cartier_kernel(C, prec)
+
+File <string>:23, in __add__(self, other)
+
+AttributeError: 'as_form' object has no attribute 'function'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcartier_kernel(AS)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ltier_kernel(AS)[?7h[?12l[?25h[?25l[?7lsage: cartier_kernel(AS)

+[?7h[?12l[?25h[?2004l[?7h[(1) * dx, (x) * dx]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcartier_kernel(AS)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lier_kernel(AS)[?7h[?12l[?25h[?25l[?7lsage: cartier_kernel(AS)

+[?7h[?12l[?25h[?2004l[?7h[(1) * dx, (x) * dx]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcartier_kernel(AS)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lier_kernel(AS)[?7h[?12l[?25h[?25l[?7lsage: cartier_kernel(AS)

+[?7h[?12l[?25h[?2004l[?7h[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[(1) * dx, (x) * dx, (x^3) * dx]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[(1) * dx, (x) * dx, (x^3) * dx]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[(1) * dx, (x) * dx, (x^3) * dx]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[(1) * dx, (x^2 + z0) * dx, (x) * dx, (x^3) * dx]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ltess.sage')[?7h[?12l[?25h[?25l[?7l(ests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

+[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx]
+superelliptic p rank test:
+---------------------------------------------------------------------------
+KeyError                                  Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/structure/category_object.pyx:839, in sage.structure.category_object.CategoryObject.getattr_from_category()
+    838 try:
+--> 839     return self.__cached_methods[name]
+    840 except KeyError:
+
+KeyError: 'p'
+
+During handling of the above exception, another exception occurred:
+
+AttributeError                            Traceback (most recent call last)
+Input In [51], in <cell line: 1>()
+----> 1 load('tests.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:7, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:5, in <module>
+
+File /ext/sage/9.7/src/sage/structure/category_object.pyx:833, in sage.structure.category_object.CategoryObject.__getattr__()
+    831         AttributeError: 'PrimeNumbers_with_category' object has no attribute 'sadfasdf'
+    832     """
+--> 833     return self.getattr_from_category(name)
+    834 
+    835 cdef getattr_from_category(self, name):
+
+File /ext/sage/9.7/src/sage/structure/category_object.pyx:848, in sage.structure.category_object.CategoryObject.getattr_from_category()
+    846     cls = self._category.parent_class
+    847 
+--> 848 attr = getattr_from_other_class(self, cls, name)
+    849 self.__cached_methods[name] = attr
+    850 return attr
+
+File /ext/sage/9.7/src/sage/cpython/getattr.pyx:356, in sage.cpython.getattr.getattr_from_other_class()
+    354     dummy_error_message.cls = type(self)
+    355     dummy_error_message.name = name
+--> 356     raise AttributeError(dummy_error_message)
+    357 cdef PyObject* attr = instance_getattr(cls, name)
+    358 if attr is NULL:
+
+AttributeError: 'HyperellipticCurve_FiniteField_with_category' object has no attribute 'p'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

+[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx]
+superelliptic p rank test:
+2
+---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [52], in <cell line: 1>()
+----> 1 load('tests.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:7, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:6, in <module>
+
+NameError: name 'superelliptic_curve' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l;[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

+[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx]
+superelliptic p rank test:
+2
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [53], in <cell line: 1>()
+----> 1 load('tests.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:7, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:7, in <module>
+
+File <string>:170, in p_rank(self)
+
+File /ext/sage/9.7/src/sage/matrix/special.py:922, in identity_matrix(ring, n, sparse)
+    920     n = ring
+    921     ring = ZZ
+--> 922 return matrix_space.MatrixSpace(ring, n, n, sparse)(1)
+
+File /ext/sage/9.7/src/sage/misc/classcall_metaclass.pyx:320, in sage.misc.classcall_metaclass.ClasscallMetaclass.__call__()
+    318 """
+    319 if cls.classcall is not None:
+--> 320     return cls.classcall(cls, *args, **kwds)
+    321 else:
+    322     # Fast version of type.__call__(cls, *args, **kwds)
+
+File /ext/sage/9.7/src/sage/matrix/matrix_space.py:561, in MatrixSpace.__classcall__(cls, base_ring, nrows, ncols, sparse, implementation, **kwds)
+    516 """
+    517 Normalize the arguments to call the ``__init__`` constructor.
+    518 
+   (...)
+    558     False
+    559 """
+    560 if base_ring not in _Rings:
+--> 561     raise TypeError("base_ring (=%s) must be a ring"%base_ring)
+    562 nrows = int(nrows)
+    563 if ncols is None:
+
+TypeError: base_ring (=3) must be a ring
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx^11.quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: x

+[?7h[?12l[?25h[?2004l[?7hx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprint(f^2)[?7h[?12l[?25h[?25l[?7larent(A)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: parent(x)

+[?7h[?12l[?25h[?2004l[?7hUnivariate Polynomial Ring in x over Finite Field of size 67
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l?superelliptic_cech[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lsage: ?superelliptic

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+OSError                                   Traceback (most recent call last)
+Input In [56], in <cell line: 1>()
+----> 1 get_ipython().run_line_magic('pinfo', 'superelliptic')
+
+File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:2305, in InteractiveShell.run_line_magic(self, magic_name, line, _stack_depth)
+   2303     kwargs['local_ns'] = self.get_local_scope(stack_depth)
+   2304 with self.builtin_trap:
+-> 2305     result = fn(*args, **kwargs)
+   2306 return result
+
+File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/magics/namespace.py:58, in NamespaceMagics.pinfo(self, parameter_s, namespaces)
+     56     self.psearch(oname)
+     57 else:
+---> 58     self.shell._inspect('pinfo', oname, detail_level=detail_level,
+     59                         namespaces=namespaces)
+
+File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:1685, in InteractiveShell._inspect(self, meth, oname, namespaces, **kw)
+   1683     pmethod(info.obj, oname, formatter)
+   1684 elif meth == 'pinfo':
+-> 1685     pmethod(
+   1686         info.obj,
+   1687         oname,
+   1688         formatter,
+   1689         info,
+   1690         enable_html_pager=self.enable_html_pager,
+   1691         **kw,
+   1692     )
+   1693 else:
+   1694     pmethod(info.obj, oname)
+
+File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/oinspect.py:698, in Inspector.pinfo(self, obj, oname, formatter, info, detail_level, enable_html_pager, omit_sections)
+    665 def pinfo(
+    666     self,
+    667     obj,
+   (...)
+    673     omit_sections=(),
+    674 ):
+    675     """Show detailed information about an object.
+    676 
+    677     Optional arguments:
+   (...)
+    696     - omit_sections: set of section keys and titles to omit
+    697     """
+--> 698     info = self._get_info(
+    699         obj, oname, formatter, info, detail_level, omit_sections=omit_sections
+    700     )
+    701     if not enable_html_pager:
+    702         del info['text/html']
+
+File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/oinspect.py:591, in Inspector._get_info(self, obj, oname, formatter, info, detail_level, omit_sections)
+    571 def _get_info(
+    572     self, obj, oname="", formatter=None, info=None, detail_level=0, omit_sections=()
+    573 ):
+    574     """Retrieve an info dict and format it.
+    575 
+    576     Parameters
+   (...)
+    588         Titles or keys to omit from output (can be set, tuple, etc., anything supporting `in`)
+    589     """
+--> 591     info = self.info(obj, oname=oname, info=info, detail_level=detail_level)
+    593     _mime = {
+    594         'text/plain': [],
+    595         'text/html': '',
+    596     }
+    598     def append_field(bundle, title:str, key:str, formatter=None):
+
+File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/oinspect.py:762, in Inspector.info(self, obj, oname, info, detail_level)
+    760             ds += "\nDocstring:\n" + obj.__doc__
+    761 else:
+--> 762     ds = getdoc(obj)
+    763     if ds is None:
+    764         ds = '<no docstring>'
+
+File /ext/sage/9.7/src/sage/misc/lazy_import.pyx:391, in sage.misc.lazy_import.LazyImport.__call__()
+    389         True
+    390     """
+--> 391     return self.get_object()(*args, **kwds)
+    392 
+    393 def __repr__(self):
+
+File /ext/sage/9.7/src/sage/misc/sageinspect.py:2107, in sage_getdoc(obj, obj_name, embedded)
+   2105 r = sage_getdoc_original(obj)
+   2106 s = sage.misc.sagedoc.format(r, embedded=embedded)
+-> 2107 f = sage_getfile(obj)
+   2108 if f and os.path.exists(f):
+   2109     from sage.doctest.control import skipfile
+
+File /ext/sage/9.7/src/sage/misc/sageinspect.py:1414, in sage_getfile(obj)
+   1412 # No go? fall back to inspect.
+   1413 try:
+-> 1414     sourcefile = inspect.getabsfile(obj)
+   1415 except TypeError: # this happens for Python builtins
+   1416     return ''
+
+File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/inspect.py:844, in getabsfile(object, _filename)
+    839 """Return an absolute path to the source or compiled file for an object.
+    840 
+    841 The idea is for each object to have a unique origin, so this routine
+    842 normalizes the result as much as possible."""
+    843 if _filename is None:
+--> 844     _filename = getsourcefile(object) or getfile(object)
+    845 return os.path.normcase(os.path.abspath(_filename))
+
+File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/inspect.py:817, in getsourcefile(object)
+    813 def getsourcefile(object):
+    814     """Return the filename that can be used to locate an object's source.
+    815     Return None if no way can be identified to get the source.
+    816     """
+--> 817     filename = getfile(object)
+    818     all_bytecode_suffixes = importlib.machinery.DEBUG_BYTECODE_SUFFIXES[:]
+    819     all_bytecode_suffixes += importlib.machinery.OPTIMIZED_BYTECODE_SUFFIXES[:]
+
+File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/inspect.py:785, in getfile(object)
+    783             return module.__file__
+    784         if object.__module__ == '__main__':
+--> 785             raise OSError('source code not available')
+    786     raise TypeError('{!r} is a built-in class'.format(object))
+    787 if ismethod(object):
+
+OSError: source code not available
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lstr(E.local_data(2))[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lsage: superelliptic

+ superelliptic          superelliptic_drw_form

+ superelliptic/         superelliptic_form    

+ superelliptic_cech     superelliptic_function

+

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

+ superelliptic         

+

+

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

+

+

+

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

+ superelliptic          superelliptic_drw_form

+ superelliptic/         superelliptic_form    

+ superelliptic_cech     superelliptic_function[?7h[?12l[?25h[?25l[?7ll

+

+

+[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupe[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

+[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx]
+superelliptic p rank test:
+2
+[ 0 39  0]
+[19  0 29]
+[ 0 21  0]
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [57], in <cell line: 1>()
+----> 1 load('tests.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:7, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:8, in <module>
+
+File <string>:170, in p_rank(self)
+
+File /ext/sage/9.7/src/sage/matrix/special.py:922, in identity_matrix(ring, n, sparse)
+    920     n = ring
+    921     ring = ZZ
+--> 922 return matrix_space.MatrixSpace(ring, n, n, sparse)(1)
+
+File /ext/sage/9.7/src/sage/misc/classcall_metaclass.pyx:320, in sage.misc.classcall_metaclass.ClasscallMetaclass.__call__()
+    318 """
+    319 if cls.classcall is not None:
+--> 320     return cls.classcall(cls, *args, **kwds)
+    321 else:
+    322     # Fast version of type.__call__(cls, *args, **kwds)
+
+File /ext/sage/9.7/src/sage/matrix/matrix_space.py:561, in MatrixSpace.__classcall__(cls, base_ring, nrows, ncols, sparse, implementation, **kwds)
+    516 """
+    517 Normalize the arguments to call the ``__init__`` constructor.
+    518 
+   (...)
+    558     False
+    559 """
+    560 if base_ring not in _Rings:
+--> 561     raise TypeError("base_ring (=%s) must be a ring"%base_ring)
+    562 nrows = int(nrows)
+    563 if ncols is None:
+
+TypeError: base_ring (=3) must be a ring
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cartier_matrix()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.one[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.genus()

+[?7h[?12l[?25h[?2004l[?7h3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lisinstance(C_super.x, superelliptic_function)[?7h[?12l[?25h[?25l[?7lid[?7h[?12l[?25h[?25l[?7lide[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: identity_matrix(3)

+[?7h[?12l[?25h[?2004l[?7h[1 0 0]
+[0 1 0]
+[0 0 1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

+[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx]
+superelliptic p rank test:
+2
+[ 0 39  0]
+[19  0 29]
+[ 0 21  0]
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [60], in <cell line: 1>()
+----> 1 load('tests.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:7, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:8, in <module>
+
+File /ext/sage/9.7/src/sage/matrix/special.py:922, in identity_matrix(ring, n, sparse)
+    920     n = ring
+    921     ring = ZZ
+--> 922 return matrix_space.MatrixSpace(ring, n, n, sparse)(1)
+
+File /ext/sage/9.7/src/sage/misc/classcall_metaclass.pyx:320, in sage.misc.classcall_metaclass.ClasscallMetaclass.__call__()
+    318 """
+    319 if cls.classcall is not None:
+--> 320     return cls.classcall(cls, *args, **kwds)
+    321 else:
+    322     # Fast version of type.__call__(cls, *args, **kwds)
+
+File /ext/sage/9.7/src/sage/matrix/matrix_space.py:561, in MatrixSpace.__classcall__(cls, base_ring, nrows, ncols, sparse, implementation, **kwds)
+    516 """
+    517 Normalize the arguments to call the ``__init__`` constructor.
+    518 
+   (...)
+    558     False
+    559 """
+    560 if base_ring not in _Rings:
+--> 561     raise TypeError("base_ring (=%s) must be a ring"%base_ring)
+    562 nrows = int(nrows)
+    563 if ncols is None:
+
+TypeError: base_ring (=2*x^18 + x^15 + x^14 + x^11) must be a ring
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lidentity_matrix(3)[?7h[?12l[?25h[?25l[?7lid[?7h[?12l[?25h[?25l[?7lide[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ltity_matrix(3)[?7h[?12l[?25h[?25l[?7lsage: identity_matrix(3)

+[?7h[?12l[?25h[?2004l[?7h[1 0 0]
+[0 1 0]
+[0 0 1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgX = (two_gX_minus_2+2)/2[?7h[?12l[?25h[?25l[?7lsage: g

+[?7h[?12l[?25h[?2004l[?7h2*x^18 + x^15 + x^14 + x^11
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lhight[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.genus()

+[?7h[?12l[?25h[?2004l[?7h3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

+[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx]
+superelliptic p rank test:
+2
+[ 0 39  0]
+[19  0 29]
+[ 0 21  0]
+[1 0 0]
+[0 1 0]
+[0 0 1]
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [64], in <cell line: 1>()
+----> 1 load('tests.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:7, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:9, in <module>
+
+File <string>:170, in p_rank(self)
+
+File /ext/sage/9.7/src/sage/matrix/special.py:922, in identity_matrix(ring, n, sparse)
+    920     n = ring
+    921     ring = ZZ
+--> 922 return matrix_space.MatrixSpace(ring, n, n, sparse)(1)
+
+File /ext/sage/9.7/src/sage/misc/classcall_metaclass.pyx:320, in sage.misc.classcall_metaclass.ClasscallMetaclass.__call__()
+    318 """
+    319 if cls.classcall is not None:
+--> 320     return cls.classcall(cls, *args, **kwds)
+    321 else:
+    322     # Fast version of type.__call__(cls, *args, **kwds)
+
+File /ext/sage/9.7/src/sage/matrix/matrix_space.py:561, in MatrixSpace.__classcall__(cls, base_ring, nrows, ncols, sparse, implementation, **kwds)
+    516 """
+    517 Normalize the arguments to call the ``__init__`` constructor.
+    518 
+   (...)
+    558     False
+    559 """
+    560 if base_ring not in _Rings:
+--> 561     raise TypeError("base_ring (=%s) must be a ring"%base_ring)
+    562 nrows = int(nrows)
+    563 if ncols is None:
+
+TypeError: base_ring (=3) must be a ring
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

+[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx]
+superelliptic p rank test:
+2
+[66 39  0]
+[19 66 29]
+[ 0 21 66]
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [65], in <cell line: 1>()
+----> 1 load('tests.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:7, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:8, in <module>
+
+File <string>:170, in p_rank(self)
+
+File /ext/sage/9.7/src/sage/matrix/special.py:922, in identity_matrix(ring, n, sparse)
+    920     n = ring
+    921     ring = ZZ
+--> 922 return matrix_space.MatrixSpace(ring, n, n, sparse)(1)
+
+File /ext/sage/9.7/src/sage/misc/classcall_metaclass.pyx:320, in sage.misc.classcall_metaclass.ClasscallMetaclass.__call__()
+    318 """
+    319 if cls.classcall is not None:
+--> 320     return cls.classcall(cls, *args, **kwds)
+    321 else:
+    322     # Fast version of type.__call__(cls, *args, **kwds)
+
+File /ext/sage/9.7/src/sage/matrix/matrix_space.py:561, in MatrixSpace.__classcall__(cls, base_ring, nrows, ncols, sparse, implementation, **kwds)
+    516 """
+    517 Normalize the arguments to call the ``__init__`` constructor.
+    518 
+   (...)
+    558     False
+    559 """
+    560 if base_ring not in _Rings:
+--> 561     raise TypeError("base_ring (=%s) must be a ring"%base_ring)
+    562 nrows = int(nrows)
+    563 if ncols is None:
+
+TypeError: base_ring (=3) must be a ring
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

+[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx]
+superelliptic p rank test:
+2
+[66 39  0]
+[19 66 29]
+[ 0 21 66]
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [66], in <cell line: 1>()
+----> 1 load('tests.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:7, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:8, in <module>
+
+File <string>:170, in p_rank(self)
+
+File /ext/sage/9.7/src/sage/matrix/special.py:922, in identity_matrix(ring, n, sparse)
+    920     n = ring
+    921     ring = ZZ
+--> 922 return matrix_space.MatrixSpace(ring, n, n, sparse)(1)
+
+File /ext/sage/9.7/src/sage/misc/classcall_metaclass.pyx:320, in sage.misc.classcall_metaclass.ClasscallMetaclass.__call__()
+    318 """
+    319 if cls.classcall is not None:
+--> 320     return cls.classcall(cls, *args, **kwds)
+    321 else:
+    322     # Fast version of type.__call__(cls, *args, **kwds)
+
+File /ext/sage/9.7/src/sage/matrix/matrix_space.py:561, in MatrixSpace.__classcall__(cls, base_ring, nrows, ncols, sparse, implementation, **kwds)
+    516 """
+    517 Normalize the arguments to call the ``__init__`` constructor.
+    518 
+   (...)
+    558     False
+    559 """
+    560 if base_ring not in _Rings:
+--> 561     raise TypeError("base_ring (=%s) must be a ring"%base_ring)
+    562 nrows = int(nrows)
+    563 if ncols is None:
+
+TypeError: base_ring (=3) must be a ring
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l?superelliptic[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lid[?7h[?12l[?25h[?25l[?7lide[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: ?identity_matrix

+[?7h[?12l[?25h[?2004l[?1049h[?1h=
Signature:      identity_matrix(ring, n=0, sparse=False)
+Docstring:     
+   This function is available as identity_matrix(...) and
+   matrix.identity(...).
+
+   Return the n x n identity matrix over the given ring.
+
+   The default ring is the integers.
+
+   EXAMPLES:
+
+      sage: M = identity_matrix(QQ, 2); M
+      [1 0]
+      [0 1]
+      sage: M.parent()
+      Full MatrixSpace of 2 by 2 dense matrices over Rational Field
+      sage: M = identity_matrix(2); M
+      [1 0]
+      [0 1]
+      sage: M.parent()
+      Full MatrixSpace of 2 by 2 dense matrices over Integer Ring
+      sage: M.is_mutable()
+      True
+      sage: M = identity_matrix(3, sparse=True); M
+      [1 0 0]
+      [0 1 0]
+:
      [0 0 1]
+:
      sage: M.parent()
+:
      Full MatrixSpace of 3 by 3 sparse matrices over Integer Ring
+:
      sage: M.is_mutable()
+:
      True
+:
Init docstring: Initialize self.  See help(type(self)) for accurate signature.
+:
File:           /ext/sage/9.7/src/sage/matrix/special.py
+:
Type:           function
+:

(END)

(END)

(END)

(END)
M   The default ring is the integers.
+M
+M   Return the n x n identity matrix over the given ring.
+M
+M   matrix.identity(...).
+M   This function is available as identity_matrix(...) and
+MDocstring:     
+MSignature:      identity_matrix(ring, n=0, sparse=False)
+
:
 ::ww
:
      [0 0 1]
+:
 ::qq
[?1l>[?1049l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

+[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx]
+superelliptic p rank test:
+2
+[66 39  0]
+[19 66 29]
+[ 0 21 66]
+0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.a_number()

+[?7h[?12l[?25h[?2004l[?7h1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lX[?7h[?12l[?25h[?25l[?7lsage: X

+[?7h[?12l[?25h[?2004l[?7hHyperelliptic Curve over Finite Field of size 67 defined by y^2 = x^7 + x^3 + x
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lX[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lnumber[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: X.a_number()

+[?7h[?12l[?25h[?2004l[?7h1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('tests.sage')

+[?7h[?12l[?25h[?2004l[(1) * dx, (z0) * dx, (x) * dx, (x^3) * dx]
+a-number test:
+True
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7lini.sage')[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l(t.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [73], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:25, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:10, in <module>
+
+TypeError: 'function' object cannot be interpreted as an integer
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [74], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:25, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:12, in <module>
+
+File /ext/sage/9.7/src/sage/misc/functional.py:639, in symbolic_prod(expression, *args, **kwds)
+    637 from .misc_c import prod as c_prod
+    638 if hasattr(expression, 'prod'):
+--> 639     return expression.prod(*args, **kwds)
+    640 elif len(args) <= 1:
+    641     return c_prod(expression, *args)
+
+TypeError: Monoids.ParentMethods.prod() takes 2 positional arguments but 7 were given
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [75], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:25, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:12, in <module>
+
+File /ext/sage/9.7/src/sage/misc/functional.py:639, in symbolic_prod(expression, *args, **kwds)
+    637 from .misc_c import prod as c_prod
+    638 if hasattr(expression, 'prod'):
+--> 639     return expression.prod(*args, **kwds)
+    640 elif len(args) <= 1:
+    641     return c_prod(expression, *args)
+
+TypeError: Monoids.ParentMethods.prod() takes 2 positional arguments but 7 were given
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [76], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:25, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:12, in <module>
+
+File /ext/sage/9.7/src/sage/misc/functional.py:639, in symbolic_prod(expression, *args, **kwds)
+    637 from .misc_c import prod as c_prod
+    638 if hasattr(expression, 'prod'):
+--> 639     return expression.prod(*args, **kwds)
+    640 elif len(args) <= 1:
+    641     return c_prod(expression, *args)
+
+TypeError: Monoids.ParentMethods.prod() takes 2 positional arguments but 7 were given
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [77], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:25, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:12, in <module>
+
+File /ext/sage/9.7/src/sage/misc/functional.py:639, in symbolic_prod(expression, *args, **kwds)
+    637 from .misc_c import prod as c_prod
+    638 if hasattr(expression, 'prod'):
+--> 639     return expression.prod(*args, **kwds)
+    640 elif len(args) <= 1:
+    641     return c_prod(expression, *args)
+
+TypeError: Monoids.ParentMethods.prod() takes 2 positional arguments but 7 were given
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(0, 0, 0, 0, 0, 0, 0)
+(0, 0, 0, 0, 0, 0, 0) x^7
+x^7
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [78], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:25, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:23, in <module>
+
+AttributeError: 'as_cover' object has no attribute 'a_number'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(0, 0, 0, 0, 0, 0, 0)
+(0, 0, 0, 0, 0, 0, 0) x^7
+x^7
+x^7 -2
+(0, 0, 0, 0, 0, 0, 1)
+(0, 0, 0, 0, 0, 0, 1) x^7
+x^7
+x^7 -2
+(0, 0, 0, 0, 0, 0, 2)
+(0, 0, 0, 0, 0, 0, 2) x^7
+x^7
+x^7 -2
+(0, 0, 0, 0, 0, 1, 0)
+(0, 0, 0, 0, 0, 1, 0) x^7
+x^7 + x^5
+x^7 + x^5 -3
+(0, 0, 0, 0, 0, 1, 1)
+(0, 0, 0, 0, 0, 1, 1) x^7
+x^7 + x^5
+x^7 + x^5 -3
+(0, 0, 0, 0, 0, 1, 2)
+(0, 0, 0, 0, 0, 1, 2) x^7
+x^7 + x^5
+x^7 + x^5 -3
+(0, 0, 0, 0, 0, 2, 0)
+(0, 0, 0, 0, 0, 2, 0) x^7
+x^7 + 2*x^5
+x^7 + 2*x^5 -3
+(0, 0, 0, 0, 0, 2, 1)
+(0, 0, 0, 0, 0, 2, 1) x^7
+x^7 + 2*x^5
+x^7 + 2*x^5 -3
+(0, 0, 0, 0, 0, 2, 2)
+(0, 0, 0, 0, 0, 2, 2) x^7
+x^7 + 2*x^5
+x^7 + 2*x^5 -3
+(0, 0, 0, 0, 1, 0, 0)
+(0, 0, 0, 0, 1, 0, 0) x^7
+x^7 + x^4
+x^7 + x^4 -2
+(0, 0, 0, 0, 1, 0, 1)
+(0, 0, 0, 0, 1, 0, 1) x^7
+x^7 + x^4
+x^7 + x^4 -2
+(0, 0, 0, 0, 1, 0, 2)
+(0, 0, 0, 0, 1, 0, 2) x^7
+x^7 + x^4
+x^7 + x^4 -2
+(0, 0, 0, 0, 1, 1, 0)
+(0, 0, 0, 0, 1, 1, 0) x^7
+x^7 + x^5 + x^4
+x^7 + x^5 + x^4 -3
+(0, 0, 0, 0, 1, 1, 1)
+(0, 0, 0, 0, 1, 1, 1) x^7
+x^7 + x^5 + x^4
+^Csage/rings/polynomial/polynomial_zmod_flint.pyx:7: DeprecationWarning: invalid escape sequence '\Z'
+  """
+sage/rings/polynomial/polynomial_zmod_flint.pyx:7: DeprecationWarning: invalid escape sequence '\Z'
+  """
+---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [79], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:25, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:22, in <module>
+
+File <string>:44, in __init__(self, C, list_of_fcts, prec)
+
+File <string>:167, in artin_schreier_transform(power_series, prec)
+
+File <string>:12, in new_reverse(power_series, prec)
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1831, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
+   1829 if x:
+   1830     raise ValueError("must not specify %s keyword and positional argument" % name)
+-> 1831 a = self(kwds[name])
+   1832 del kwds[name]
+   1833 try:
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1852, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
+   1850         x = x[0]
+   1851 
+-> 1852     return self.__u(*x)*(x[0]**self.__n)
+   1853 
+   1854 def __pari__(self):
+
+File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:365, in sage.rings.power_series_poly.PowerSeries_poly.__call__()
+    363         x[0] = a
+    364         x = tuple(x)
+--> 365     return self.__f(x)
+    366 
+    367 def _unsafe_mutate(self, i, value):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zmod_flint.pyx:332, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint.__call__()
+    330             nmod_poly_compose(&t.x, &self.x, &y.x)
+    331             return t
+--> 332     return Polynomial.__call__(self, *x, **kwds)
+    333 
+    334 @coerce_binop
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:898, in sage.rings.polynomial.polynomial_element.Polynomial.__call__()
+    896             return result
+    897         pol._compiled = CompiledPolynomialFunction(pol.list())
+--> 898     return pol._compiled.eval(a)
+    899 
+    900 def compose_trunc(self, Polynomial other, long n):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:125, in sage.rings.polynomial.polynomial_compiled.CompiledPolynomialFunction.eval()
+    123 cdef object temp
+    124 try:
+--> 125     pd_eval(self._dag, x, self._coeffs)  #see further down
+    126     temp = self._dag.value               #for an explanation
+    127     pd_clean(self._dag)                  #of these 3 lines
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
+    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
+    352     if pd.value is None:
+--> 353         pd.eval(vars, coeffs)
+    354     pd.hits += 1
+    355 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
+    505 
+    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
+--> 507         pd_eval(self.left, vars, coeffs)
+    508         pd_eval(self.right, vars, coeffs)
+    509         self.value = self.left.value * self.right.value + coeffs[self.index]
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
+    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
+    352     if pd.value is None:
+--> 353         pd.eval(vars, coeffs)
+    354     pd.hits += 1
+    355 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
+    505 
+    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
+--> 507         pd_eval(self.left, vars, coeffs)
+    508         pd_eval(self.right, vars, coeffs)
+    509         self.value = self.left.value * self.right.value + coeffs[self.index]
+
+    [... skipping similar frames: sage.rings.polynomial.polynomial_compiled.pd_eval at line 353 (42 times), sage.rings.polynomial.polynomial_compiled.abc_pd.eval at line 507 (41 times)]
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
+    505 
+    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
+--> 507         pd_eval(self.left, vars, coeffs)
+    508         pd_eval(self.right, vars, coeffs)
+    509         self.value = self.left.value * self.right.value + coeffs[self.index]
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
+    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
+    352     if pd.value is None:
+--> 353         pd.eval(vars, coeffs)
+    354     pd.hits += 1
+    355 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:509, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
+    507 pd_eval(self.left, vars, coeffs)
+    508 pd_eval(self.right, vars, coeffs)
+--> 509 self.value = self.left.value * self.right.value + coeffs[self.index]
+    510 pd_clean(self.left)
+    511 pd_clean(self.right)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__()
+   1512 cdef int cl = classify_elements(left, right)
+   1513 if HAVE_SAME_PARENT(cl):
+-> 1514     return (<Element>left)._mul_(right)
+   1515 if BOTH_ARE_ELEMENT(cl):
+   1516     return coercion_model.bin_op(left, right, mul)
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:913, in sage.rings.laurent_series_ring_element.LaurentSeries._mul_()
+    911 cdef LaurentSeries right = <LaurentSeries>right_r
+    912 return type(self)(self._parent,
+--> 913                   self.__u * right.__u,
+    914                   self.__n + right.__n)
+    915 
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__()
+   1512 cdef int cl = classify_elements(left, right)
+   1513 if HAVE_SAME_PARENT(cl):
+-> 1514     return (<Element>left)._mul_(right)
+   1515 if BOTH_ARE_ELEMENT(cl):
+   1516     return coercion_model.bin_op(left, right, mul)
+
+File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:540, in sage.rings.power_series_poly.PowerSeries_poly._mul_()
+    538 """
+    539 prec = self._mul_prec(right_r)
+--> 540 return PowerSeries_poly(self._parent,
+    541                         self.__f * (<PowerSeries_poly>right_r).__f,
+    542                         prec=prec,
+
+File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:44, in sage.rings.power_series_poly.PowerSeries_poly.__init__()
+     42     ValueError: series has negative valuation
+     43 """
+---> 44 R = parent._poly_ring()
+     45 if isinstance(f, Element):
+     46     if (<Element>f)._parent is R:
+
+File /ext/sage/9.7/src/sage/rings/power_series_ring.py:961, in PowerSeriesRing_generic._poly_ring(self)
+    958         pass
+    959     return False
+--> 961 def _poly_ring(self):
+    962     """
+    963     Return the underlying polynomial ring used to represent elements of
+    964     this power series ring.
+   (...)
+    970         Univariate Polynomial Ring in t over Integer Ring
+    971     """
+    972     return self.__poly_ring
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lx^7
+x^7 -2
+x^7
+x^7 -2
+x^7
+x^7 -2
+x^7 + x^5
+x^7 + x^5 -3
+x^7 + x^5
+^C---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [80], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:25, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File <string>:313, in a_number(self)
+
+File <string>:155, in cartier_matrix(self, prec)
+
+File <string>:70, in coordinates(self, basis)
+
+File <string>:137, in holomorphic_differentials_basis(self, threshold)
+
+File <string>:423, in holomorphic_combinations(S)
+
+File <string>:45, in __add__(self, other)
+
+File <string>:10, in __init__(self, C, g)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:647, in PolynomialRing(base_ring, *args, **kwds)
+    644         raise TypeError("variable names specified twice inconsistently: %r and %r" % (names, kwnames))
+    646 if multivariate or len(names) != 1:
+--> 647     return _multi_variate(base_ring, names, **kwds)
+    648 else:
+    649     return _single_variate(base_ring, names, **kwds)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:762, in _multi_variate(base_ring, names, sparse, order, implementation)
+    760 from sage.rings.polynomial.term_order import TermOrder
+    761 n = len(names)
+--> 762 order = TermOrder(order, n)
+    764 # "implementation" must be last
+    765 key = [base_ring, names, n, order, implementation]
+
+File /ext/sage/9.7/src/sage/rings/polynomial/term_order.py:796, in TermOrder.__init__(self, name, n, force)
+    794         self._singular_str = singular_name_mapping.get(name,name)
+    795         self._macaulay2_str = macaulay2_name_mapping.get(name,name)
+--> 796         self._magma_str = magma_name_mapping.get(name,name)
+    797 else: # len(block_names) > 1, and hence block order represented by a string
+    798     length = 0
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lx^7
+x^7 4
+x^7
+x^7 4
+x^7
+x^7 4
+x^7 + x^5
+x^7 + x^5 3
+x^7 + x^5
+x^7 + x^5 3
+x^7 + x^5
+x^7 + x^5 3
+x^7 + 2*x^5
+x^7 + 2*x^5 3
+x^7 + 2*x^5
+x^7 + 2*x^5 3
+x^7 + 2*x^5
+x^7 + 2*x^5 3
+x^7 + x^4
+x^7 + x^4 4
+x^7 + x^4
+x^7 + x^4 4
+x^7 + x^4
+x^7 + x^4 4
+x^7 + x^5 + x^4
+x^7 + x^5 + x^4 3
+x^7 + x^5 + x^4
+x^7 + x^5 + x^4 3
+x^7 + x^5 + x^4
+^C---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [81], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:25, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File <string>:313, in a_number(self)
+
+File <string>:155, in cartier_matrix(self, prec)
+
+File <string>:139, in cartier(self)
+
+File <string>:60, in cartier(self)
+
+File <string>:15, in __add__(self, other)
+
+File <string>:217, in reduction(C, g)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:649, in PolynomialRing(base_ring, *args, **kwds)
+    647     return _multi_variate(base_ring, names, **kwds)
+    648 else:
+--> 649     return _single_variate(base_ring, names, **kwds)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:683, in _single_variate(base_ring, name, sparse, implementation, order)
+    681 # "implementation" must be last
+    682 key = [base_ring, name, sparse, implementation]
+--> 683 R = _get_from_cache(key)
+    684 if R is not None:
+    685     return R
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:668, in _get_from_cache(key)
+    666 def _get_from_cache(key):
+    667     key = tuple(key)
+--> 668     return _cache.get(key)
+
+File /ext/sage/9.7/src/sage/misc/weak_dict.pyx:662, in sage.misc.weak_dict.WeakValueDictionary.get()
+    660 
+    661         """
+--> 662         cdef PyObject * wr = PyDict_GetItemWithError(self, k)
+    663         if wr == NULL:
+    664             return d
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:783, in FractionField_generic.__hash__(self)
+    769 """
+    770 Compute the hash of ``self``.
+    771 
+   (...)
+    779     True
+    780 """
+    781 # to avoid having exactly the same hash as the base ring,
+    782 # we change this hash using a random number
+--> 783 return hash(self._R) ^ 147068341996611
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lx^7 4
+x^7 4
+x^7 4
+x^7 + x^5 3
+x^7 + x^5 3
+x^7 + x^5 3
+x^7 + 2*x^5 3
+x^7 + 2*x^5 3
+x^7 + 2*x^5 3
+x^7 + x^4 4
+x^7 + x^4 4
+x^7 + x^4 4
+x^7 + x^5 + x^4 3
+x^7 + x^5 + x^4 3
+x^7 + x^5 + x^4 3
+x^7 + 2*x^5 + x^4 3
+x^7 + 2*x^5 + x^4 3
+x^7 + 2*x^5 + x^4 3
+x^7 + 2*x^4 4
+x^7 + 2*x^4 4
+x^7 + 2*x^4 4
+x^7 + x^5 + 2*x^4 3
+x^7 + x^5 + 2*x^4 3
+x^7 + x^5 + 2*x^4 3
+x^7 + 2*x^5 + 2*x^4 3
+x^7 + 2*x^5 + 2*x^4 3
+x^7 + 2*x^5 + 2*x^4 3
+x^7 4
+x^7 4
+x^7 4
+x^7 + x^5 3
+x^7 + x^5 3
+x^7 + x^5 3
+x^7 + 2*x^5 3
+x^7 + 2*x^5 3
+x^7 + 2*x^5 3
+x^7 + x^4 4
+x^7 + x^4 4
+x^7 + x^4 4
+x^7 + x^5 + x^4 3
+x^7 + x^5 + x^4 3
+x^7 + x^5 + x^4 3
+x^7 + 2*x^5 + x^4 3
+x^7 + 2*x^5 + x^4 3
+x^7 + 2*x^5 + x^4 3
+x^7 + 2*x^4 4
+x^7 + 2*x^4 4
+x^7 + 2*x^4 4
+x^7 + x^5 + 2*x^4 3
+x^7 + x^5 + 2*x^4 3
+x^7 + x^5 + 2*x^4 3
+x^7 + 2*x^5 + 2*x^4 3
+x^7 + 2*x^5 + 2*x^4 3
+x^7 + 2*x^5 + 2*x^4 3
+x^7 4
+x^7 4
+x^7 4
+x^7 + x^5 3
+x^7 + x^5 3
+x^7 + x^5 3
+x^7 + 2*x^5 3
+x^7 + 2*x^5 3
+x^7 + 2*x^5 3
+x^7 + x^4 4
+x^7 + x^4 4
+x^7 + x^4 4
+x^7 + x^5 + x^4 3
+x^7 + x^5 + x^4 3
+x^7 + x^5 + x^4 3
+x^7 + 2*x^5 + x^4 3
+x^7 + 2*x^5 + x^4 3
+x^7 + 2*x^5 + x^4 3
+x^7 + 2*x^4 4
+x^7 + 2*x^4 4
+x^7 + 2*x^4 4
+x^7 + x^5 + 2*x^4 3
+x^7 + x^5 + 2*x^4 3
+x^7 + x^5 + 2*x^4 3
+x^7 + 2*x^5 + 2*x^4 3
+x^7 + 2*x^5 + 2*x^4 3
+x^7 + 2*x^5 + 2*x^4 3
+x^7 + x^2 4
+x^7 + x^2 4
+x^7 + x^2 4
+x^7 + x^5 + x^2 3
+x^7 + x^5 + x^2 3
+x^7 + x^5 + x^2 3
+x^7 + 2*x^5 + x^2 3
+x^7 + 2*x^5 + x^2 3
+x^7 + 2*x^5 + x^2 3
+x^7 + x^4 + x^2 4
+x^7 + x^4 + x^2 4
+x^7 + x^4 + x^2 4
+x^7 + x^5 + x^4 + x^2 3
+x^7 + x^5 + x^4 + x^2 3
+x^7 + x^5 + x^4 + x^2 3
+x^7 + 2*x^5 + x^4 + x^2 3
+x^7 + 2*x^5 + x^4 + x^2 3
+x^7 + 2*x^5 + x^4 + x^2 3
+x^7 + 2*x^4 + x^2 4
+x^7 + 2*x^4 + x^2 4
+x^7 + 2*x^4 + x^2 4
+x^7 + x^5 + 2*x^4 + x^2 3
+x^7 + x^5 + 2*x^4 + x^2 3
+x^7 + x^5 + 2*x^4 + x^2 3
+x^7 + 2*x^5 + 2*x^4 + x^2 3
+x^7 + 2*x^5 + 2*x^4 + x^2 3
+x^7 + 2*x^5 + 2*x^4 + x^2 3
+x^7 + x^2 4
+x^7 + x^2 4
+x^7 + x^2 4
+x^7 + x^5 + x^2 3
+x^7 + x^5 + x^2 3
+x^7 + x^5 + x^2 3
+x^7 + 2*x^5 + x^2 3
+x^7 + 2*x^5 + x^2 3
+x^7 + 2*x^5 + x^2 3
+x^7 + x^4 + x^2 4
+x^7 + x^4 + x^2 4
+x^7 + x^4 + x^2 4
+x^7 + x^5 + x^4 + x^2 3
+x^7 + x^5 + x^4 + x^2 3
+x^7 + x^5 + x^4 + x^2 3
+x^7 + 2*x^5 + x^4 + x^2 3
+x^7 + 2*x^5 + x^4 + x^2 3
+x^7 + 2*x^5 + x^4 + x^2 3
+x^7 + 2*x^4 + x^2 4
+x^7 + 2*x^4 + x^2 4
+x^7 + 2*x^4 + x^2 4
+x^7 + x^5 + 2*x^4 + x^2 3
+x^7 + x^5 + 2*x^4 + x^2 3
+x^7 + x^5 + 2*x^4 + x^2 3
+x^7 + 2*x^5 + 2*x^4 + x^2 3
+x^7 + 2*x^5 + 2*x^4 + x^2 3
+x^7 + 2*x^5 + 2*x^4 + x^2 3
+x^7 + x^2 4
+x^7 + x^2 4
+x^7 + x^2 4
+x^7 + x^5 + x^2 3
+x^7 + x^5 + x^2 3
+x^7 + x^5 + x^2 3
+x^7 + 2*x^5 + x^2 3
+x^7 + 2*x^5 + x^2 3
+x^7 + 2*x^5 + x^2 3
+x^7 + x^4 + x^2 4
+x^7 + x^4 + x^2 4
+x^7 + x^4 + x^2 4
+x^7 + x^5 + x^4 + x^2 3
+x^7 + x^5 + x^4 + x^2 3
+x^7 + x^5 + x^4 + x^2 3
+x^7 + 2*x^5 + x^4 + x^2 3
+x^7 + 2*x^5 + x^4 + x^2 3
+x^7 + 2*x^5 + x^4 + x^2 3
+x^7 + 2*x^4 + x^2 4
+x^7 + 2*x^4 + x^2 4
+x^7 + 2*x^4 + x^2 4
+x^7 + x^5 + 2*x^4 + x^2 3
+x^7 + x^5 + 2*x^4 + x^2 3
+^C---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [82], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:25, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:19, in <module>
+
+File <string>:44, in __init__(self, C, list_of_fcts, prec)
+
+File <string>:167, in artin_schreier_transform(power_series, prec)
+
+File <string>:12, in new_reverse(power_series, prec)
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1831, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
+   1829 if x:
+   1830     raise ValueError("must not specify %s keyword and positional argument" % name)
+-> 1831 a = self(kwds[name])
+   1832 del kwds[name]
+   1833 try:
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1852, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
+   1850         x = x[0]
+   1851 
+-> 1852     return self.__u(*x)*(x[0]**self.__n)
+   1853 
+   1854 def __pari__(self):
+
+File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:365, in sage.rings.power_series_poly.PowerSeries_poly.__call__()
+    363         x[0] = a
+    364         x = tuple(x)
+--> 365     return self.__f(x)
+    366 
+    367 def _unsafe_mutate(self, i, value):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zmod_flint.pyx:332, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint.__call__()
+    330             nmod_poly_compose(&t.x, &self.x, &y.x)
+    331             return t
+--> 332     return Polynomial.__call__(self, *x, **kwds)
+    333 
+    334 @coerce_binop
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:898, in sage.rings.polynomial.polynomial_element.Polynomial.__call__()
+    896             return result
+    897         pol._compiled = CompiledPolynomialFunction(pol.list())
+--> 898     return pol._compiled.eval(a)
+    899 
+    900 def compose_trunc(self, Polynomial other, long n):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:125, in sage.rings.polynomial.polynomial_compiled.CompiledPolynomialFunction.eval()
+    123 cdef object temp
+    124 try:
+--> 125     pd_eval(self._dag, x, self._coeffs)  #see further down
+    126     temp = self._dag.value               #for an explanation
+    127     pd_clean(self._dag)                  #of these 3 lines
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
+    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
+    352     if pd.value is None:
+--> 353         pd.eval(vars, coeffs)
+    354     pd.hits += 1
+    355 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
+    505 
+    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
+--> 507         pd_eval(self.left, vars, coeffs)
+    508         pd_eval(self.right, vars, coeffs)
+    509         self.value = self.left.value * self.right.value + coeffs[self.index]
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
+    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
+    352     if pd.value is None:
+--> 353         pd.eval(vars, coeffs)
+    354     pd.hits += 1
+    355 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
+    505 
+    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
+--> 507         pd_eval(self.left, vars, coeffs)
+    508         pd_eval(self.right, vars, coeffs)
+    509         self.value = self.left.value * self.right.value + coeffs[self.index]
+
+    [... skipping similar frames: sage.rings.polynomial.polynomial_compiled.pd_eval at line 353 (9 times), sage.rings.polynomial.polynomial_compiled.abc_pd.eval at line 507 (8 times)]
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
+    505 
+    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
+--> 507         pd_eval(self.left, vars, coeffs)
+    508         pd_eval(self.right, vars, coeffs)
+    509         self.value = self.left.value * self.right.value + coeffs[self.index]
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
+    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
+    352     if pd.value is None:
+--> 353         pd.eval(vars, coeffs)
+    354     pd.hits += 1
+    355 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:509, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
+    507 pd_eval(self.left, vars, coeffs)
+    508 pd_eval(self.right, vars, coeffs)
+--> 509 self.value = self.left.value * self.right.value + coeffs[self.index]
+    510 pd_clean(self.left)
+    511 pd_clean(self.right)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__()
+   1512 cdef int cl = classify_elements(left, right)
+   1513 if HAVE_SAME_PARENT(cl):
+-> 1514     return (<Element>left)._mul_(right)
+   1515 if BOTH_ARE_ELEMENT(cl):
+   1516     return coercion_model.bin_op(left, right, mul)
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:913, in sage.rings.laurent_series_ring_element.LaurentSeries._mul_()
+    911 cdef LaurentSeries right = <LaurentSeries>right_r
+    912 return type(self)(self._parent,
+--> 913                   self.__u * right.__u,
+    914                   self.__n + right.__n)
+    915 
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__()
+   1512 cdef int cl = classify_elements(left, right)
+   1513 if HAVE_SAME_PARENT(cl):
+-> 1514     return (<Element>left)._mul_(right)
+   1515 if BOTH_ARE_ELEMENT(cl):
+   1516     return coercion_model.bin_op(left, right, mul)
+
+File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:540, in sage.rings.power_series_poly.PowerSeries_poly._mul_()
+    538 """
+    539 prec = self._mul_prec(right_r)
+--> 540 return PowerSeries_poly(self._parent,
+    541                         self.__f * (<PowerSeries_poly>right_r).__f,
+    542                         prec=prec,
+
+File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:44, in sage.rings.power_series_poly.PowerSeries_poly.__init__()
+     42     ValueError: series has negative valuation
+     43 """
+---> 44 R = parent._poly_ring()
+     45 if isinstance(f, Element):
+     46     if (<Element>f)._parent is R:
+
+File /ext/sage/9.7/src/sage/rings/power_series_ring.py:961, in PowerSeriesRing_generic._poly_ring(self)
+    958         pass
+    959     return False
+--> 961 def _poly_ring(self):
+    962     """
+    963     Return the underlying polynomial ring used to represent elements of
+    964     this power series ring.
+   (...)
+    970         Univariate Polynomial Ring in t over Integer Ring
+    971     """
+    972     return self.__poly_ring
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.a_number()[?7h[?12l[?25h[?25l[?7lsage: C

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^1 = x over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 - x, 2)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(x)[?7h[?12l[?25h[?25l[?7lsage: p

+[?7h[?12l[?25h[?2004l[?7h3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.a_nmber()[?7h[?12l[?25h[?25l[?7lbasis_of_cohomology()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lring[?7h[?12l[?25h[?25l[?7lsage: C.base_ring

+[?7h[?12l[?25h[?2004l[?7hFinite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.base_ring[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)^(-1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf(C.y[?7h[?12l[?25h[?25l[?7lf(C.y[?7h[?12l[?25h[?25l[?7l (C.y[?7h[?12l[?25h[?25l[?7l=(C.y[?7h[?12l[?25h[?25l[?7l (C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: ff = (C.y)^3/(C.x)^3

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = (C.y)^3/(C.x)^3[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: ff

+[?7h[?12l[?25h[?2004l[?7h((x^2 + 2)/x^2)*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((AS.x)^(-1)*AS.dx).cartier()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((AS.x)^(-1)*AS.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.x)^(11)/(C.y)^3*C.dx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly-[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: (C.y)/(C.x)^2

+[?7h[?12l[?25h[?2004l[?7h1/x^2*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y)/(C.x)^2[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.y)/(C.x)^2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((C.y)/(C.x)^2).expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht + O(t^21)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: 5/3-3

+[?7h[?12l[?25h[?2004l[?7h-4/3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l7%3[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: 7/3-3

+[?7h[?12l[?25h[?2004l[?7h-2/3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.base_ring[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C/y)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7ly)^3/[?7h[?12l[?25h[?25l[?7l.y)^3/[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7lsage: (C.y)^3/(C.x)^4

+[?7h[?12l[?25h[?2004l[?7h((x^2 + 2)/x^3)*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y)^3/(C.x)^4[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.y)^3/(C.x)^4)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((C.y)^3/(C.x)^4).expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht^-1 + O(t^19)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.y)^3/(C.x)^4).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y)^3/(C.x)^4[?7h[?12l[?25h[?25l[?7l(C.y)^3/(C.x)^4).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.y)^3/(C.x)^4).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf((C.y)^3/(C.x)^4)[?7h[?12l[?25h[?25l[?7lf((C.y)^3/(C.x)^4)[?7h[?12l[?25h[?25l[?7l ((C.y)^3/(C.x)^4)[?7h[?12l[?25h[?25l[?7l=((C.y)^3/(C.x)^4)[?7h[?12l[?25h[?25l[?7l ((C.y)^3/(C.x)^4)[?7h[?12l[?25h[?25l[?7lsage: ff = ((C.y)^3/(C.x)^4)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = ((C.y)^3/(C.x)^4)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: ff

+[?7h[?12l[?25h[?2004l[?7h((x^2 + 2)/x^3)*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff[?7h[?12l[?25h[?25l[?7l = ((C.y)^3/(C.x)^4)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7lsage: ff = ((C.y)^3/(C.x)^2)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = ((C.y)^3/(C.x)^2)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion_at_infty[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ff.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht^-5 + 2*t^-1 + 2*t^3 + 2*t^7 + t^11 + O(t^15)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: ff

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

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.base_ring[?7h[?12l[?25h[?25l[?7lfrobenus_matrix(prec=50).transpose().kernel().basis()[0][?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(prec=50).transpose().kernel().basis()[0][?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lobenius_matrix(prec=50).transpose().kernel().basis()[0][?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix(prec=50).transpose().kernel().basis()[0]

+[?7h[?12l[?25h[?2004l[?7h(1)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50).transpose().kernel().basis()[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.frobenius_matrix(prec=50)

+[?7h[?12l[?25h[?2004l[?7h[0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR.<x> = PolynomialRing(ZZ)[?7h[?12l[?25h[?25l[?7lsage: R.<x> = PolynomialRing(ZZ)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff[?7h[?12l[?25h[?25l[?7l = superelliptic_function(C, y/x)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx^n + a[0][?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3-x[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: f = x^3 - x

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR.<x> = PolynomialRing(ZZ)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM = hypellfrob(p, 1, f)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 1, f)[?7h[?12l[?25h[?25l[?7l3, 1, f)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: M = hypellfrob(3, 1, f)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [105], in <cell line: 1>()
+----> 1 M = hypellfrob(Integer(3), Integer(1), f)
+
+NameError: name 'hypellfrob' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrom sage.schemes.hyperelliptic_curves.hypellfrob import hypellfrob[?7h[?12l[?25h[?25l[?7lsage: from sage.schemes.hyperelliptic_curves.hypellfrob import hypellfrob

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrom sage.schemes.hyperelliptic_curves.hypellfrob import hypellfrob[?7h[?12l[?25h[?25l[?7lM = hypellfrob(3, 1, f)[?7h[?12l[?25h[?25l[?7lsage: M = hypellfrob(3, 1, f)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [107], in <cell line: 1>()
+----> 1 M = hypellfrob(Integer(3), Integer(1), f)
+
+File /ext/sage/9.7/src/sage/schemes/hyperelliptic_curves/hypellfrob.pyx:238, in sage.schemes.hyperelliptic_curves.hypellfrob.hypellfrob()
+    236 bound = (len(Q) - 1) * (2*N - 1)
+    237 if p <= bound:
+--> 238     raise ValueError("In the current implementation, p must be greater "
+    239                      "than (2g+1)(2N-1) = %s" % bound)
+    240 
+
+ValueError: In the current implementation, p must be greater than (2g+1)(2N-1) = 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lsage: g

+[?7h[?12l[?25h[?2004l[?7h((2*x^4 + 2*x^2 + 2)/x^3)*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.discriminant().factor()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates()

+[?7h[?12l[?25h[?2004l[?7h[1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.frobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lbase_rng[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.frobenius_matrix(prec=50)[?7h[?12l[?25h[?25l[?7lcartier_matrix()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.

+  C.a_number                               C.basis_of_cohomology                    C.degrees_de_rham0                        

+  C.base_ring                              C.cartier_matrix                         C.degrees_de_rham1                        

+  C.basis_de_rham_degrees                  C.characteristic                         C.degrees_holomorphic_differentials      >

+  C.basis_holomorphic_differentials_degree C.de_rham_basis                          C.dr_frobenius_matrix                     

+ [?7h[?12l[?25h[?25l[?7la_number

+ C.a_number                              

+

+

+

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

+ C.a_number                               C.basis_of_cohomology                   [?7h[?12l[?25h[?25l[?7l()

+

+

+

+

+[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.basis_of_cohomology()

+[?7h[?12l[?25h[?2004l[?7h[2/x*y]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+ [?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: gg = (C.y)/(C.x)

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

+

+ [?7h[?12l[?25h[?25l[?7lgg = (C.y)/(C.x)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7log^8*[?7h[?12l[?25h[?25l[?7lmg^8*[?7h[?12l[?25h[?25l[?7l g^8*[?7h[?12l[?25h[?25l[?7l=g^8*[?7h[?12l[?25h[?25l[?7l g^8*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lfn[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om = gg^8*gg.diffn()

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

+ [?7h[?12l[?25h[?25l[?7lom = gg^8*gg.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.expansion_at_ifty()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: om.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7h2*t^-10 + 2*t^-6 + t^-2 + O(1)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7lsage: om.expansion_at_infty(prec = 30)

+[?7h[?12l[?25h[?2004l[?7h2*t^-10 + 2*t^-6 + t^-2 + t^2 + 2*t^6 + t^10 + O(t^20)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7lsage: v

+[?7h[?12l[?25h[?2004l[?7h1/x^2*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.basis_of_cohomology()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lY[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lv)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7ly)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: C.y*v*(v - C.y)

+[?7h[?12l[?25h[?2004l[?7h((2*x^4 + 2*x^2 + 2)/x^3)*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.expansion_at_infty(prec = 30)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

+[?7h[?12l[?25h[?2004l[?7h((-x^10 + x^6 + x^4 - 1)/(x^5*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y*v*(v - C.y)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7lx.cartier()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx[?7h[?12l[?25h[?25l[?7l.C.dx[?7h[?12l[?25h[?25l[?7lxC.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.xC.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*C.dx[?7h[?12l[?25h[?25l[?7lC.dx[?7h[?12l[?25h[?25l[?7l.C.dx[?7h[?12l[?25h[?25l[?7lyC.dx[?7h[?12l[?25h[?25l[?7l()C.dx[?7h[?12l[?25h[?25l[?7l()^C.dx[?7h[?12l[?25h[?25l[?7l(C.dx[?7h[?12l[?25h[?25l[?7l-C.dx[?7h[?12l[?25h[?25l[?7l1C.dx[?7h[?12l[?25h[?25l[?7l()C.dx[?7h[?12l[?25h[?25l[?7l()*C.dx[?7h[?12l[?25h[?25l[?7lsage: (C.x*C.y)^(-1)*C.dx

+[?7h[?12l[?25h[?2004l[?7h(1/(x*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x*C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo(C.x*C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7lm(C.x*C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l1(C.x*C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l (C.x*C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l=(C.x*C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l (C.x*C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om1 = (C.x*C.y)^(-1)*C.dx

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = (C.x*C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.jth_component(3[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht^2 + t^6 + O(t^12)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[1]
+3*X^18 + 2*X^16 + 2*X^14 + 8*X^10 - 2*X^9 - 4*X^8 + 6*X^7 + 4*X^6 - 6*X^5 + 2*X^4 + 2*X^3 + 2*X^2 - 1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y*v*(v - C.y)[?7h[?12l[?25h[?25l[?7lsage: C

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.y*v*(v - C.y)[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

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

+[?7h[?12l[?25h[?2004l0 dx
+[1]
+3*X^18 + 2*X^16 + 2*X^14 + 8*X^10 - 2*X^9 - 4*X^8 + 6*X^7 + 4*X^6 - 6*X^5 + 2*X^4 + 2*X^3 + 2*X^2 - 1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l((x^3 - x^2 - x + 1)/(x^3*y)) dx
+[1]
+3*X^18 + 2*X^16 + 2*X^14 + 8*X^10 - 2*X^9 - 4*X^8 + 6*X^7 + 4*X^6 - 6*X^5 + 2*X^4 + 2*X^3 + 2*X^2 - 1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0 dx
+[1]
+3*X^18 + 2*X^16 + 2*X^14 + 8*X^10 - 2*X^9 - 4*X^8 + 6*X^7 + 4*X^6 - 6*X^5 + 2*X^4 + 2*X^3 + 2*X^2 - 1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0 dx
+[1]
+3*X^18 + 2*X^16 - X^15 + 2*X^14 + 3*X^13 + 2*X^12 - 3*X^11 + 2*X^10 - X^9 + 2*X^8 + 6*X^7 + 2*X^6 - 6*X^5 + 2*X^4 + 2*X^3 + 2*X^2 - 1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0 dx
+[1]
+3*X^18 + 2*X^16 - 2*X^15 + 2*X^14 + 6*X^13 + 2*X^12 - 6*X^11 + 2*X^10 - 2*X^9 + 2*X^8 + 12*X^7 + 2*X^6 - 12*X^5 + 2*X^4 + 4*X^3 + 2*X^2 - 1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0 dx
+[1]
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x*C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()%[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: (-10)%3

+[?7h[?12l[?25h[?2004l[?7h2
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-10)%3[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()%[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7lsage: (3/2)%9

+[?7h[?12l[?25h[?2004l[?7h6
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(3/2)%9[?7h[?12l[?25h[?25l[?7lC.x*C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.x/C.y).expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht + t^5 + 2*t^9 + 2*t^13 + t^17 + O(t^21)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1621228612.factor()[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7lsage: 19/3-4

+[?7h[?12l[?25h[?2004l[?7h7/3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l19/3-4[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7lsage: 17/3-4

+[?7h[?12l[?25h[?2004l[?7h5/3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l17/3-4[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7lsage: 13/3-4

+[?7h[?12l[?25h[?2004l[?7h1/3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l13/3-4[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7lsage: 11/3-4

+[?7h[?12l[?25h[?2004l[?7h-1/3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l7/3-3[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7lsage: 7/3-4

+[?7h[?12l[?25h[?2004l[?7h-5/3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l5/3-3[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7lsage: 5/3-4

+[?7h[?12l[?25h[?2004l[?7h-7/3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0 dx
+[1]
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+[0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0 dx
+[1]
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+[0]
+[0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor m in range(1, p^2):[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion_at_infty[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f2.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht^-11 + 2*t^-7 + 2*t^-3 + t + 2*t^5 + O(t^9)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: f2

+[?7h[?12l[?25h[?2004l[?7h(x^8/(x^4 + x^2 + 1))*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf2[?7h[?12l[?25h[?25l[?7l1 = superelliptic_function(C_super, 1)[?7h[?12l[?25h[?25l[?7lsage: f1

+[?7h[?12l[?25h[?2004l[?7h((x^10 + 2*x^2 + 2)/(x^6 + 2*x^4))*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg = (C.y)/(C.x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRHS = ceil(m*(k+1)/p) - ceil(m*k/p)[?7h[?12l[?25h[?25l[?7lxy.<x, y> = PolynomialRing(GF(3), 2)[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.<x> = PolynomialRing(QQ)[?7h[?12l[?25h[?25l[?7l<[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l>[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lP[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lynomialRing(QQ)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lG)[?7h[?12l[?25h[?25l[?7lF)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: Rx.<x> = PolynomialRing(GF(3))

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx.<x> = PolynomialRing(GF(3))[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg = (C.y)/(C.x)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp = 5[?7h[?12l[?25h[?25l[?7lrint(LHS == RHS)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l8)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l4)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l+)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l+)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: print((x^8).quo_rem(x^4 + x^2 + 1))

+[?7h[?12l[?25h[?2004l(x^4 + 2*x^2, x^2)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x/C.y).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()^(11)/(C.y)^3*C.dx[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l2/(C.y)*(C.dx)[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(C.x)^2*C.y/(C.y)^4 + (C.y)^2 + 1)[?7h[?12l[?25h[?25l[?7lg(C.x)^2*C.y/(C.y)^4 + (C.y)^2 + 1)[?7h[?12l[?25h[?25l[?7l (C.x)^2*C.y/(C.y)^4 + (C.y)^2 + 1)[?7h[?12l[?25h[?25l[?7l=(C.x)^2*C.y/(C.y)^4 + (C.y)^2 + 1)[?7h[?12l[?25h[?25l[?7l (C.x)^2*C.y/(C.y)^4 + (C.y)^2 + 1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: gg = (C.x)^2*C.y/((C.y)^4 + (C.y)^2 + 1)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [26], in <cell line: 1>()
+----> 1 gg = (C.x)**Integer(2)*C.y/((C.y)**Integer(4) + (C.y)**Integer(2) + Integer(1))
+
+File <string>:38, in __add__(self, other)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
+    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
+    493     """
+--> 494     return self.getattr_from_category(name)
+    495 
+    496 cdef getattr_from_category(self, name):
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
+    505     else:
+    506         cls = P._abstract_element_class
+--> 507     return getattr_from_other_class(self, cls, name)
+    508 
+    509 def __dir__(self):
+
+File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
+    359     dummy_error_message.cls = type(self)
+    360     dummy_error_message.name = name
+--> 361     raise AttributeError(dummy_error_message)
+    362 attribute = <object>attr
+    363 # Check for a descriptor (__get__ in Python)
+
+AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0 dx
+[1]
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+[0]
+[0]
+t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [1], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:25, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:14, in <module>
+
+NameError: name 'g' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1[?7h[?12l[?25h[?25l[?7lor m in range(1, p^2):[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: forma

+[?7h[?12l[?25h[?2004l[?7h((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lforma[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsion_at_infty[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: forma.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7h2*t^-8 + 2*t^-4 + O(t^2)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lforma.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7lsage: forma.expansion_at_infty(prec=30)

+[?7h[?12l[?25h[?2004l[?7h2*t^-8 + 2*t^-4 + 2*t^4 + 2*t^8 + O(t^22)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lforma.expansion_at_infty(prec=30)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: forma

+[?7h[?12l[?25h[?2004l[?7h((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lTraceback (most recent call last):
+
+  File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
+    exec(code_obj, self.user_global_ns, self.user_ns)
+
+  Input In [6] in <cell line: 1>
+    load('init.sage')
+
+  File sage/misc/persist.pyx:175 in sage.misc.persist.load
+    sage.repl.load.load(filename, globals())
+
+  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
+    exec(preparse_file(f.read()) + "\n", globals)
+
+  File <string>:25 in <module>
+
+  File sage/misc/persist.pyx:175 in sage.misc.persist.load
+    sage.repl.load.load(filename, globals())
+
+  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
+    exec(preparse_file(f.read()) + "\n", globals)
+
+  File <string>:14
+    forma2 = ((xx**_sage_const_4  + xx**_sage_const_2  + C.one)/(xx**_sage_const_6 *C.y)) C.dx
+                                                                                          ^
+SyntaxError: invalid syntax
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+((x^4 + x^2 + 1)/(x^6*y)) dx
+---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [7], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:25, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:16, in <module>
+
+NameError: name 'g' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lforma[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: forma1

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [8], in <cell line: 1>()
+----> 1 forma1
+
+NameError: name 'forma1' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lforma1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: forma2

+[?7h[?12l[?25h[?2004l[?7h((x^4 + x^2 + 1)/(x^6*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lforma2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lion_at_infty[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: forma2.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht^4 + t^8 + O(t^14)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lforma2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: forma2

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

+[?7h[?12l[?25h[?2004l((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+((x^4 + x^2 + 1)/(x^6*y)) dx
+---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [12], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:25, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:16, in <module>
+
+NameError: name 'g' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+((x^4 + x^2 + 1)/(x^6*y)) dx
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+[0]
+[0]
+t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [13], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:25, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:25, in <module>
+
+File <string>:38, in __add__(self, other)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
+    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
+    493     """
+--> 494     return self.getattr_from_category(name)
+    495 
+    496 cdef getattr_from_category(self, name):
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
+    505     else:
+    506         cls = P._abstract_element_class
+--> 507     return getattr_from_other_class(self, cls, name)
+    508 
+    509 def __dir__(self):
+
+File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
+    359     dummy_error_message.cls = type(self)
+    360     dummy_error_message.name = name
+--> 361     raise AttributeError(dummy_error_message)
+    362 attribute = <object>attr
+    363 # Check for a descriptor (__get__ in Python)
+
+AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+((x^4 + x^2 + 1)/(x^6*y)) dx
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+[0]
+[0]
+t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
+((x^10 - x^6 + 1)/(x^2*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x/C.y).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lx^11)quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (x^10 - x^6 + 1).quo_rem(x^2 - 1)

+[?7h[?12l[?25h[?2004l[?7h(x^8 + x^6, 1)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^10 - x^6 + 1).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l^).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l8).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l+).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7lx).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l^).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l6).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l - 1)[?7h[?12l[?25h[?25l[?7l3 - 1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7lsage: (x^8+x^6).quo_rem(x^3 - x)

+[?7h[?12l[?25h[?2004l[?7h(x^5 + 2*x^3 + 2*x, 2*x^2)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion(x^11, x^3 - x)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc_expansion(x^11, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l8, x^3 - x)[?7h[?12l[?25h[?25l[?7l , x^3 - x)[?7h[?12l[?25h[?25l[?7l+, x^3 - x)[?7h[?12l[?25h[?25l[?7l , x^3 - x)[?7h[?12l[?25h[?25l[?7lx, x^3 - x)[?7h[?12l[?25h[?25l[?7l^, x^3 - x)[?7h[?12l[?25h[?25l[?7l6, x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(x^8 + x^6, x^3 - x)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [17], in <cell line: 1>()
+----> 1 adic_expansion(x**Integer(8) + x**Integer(6), x**Integer(3) - x)
+
+NameError: name 'adic_expansion' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lfty/[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft

+ drafty/draft.sage  drafty/draft4.sage

+ drafty/draft2.sage drafty/draft5.sage

+ drafty/draft3.sage drafty/draft6.sage

+

+ [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.sage

+ drafty/draft.sage 

+

+

+ <unknown> [?7h[?12l[?25h[?25l[?7l2.sage

+ drafty/draft.sage 

+ drafty/draft2.sage[?7h[?12l[?25h[?25l[?7l3

+

+ drafty/draft2.sage

+ drafty/draft3.sage[?7h[?12l[?25h[?25l[?7l4

+ drafty/draft4.sage

+

+ drafty/draft3.sage[?7h[?12l[?25h[?25l[?7l5

+ drafty/draft4.sage

+ drafty/draft5.sage[?7h[?12l[?25h[?25l[?7l'

+

+

+

+[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft5.sage')

+[?7h[?12l[?25h[?2004l((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx
+t^-40 + O(t^-30)
+[2, 1, x^2 + 2*x + 2, 2*x^2 + 2*x + 1, x^2 + 1, x^2 + x + 2, 2*x]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+ [?7h[?12l[?25h[?25l[?7lload('drafty/draft5.sage')[?7h[?12l[?25h[?25l[?7ladic_expansion(x^8 + x^6, x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(x^8 + x^6, x^3 - x)

+[?7h[?12l[?25h[?2004l[?7h[x^2, 2*x, 2*x^2]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft5.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7l(nit.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+((x^4 + x^2 + 1)/(x^6*y)) dx
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+[0]
+[0]
+t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
+((x^10 - x^6 + 1)/(x^2*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: xx^11/(C.y)^3*C.dx

+[?7h[?12l[?25h[?2004l[?7h(x^10/(x^2*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx^11/(C.y)^3*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx^11/(C.y)^3*C.dx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: xx^9*C.y*C.y*C.y.diffn()

+[?7h[?12l[?25h[?2004l[?7h((x^12 - x^10)/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

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

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

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

+[?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(x^8+x^6).quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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(x^9*(x^3-x)^2 +[?7h[?12l[?25h[?25l[?7ld(x^9*(x^3-x)^2 +[?7h[?12l[?25h[?25l[?7li(x^9*(x^3-x)^2 +[?7h[?12l[?25h[?25l[?7lc(x^9*(x^3-x)^2 +[?7h[?12l[?25h[?25l[?7l_(x^9*(x^3-x)^2 +[?7h[?12l[?25h[?25l[?7le(x^9*(x^3-x)^2 +[?7h[?12l[?25h[?25l[?7lx(x^9*(x^3-x)^2 +[?7h[?12l[?25h[?25l[?7lp(x^9*(x^3-x)^2 +[?7h[?12l[?25h[?25l[?7la(x^9*(x^3-x)^2 +[?7h[?12l[?25h[?25l[?7ln(x^9*(x^3-x)^2 +[?7h[?12l[?25h[?25l[?7ls(x^9*(x^3-x)^2 +[?7h[?12l[?25h[?25l[?7li(x^9*(x^3-x)^2 +[?7h[?12l[?25h[?25l[?7lo(x^9*(x^3-x)^2 +[?7h[?12l[?25h[?25l[?7ln(x^9*(x^3-x)^2 +[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(x^9*(x^3-x)^2 - x^4 - x^2 - 1, x^3 - x)

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

+[?7h[?12l[?25h[?2004l0 dx
+((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+((x^4 + x^2 + 1)/(x^6*y)) dx
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+[0]
+[0]
+t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
+((x^10 - x^6 + 1)/(x^2*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l11/3-4[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7lsage: 19/3-4

+[?7h[?12l[?25h[?2004l[?7h7/3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l19/3-4[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l/3-4[?7h[?12l[?25h[?25l[?7lsage: 17/3-4

+[?7h[?12l[?25h[?2004l[?7h5/3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l17/3-4[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l/3-4[?7h[?12l[?25h[?25l[?7lsage: 13/3-4

+[?7h[?12l[?25h[?2004l[?7h1/3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l13/3-4[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l/3-4[?7h[?12l[?25h[?25l[?7lsage: 11/3-4

+[?7h[?12l[?25h[?2004l[?7h-1/3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l7/3-4[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l3-4[?7h[?12l[?25h[?25l[?7lsage: 7/3-4

+[?7h[?12l[?25h[?2004l[?7h-5/3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l5/3-4[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l3-4[?7h[?12l[?25h[?25l[?7lsage: 5/3-4

+[?7h[?12l[?25h[?2004l[?7h-7/3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0 dx
+((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+f2 ((-x^6 - 1)/(x^2*y - y)) dx
+((x^4 + x^2 + 1)/(x^6*y)) dx
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+[0]
+[0]
+t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
+((x^10 - x^6 + 1)/(x^2*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lega[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lforma2[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: forma

+[?7h[?12l[?25h[?2004l[?7h((-x^6 - 1)/(x^2*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lforma[?7h[?12l[?25h[?25l[?7l.expansion_at_infty(prec=30)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lpansion_at_infty(prec=30)[?7h[?12l[?25h[?25l[?7lsage: forma.expansion_at_infty(prec=30)

+[?7h[?12l[?25h[?2004l[?7h2*t^-8 + 2*t^-4 + 2*t^4 + 2*t^8 + t^16 + t^20 + O(t^22)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lforma.expansion_at_infty(prec=30)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0 dx
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+f2 ((-x^6 - 1)/(x^2*y - y)) dx
+((x^4 + x^2 + 1)/(x^6*y)) dx
+[0]
+[0]
+t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
+((x^10 - x^6 + 1)/(x^2*y - y)) dx
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [11], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:25, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:31, in <module>
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:4496, in sage.structure.element.coerce_binop.new_method()
+   4494     return method(self, other, *args, **kwargs)
+   4495 else:
+-> 4496     a, b = coercion_model.canonical_coercion(self, other)
+   4497     if a is self:
+   4498         return method(a, b, *args, **kwargs)
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1393, in sage.structure.coerce.CoercionModel.canonical_coercion()
+   1391         self._record_exception()
+   1392 
+-> 1393 raise TypeError("no common canonical parent for objects with parents: '%s' and '%s'"%(xp, yp))
+   1394 
+   1395 
+
+TypeError: no common canonical parent for objects with parents: 'Univariate Polynomial Ring in x over Finite Field of size 3' and 'Univariate Polynomial Ring in X over Rational Field'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0 dx
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+f2 ((-x^6 - 1)/(x^2*y - y)) dx
+((x^4 + x^2 + 1)/(x^6*y)) dx
+[0]
+[0]
+t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
+((x^10 - x^6 + 1)/(x^2*y - y)) dx
+(x^7 + x, 0)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^8+x^6).quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (x^7+x).quo_rem(x^3 - x)

+[?7h[?12l[?25h[?2004l[?7h(x^4 + x^2 + 1, 2*x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg = (C.x)^2*C.y/((C.y)^4 + (C.y)^2 + 1)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg = (C.x)^2*C.y/((C.y)^4 + (C.y)^2 + 1)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lforma.expansion_at_infty(prec=30)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lff.cartier()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: ffffff = (xx^10 + 2*xx^8 + xx^4 + 2*xx^2)/yy^3

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lffffff = (xx^10 + 2*xx^8 + xx^4 + 2*xx^2)/yy^3[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion_at_infty[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ffffff.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht^-11 + t^-7 + 2*t^-3 + 2*t + t^5 + O(t^9)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lffffff.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ldinates[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ffffff.coordinates()

+[?7h[?12l[?25h[?2004l[?7h[0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lffffff.coordinates()[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7l = (xx^10 + 2*xx^8 + xx^4 + 2*xx^2)/yy^3[?7h[?12l[?25h[?25l[?7l(x^7+x).quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7lffffff = (xx^10 + 2*xx^8 + xx^4 + 2*xx^2)/yy^3[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lffffff.coordinates()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: fg = (xx^7+xx)/yy

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfg = (xx^7+xx)/yy[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion_at_infty[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fg.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht^-11 + t^-7 + 2*t^-3 + 2*t + t^5 + O(t^9)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7linates[?7h[?12l[?25h[?25l[?7l*()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fg.coordinates()

+[?7h[?12l[?25h[?2004l[?7h[0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfg.coordinates()[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7l = (xx^7+xx)/yy[?7h[?12l[?25h[?25l[?7lfffff.coordinates()[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7l = (xx^10 + 2*xx^8 + xx^4 + 2*xx^2)/yy^3[?7h[?12l[?25h[?25l[?7l(x^7+x).quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: (x^7+x).quo_rem(x^3 - x)

+[?7h[?12l[?25h[?2004l[?7h(x^4 + x^2 + 1, 2*x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfg.coordinates()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l = (xx^7+xx)/yy[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fg = xx*yy/(xx^3 - xx)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfg = xx*yy/(xx^3 - xx)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ldinates()[?7h[?12l[?25h[?25l[?7lsage: fg.coordinates()

+[?7h[?12l[?25h[?2004l[?7h[0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfg.coordinates()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: fg.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht + t^5 + 2*t^9 + 2*t^13 + t^17 + O(t^21)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0 dx
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+f2 ((-x^6 - 1)/(x^2*y - y)) dx
+((x^4 + x^2 + 1)/(x^6*y)) dx
+[0]
+[0]
+t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
+((x^10 - x^6 + 1)/(x^2*y - y)) dx
+(x^7 + x, 0)
+((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+((-x^6 - 1)/(x^2*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^7+x).quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7l-10)%3[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l - 1[?7h[?12l[?25h[?25l[?7l2 - 1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (-x^6 - 1).quo_rem(x^2 - 1)

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

+[?7h[?12l[?25h[?2004l0 dx
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+f2 ((-x^6 - 1)/(x^2*y - y)) dx
+((x^4 + x^2 + 1)/(x^6*y)) dx
+[0]
+[0]
+t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
+((x^10 - x^6 + 1)/(x^2*y - y)) dx
+(x^7 + x, 0)
+((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+((-x^6 - 1)/(x^2*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ldrafty/draft5.sage')[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l(afty/draft5.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft5.sage')

+[?7h[?12l[?25h[?2004l((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx
+t^-40 + O(t^-30)
+[2, 1, x^2 + 2*x + 2, 2*x^2 + 2*x + 1, x^2 + 1, x^2 + x + 2, 2*x]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()+[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: G = 2*x^9*(x^3 - x)+2*x^4+2*x^2+2

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG = 2*x^9*(x^3 - x)+2*x^4+2*x^2+2[?7h[?12l[?25h[?25l[?7lsage: G

+[?7h[?12l[?25h[?2004l[?7h2*x^12 + x^10 + 2*x^4 + 2*x^2 + 2
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion(x^9*(x^3-x)^2 - x^4 - x^2 - 1, x^3 - x)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc_expansion(x^9*(x^3-x)^2 - x^4 - x^2 - 1, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l(), x^3 - x)[?7h[?12l[?25h[?25l[?7l(, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7lG, x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(G, x^3 - x)

+[?7h[?12l[?25h[?2004l[?7h[2, 0, 2, x, x^2 + 2]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7lsage: G

+[?7h[?12l[?25h[?2004l[?7h2*x^12 + x^10 + 2*x^4 + 2*x^2 + 2
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7l = 2*x^9*(x^3 - x)+2*x^4+2*x^2+2[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy(aaa[0].function).denominator()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l\[?7h[?12l[?25h[?25l[?7lsage: G1 = G - 2*x^4 + 2*x^6\

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG1 = G - 2*x^4 + 2*x^6\[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion(G, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1, x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(G1, x^3 - x)

+[?7h[?12l[?25h[?2004l[?7h[2, 0, 1, 0, x^2 + 2]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion(G1, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7lx, x^3 - x)[?7h[?12l[?25h[?25l[?7l^, x^3 - x)[?7h[?12l[?25h[?25l[?7l4, x^3 - x)[?7h[?12l[?25h[?25l[?7l , x^3 - x)[?7h[?12l[?25h[?25l[?7l+, x^3 - x)[?7h[?12l[?25h[?25l[?7l , x^3 - x)[?7h[?12l[?25h[?25l[?7lx, x^3 - x)[?7h[?12l[?25h[?25l[?7l^, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l , x^3 - x)[?7h[?12l[?25h[?25l[?7lx, x^3 - x)[?7h[?12l[?25h[?25l[?7l^, x^3 - x)[?7h[?12l[?25h[?25l[?7l2, x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(x^4 + x^2, x^3 - x)

+[?7h[?12l[?25h[?2004l[?7h[x, 2*x^2]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx9y2 + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lGx9y2 + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l x9y2 + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l=x9y2 + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l x9y2 + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^9y2 + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l* + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l( + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7lx + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l^ + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l3 + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l- + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7lx + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l() + x4 + x2 + 1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^4 + x2 + 1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^2 + 1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: G = x^9*(x^3 - x) + x^4 + x^2 + 1

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG = x^9*(x^3 - x) + x^4 + x^2 + 1[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7lsage: G(x+1) - G

+[?7h[?12l[?25h[?2004l[?7h2*x^3 + 2*x + 2
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG(x+1) - G[?7h[?12l[?25h[?25l[?7l1 = G2*x^4 + 2*x^6\[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l2x4 + 2x2 + 2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*x2 + 2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^2 + 2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*x4 + 2*x^2 + 2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^4 + 2*x^2 + 2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: G1 = 2*x^4 + 2*x^2 + 2

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG1 = 2*x^4 + 2*x^2 + 2[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7lsage: G1(x+1) - G

+[?7h[?12l[?25h[?2004l[?7h2*x^12 + x^10 + x^4 + 2*x^3 + x^2 + 2
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG1(x+1) - G[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: G1(x+1) - G1

+[?7h[?12l[?25h[?2004l[?7h2*x^3 + 1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg = (C.x)^2*C.y/((C.y)^4 + (C.y)^2 + 1)[?7h[?12l[?25h[?25l[?7l = len(Ifactors)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly^3/(x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g = yy^3/(xx*(xx+1)^2)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [15], in <cell line: 1>()
+----> 1 g = yy**Integer(3)/(xx*(xx+Integer(1))**Integer(2))
+
+File <string>:38, in __add__(self, other)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
+    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
+    493     """
+--> 494     return self.getattr_from_category(name)
+    495 
+    496 cdef getattr_from_category(self, name):
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
+    505     else:
+    506         cls = P._abstract_element_class
+--> 507     return getattr_from_other_class(self, cls, name)
+    508 
+    509 def __dir__(self):
+
+File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
+    359     dummy_error_message.cls = type(self)
+    360     dummy_error_message.name = name
+--> 361     raise AttributeError(dummy_error_message)
+    362 attribute = <object>attr
+    363 # Check for a descriptor (__get__ in Python)
+
+AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^3/(xx*(xx+1)^2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)^2)[?7h[?12l[?25h[?25l[?7lC)^2)[?7h[?12l[?25h[?25l[?7l.)^2)[?7h[?12l[?25h[?25l[?7lo)^2)[?7h[?12l[?25h[?25l[?7ln)^2)[?7h[?12l[?25h[?25l[?7le)^2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g = yy^3/(xx*(xx+C.one)^2)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^3/(xx*(xx+C.one)^2)[?7h[?12l[?25h[?25l[?7l.coordinates)[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates()

+[?7h[?12l[?25h[?2004l[?7h[0, 0, 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = yy^3/(xx*xx+C.one)^2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l2*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: g = yy^3/(xx^2*(xx+C.one))

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates()

+[?7h[?12l[?25h[?2004l[?7h[0, 0, 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7l = yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g = yy/xx - yy/(xx+1)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [20], in <cell line: 1>()
+----> 1 g = yy/xx - yy/(xx+Integer(1))
+
+File <string>:38, in __add__(self, other)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
+    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
+    493     """
+--> 494     return self.getattr_from_category(name)
+    495 
+    496 cdef getattr_from_category(self, name):
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
+    505     else:
+    506         cls = P._abstract_element_class
+--> 507     return getattr_from_other_class(self, cls, name)
+    508 
+    509 def __dir__(self):
+
+File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
+    359     dummy_error_message.cls = type(self)
+    360     dummy_error_message.name = name
+--> 361     raise AttributeError(dummy_error_message)
+    362 attribute = <object>attr
+    363 # Check for a descriptor (__get__ in Python)
+
+AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy/xx - yy/(xx+1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lC1)[?7h[?12l[?25h[?25l[?7l.1)[?7h[?12l[?25h[?25l[?7l.o1)[?7h[?12l[?25h[?25l[?7ln1)[?7h[?12l[?25h[?25l[?7le1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: g = yy/xx - yy/(xx+C.one)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy/xx - yy/(xx+C.one)[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates()

+[?7h[?12l[?25h[?2004l[?7h[0, 0, 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7lsage: g

+[?7h[?12l[?25h[?2004l[?7h(1/(x^2 + x))*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsion_at_infty[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht^5 + 2*t^9 + t^17 + O(t^25)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7l = yy/xx - yy/(xx+C.one)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7l = yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7lsage: g = yy^3/(xx^2*(xx+C.one))

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7lsage: g

+[?7h[?12l[?25h[?2004l[?7h(1/(x^3 + x^2))*y^3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l = yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g = yy^3/(xx*(xx+C.one)^2)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^3/(xx*(xx+C.one)^2)[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates()

+[?7h[?12l[?25h[?2004l[?7h[0, 0, 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: g.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht^3 + t^7 + t^15 + 2*t^19 + O(t^23)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: g

+[?7h[?12l[?25h[?2004l[?7h(1/(x^3 + 2*x^2 + x))*y^3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^4 = x^3 + 2*x over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft5.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('drafty/draft5.sage')[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lini[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l'drafty/draft5.sage')[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l(t.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0 dx
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+f2 ((-x^6 - 1)/(x^2*y - y)) dx
+((x^4 + x^2 + 1)/(x^6*y)) dx
+[0]
+[0]
+t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
+((x^10 - x^6 + 1)/(x^2*y - y)) dx
+(x^7 + x, 0)
+((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+((-x^6 - 1)/(x^2*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7l = yy^3/(xx*(xx+C.one)^2)[?7h[?12l[?25h[?25l[?7l()\[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g = yy^3/(xx*(xx+C.one)^2)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^3/(xx*(xx+C.one)^2)[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates()

+[?7h[?12l[?25h[?2004l[?7h[2]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7l = yy^3/(xx*(xx+C.one)^2)[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7l = yy^3/(xx*(xx+C.one)^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7lsage: g = yy^3/(xx^2*(xx+C.one))

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates()

+[?7h[?12l[?25h[?2004l[?7h[1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7l = yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7l = yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lyy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy^3/(xx*(xx+C.one)^2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l y^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l+ y^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-y^3/(x^2*(x+C.one) + y^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l y^3/(x^2*(x+C.one) + y^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g = - yy^3/(xx^2*(xx+C.one)) + yy^3/(xx*(xx+C.one)^2)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [38], in <cell line: 1>()
+----> 1 g = - yy**Integer(3)/(xx**Integer(2)*(xx+C.one)) + yy**Integer(3)/(xx*(xx+C.one)**Integer(2))
+
+TypeError: bad operand type for unary -: 'superelliptic_function'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = - yy^3/(xx^2*(xx+C.one)) + yy^3/(xx*(xx+C.one)^2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l()y^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l(()y^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l(y^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7ly^3/(x*(x+C.one)^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()-[?7h[?12l[?25h[?25l[?7lyy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7lsage: g = yy^3/(xx*(xx+C.one)^2)-yy^3/(xx^2*(xx+C.one))

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^3/(xx*(xx+C.one)^2)-yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7l.coordinates)[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates()

+[?7h[?12l[?25h[?2004l[?7h[1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7lsage: g

+[?7h[?12l[?25h[?2004l[?7h((2*x + 1)/(x^2 + x))*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx.<x> = PolynomialRing(GF(3))[?7h[?12l[?25h[?25l[?7l.<x> = PolynomialRing(ZZ)[?7h[?12l[?25h[?25l[?7l<[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l>[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lP[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7llRing(ZZ)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lG)[?7h[?12l[?25h[?25l[?7lF)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: R.<x> = PolynomialRing(GF(3))

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l = yy^3/(xx*(xx+C.one)^2)-yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: g = 2*x^4 + 2*x^2 + 2

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = 2*x^4 + 2*x^2 + 2[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lsage: g(x+1) - g

+[?7h[?12l[?25h[?2004l[?7h2*x^3 + 1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(x+1) - g[?7h[?12l[?25h[?25l[?7l = 2*x^4 + 2*x^2 + 2[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx^(f.degree())*f(1/x)[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: g = x^4 +x^2 + 1

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = x^4 +x^2 + 1[?7h[?12l[?25h[?25l[?7l(x+1) - g[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1) - g[?7h[?12l[?25h[?25l[?7lsage: g(x+1) - g

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

+[?7h[?12l[?25h[?2004l0 dx
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+f2 ((-x^6 - 1)/(x^2*y - y)) dx
+((x^4 + x^2 + 1)/(x^6*y)) dx
+[0]
+[0]
+t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
+((x^10 - x^6 + 1)/(x^2*y - y)) dx
+(x^7 + x, 0)
+((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+((-x^6 - 1)/(x^2*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(x+1) - g[?7h[?12l[?25h[?25l[?7l = x^4 +x^2 + 1[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lyy^3/(xx*(xx+C.one)^2)-yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/xx - yy/(xx+C.one)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx^4 +x^2 + 1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(x+1) - g[?7h[?12l[?25h[?25l[?7l = x^4 +x^2 + 1[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy^3/(xx*(xx+C.one)^2)-yy^3/(xx^2*(xx+C.one))[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/xx - yy/(xx+C.one)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l - yy/(xx+C.one)[?7h[?12l[?25h[?25l[?7lsage: g = yy/xx - yy/(xx+C.one)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy/xx - yy/(xx+C.one)[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: g.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht + 2*t^3 + t^5 + 2*t^9 + 2*t^13 + t^17 + O(t^21)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = yy/xx - yy/(xx+C.one)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lyy/xx - yy/(xx+C.one)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly/(x+C.one)[?7h[?12l[?25h[?25l[?7ly/(x+C.one)[?7h[?12l[?25h[?25l[?7ly/(x+C.one)[?7h[?12l[?25h[?25l[?7ly/(x+C.one)[?7h[?12l[?25h[?25l[?7ly/(x+C.one)[?7h[?12l[?25h[?25l[?7ly/(x+C.one)[?7h[?12l[?25h[?25l[?7l/(x+C.one)[?7h[?12l[?25h[?25l[?7l/(x+C.one)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^/(x+C.one)[?7h[?12l[?25h[?25l[?7l2/(x+C.one)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()&[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: g = yy^2/(xx+C.one)^2 * y/x - yy/(xx+C.one) * yy^2/xx^2

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [9], in <cell line: 1>()
+----> 1 g = yy**Integer(2)/(xx+C.one)**Integer(2) * y/x - yy/(xx+C.one) * yy**Integer(2)/xx**Integer(2)
+
+NameError: name 'y' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^2/(xx+C.one)^2 * y/x - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly/x - y/(x+C.one) * y^2/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx - y/(x+C.one) * y^2/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7l.expansion_at_ifty()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: g.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7h2*t^-1 + 2*t + 2*t^5 + t^7 + t^9 + t^11 + t^13 + 2*t^15 + 2*t^17 + O(t^19)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates()

+[?7h[?12l[?25h[?2004l[?7h[1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7lsage: g

+[?7h[?12l[?25h[?2004l[?7h((2*x + 1)/(x^2 + x))*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: g - yy/xxx

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [14], in <cell line: 1>()
+----> 1 g - yy/xxx
+
+NameError: name 'xxx' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg - yy/xxx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g - yy/xx

+[?7h[?12l[?25h[?2004l[?7h(1/(x + 1))*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg - yy/xx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(g - y/x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg - yy/xxx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l y/x[?7h[?12l[?25h[?25l[?7l+ y/x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g + yy/xx

+[?7h[?12l[?25h[?2004l[?7h(2/(x^2 + x))*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg + yy/xx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(g + y/x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (g + yy/xx).expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7h2*t + t^3 + 2*t^5 + t^9 + t^13 + 2*t^17 + O(t^21)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgy/x[?7h[?12l[?25h[?25l[?7lgy/x[?7h[?12l[?25h[?25l[?7l y/x[?7h[?12l[?25h[?25l[?7l=y/x[?7h[?12l[?25h[?25l[?7l y/x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: gg = yy/xx - yy/(xx + C.one)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg = yy/xx - yy/(xx + C.one)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lansion_at_infty[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: gg.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht + 2*t^3 + t^5 + 2*t^9 + 2*t^13 + t^17 + O(t^21)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: g

+[?7h[?12l[?25h[?2004l[?7h((2*x + 1)/(x^2 + x))*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + yy/xx[?7h[?12l[?25h[?25l[?7l=^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ly^2/(x+1)^2 \cdot y/x - y/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly^2/(x+1)^2 \cdot y/x - y/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lx+1)^2 \cdot y/x - y/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l y/x - y/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l y/x - y/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l y/x - y/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l y/x - y/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l y/x - y/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l* y/x - y/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly/x - y/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx - y/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7ly/(x+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lx+1) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7lC) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l.) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7lo) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7ln) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7le) \cdot y^2/x^2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l y^2/x^2[?7h[?12l[?25h[?25l[?7l y^2/x^2[?7h[?12l[?25h[?25l[?7l y^2/x^2[?7h[?12l[?25h[?25l[?7l y^2/x^2[?7h[?12l[?25h[?25l[?7l y^2/x^2[?7h[?12l[?25h[?25l[?7l* y^2/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly^2/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g = yy^2/(xx+1)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [21], in <cell line: 1>()
+----> 1 g = yy**Integer(2)/(xx+Integer(1))**Integer(2) * yy/xx - yy/(xx+C.one) * yy**Integer(2)/xx**Integer(2)
+
+File <string>:38, in __add__(self, other)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
+    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
+    493     """
+--> 494     return self.getattr_from_category(name)
+    495 
+    496 cdef getattr_from_category(self, name):
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
+    505     else:
+    506         cls = P._abstract_element_class
+--> 507     return getattr_from_other_class(self, cls, name)
+    508 
+    509 def __dir__(self):
+
+File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
+    359     dummy_error_message.cls = type(self)
+    360     dummy_error_message.name = name
+--> 361     raise AttributeError(dummy_error_message)
+    362 attribute = <object>attr
+    363 # Check for a descriptor (__get__ in Python)
+
+AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^2/(xx+1)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)^2 * y/x - y/(x+C.one) * y^2/x^2[?7h[?12l[?25h[?25l[?7lC)^2 * y/x - y/(x+C.one) * y^2/x^2[?7h[?12l[?25h[?25l[?7l.)^2 * y/x - y/(x+C.one) * y^2/x^2[?7h[?12l[?25h[?25l[?7lo)^2 * y/x - y/(x+C.one) * y^2/x^2[?7h[?12l[?25h[?25l[?7ln)^2 * y/x - y/(x+C.one) * y^2/x^2[?7h[?12l[?25h[?25l[?7le)^2 * y/x - y/(x+C.one) * y^2/x^2[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lordinates()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates()

+[?7h[?12l[?25h[?2004l[?7h[1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7l = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7l+/xx[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lyy/xx[?7h[?12l[?25h[?25l[?7lsage: g + yy/xx

+[?7h[?12l[?25h[?2004l[?7h(2/(x^2 + x))*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg + yy/xx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(g + y/x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: (g + yy/xx).expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7h2*t + t^3 + 2*t^5 + t^9 + t^13 + 2*t^17 + O(t^21)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(g + yy/xx).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lx^7+x).quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7lsage: (x+1)^5 - x^5

+[?7h[?12l[?25h[?2004l[?7h2*x^4 + x^3 + x^2 + 2*x + 1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ldrafty/draft5.sage')[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l(afty/draft5.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft5.sage')

+[?7h[?12l[?25h[?2004l((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx
+t^-40 + O(t^-30)
+[2, 1, x^2 + 2*x + 2, 2*x^2 + 2*x + 1, x^2 + 1, x^2 + x + 2, 2*x]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2x^4 + x^3 + x^2 + 2x - x^3 (x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg2x^4 + x^3 + x^2 + 2x - x^3 (x^3 - x)[?7h[?12l[?25h[?25l[?7l 2x^4 + x^3 + x^2 + 2x - x^3 (x^3 - x)[?7h[?12l[?25h[?25l[?7l=2x^4 + x^3 + x^2 + 2x - x^3 (x^3 - x)[?7h[?12l[?25h[?25l[?7l 2x^4 + x^3 + x^2 + 2x - x^3 (x^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*x^4 + x^3 + x^2 + 2x - x^3 (x^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*x - x^3 (x^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l* (x^3 - x)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g = 2*x^4 + x^3 + x^2 + 2*x - x^3* (x^3 - x)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = 2*x^4 + x^3 + x^2 + 2*x - x^3* (x^3 - x)[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion(x^4 + x^2, x^3 - x)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lic_expansion(x^4 + x^2, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7lg, x^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(g, x^3 - x)

+[?7h[?12l[?25h[?2004l[?7h[2, x + 1, 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: yy/xx

+[?7h[?12l[?25h[?2004l[?7h1/x*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy/xx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^/x[?7h[?12l[?25h[?25l[?7l3/x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgy^3/x^3[?7h[?12l[?25h[?25l[?7l y^3/x^3[?7h[?12l[?25h[?25l[?7l=y^3/x^3[?7h[?12l[?25h[?25l[?7l y^3/x^3[?7h[?12l[?25h[?25l[?7lsage: g = yy^3/xx^3

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^3/xx^3[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates()

+[?7h[?12l[?25h[?2004l[?7h[0, 0, 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lpansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: g.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht^3 + O(t^23)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^4 = x^3 + 2*x over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft5.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('drafty/draft5.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft5.sage')

+[?7h[?12l[?25h[?2004l((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx
+t^-40 + O(t^-30)
+[2, 1, x^2 + 2*x + 2, 2*x^2 + 2*x + 1, x^2 + 1, x^2 + x + 2, 2*x]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft5.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l(t.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0 dx
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+f2 ((-x^6 - 1)/(x^2*y - y)) dx
+((x^4 + x^2 + 1)/(x^6*y)) dx
+[0]
+[0]
+t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
+((x^10 - x^6 + 1)/(x^2*y - y)) dx
+(x^7 + x, 0)
+((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+((-x^6 - 1)/(x^2*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ldrafty/draft5.sage')[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7l = yy^3/xx^3[?7h[?12l[?25h[?25l[?7lsage: g = yy^3/xx^3

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^3/xx^3[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: g.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht^-3 + t + 2*t^5 + 2*t^9 + t^13 + O(t^17)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: g.coordinates()

+[?7h[?12l[?25h[?2004l[?7h[0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.coordinates()[?7h[?12l[?25h[?25l[?7lsage: g

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

+

+

+ [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l = hypellfrob(3, 1, f)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR.<x> = PolynomialRing(GF(3))[?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: R9 = Integers(9)

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

+

+ [?7h[?12l[?25h[?25l[?7lM = hypellfrob(3, 1, f)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lmatrix(QQ, [[1, 1], [0, 0]])[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[[][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l7]][?7h[?12l[?25h[?25l[?7l,]][?7h[?12l[?25h[?25l[?7l ]][?7h[?12l[?25h[?25l[?7l4]][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l,][?7h[?12l[?25h[?25l[?7l ][?7h[?12l[?25h[?25l[?7l[[][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l3]][?7h[?12l[?25h[?25l[?7l,]][?7h[?12l[?25h[?25l[?7l ]][?7h[?12l[?25h[?25l[?7l4]][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: M = matrix(R9, [[7, 4], [3, 4]])

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

+ [?7h[?12l[?25h[?25l[?7lM = matrix(R9, [[7, 4], [3, 4]])[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: M^3

+[?7h[?12l[?25h[?2004l[?7h[1 6]
+[0 1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM^3[?7h[?12l[?25h[?25l[?7l.transpose().image().basis()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: M.determinant()

+[?7h[?12l[?25h[?2004l[?7h7
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM.determinant()[?7h[?12l[?25h[?25l[?7l^3[?7h[?12l[?25h[?25l[?7l = matrix(R9, [[7, 4], [3, 4]])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l8]])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: M = matrix(R9, [[7, 4], [3, 8]])

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM = matrix(R9, [[7, 4], [3, 8]])[?7h[?12l[?25h[?25l[?7l^3[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: M^3

+[?7h[?12l[?25h[?2004l[?7h[4 4]
+[3 5]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = matrix(R9, [[7, 4], [3, 8]])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l4]])[?7h[?12l[?25h[?25l[?7lsage: M = matrix(R9, [[7, 4], [3, 4]])

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM = matrix(R9, [[7, 4], [3, 4]])[?7h[?12l[?25h[?25l[?7l^3[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: M^3

+[?7h[?12l[?25h[?2004l[?7h[1 6]
+[0 1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx^9*C.y*C.y*C.y.diffn()[?7h[?12l[?25h[?25l[?7lsage: x

+[?7h[?12l[?25h[?2004l[?7hx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x+1)^5 - x^5[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+1)^5 - x^5[?7h[?12l[?25h[?25l[?7lsage: (x+1)^5 - x^5

+[?7h[?12l[?25h[?2004l[?7h2*x^4 + x^3 + x^2 + 2*x + 1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2+2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = yy/xx - yy/(xx + C.one)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2x^4 + x^3 + x^2 + 2x + x^3 (x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l* (x^3 - x)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(x^3 - x)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*x + x^3*(x^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*x^4 + x^3 + x^2 + 2*x + x^3*(x^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: gg = 2*x^4 + x^3 + x^2 + 2*x + x^3*(x^3 - x)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg = 2*x^4 + x^3 + x^2 + 2*x + x^3*(x^3 - x)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lsage: gg

+[?7h[?12l[?25h[?2004l[?7hx^6 + x^4 + x^3 + x^2 + 2*x
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion(g, x^3 - x)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc_expansion(g, x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(g, x^3 - x)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [54], in <cell line: 1>()
+----> 1 adic_expansion(g, x**Integer(3) - x)
+
+File <string>:17, in adic_expansion(g, h)
+
+AttributeError: 'superelliptic_function' object has no attribute 'degree'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion(g, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg, x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(gg, x^3 - x)

+[?7h[?12l[?25h[?2004l[?7h[1, 1, 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM^3[?7h[?12l[?25h[?25l[?7l = matrix(R9, [[7, 4], [3, 4]])[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l matrix(R9, [[7, 4], [3, 4]])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l], [3, 4])[?7h[?12l[?25h[?25l[?7l], [3, 4])[?7h[?12l[?25h[?25l[?7l], [3, 4])[?7h[?12l[?25h[?25l[?7l], [3, 4])[?7h[?12l[?25h[?25l[?7l4], [3, 4])[?7h[?12l[?25h[?25l[?7l,], [3, 4])[?7h[?12l[?25h[?25l[?7l ], [3, 4])[?7h[?12l[?25h[?25l[?7l4], [3, 4])[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l6]])[?7h[?12l[?25h[?25l[?7l,]])[?7h[?12l[?25h[?25l[?7l ]])[?7h[?12l[?25h[?25l[?7l3]])[?7h[?12l[?25h[?25l[?7l4]])[?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l4]])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: M = matrix(R9, [[4, 4], [6, 4]])

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM = matrix(R9, [[4, 4], [6, 4]])[?7h[?12l[?25h[?25l[?7l^3[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: M^3

+[?7h[?12l[?25h[?2004l[?7h[1 0]
+[0 1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM^3[?7h[?12l[?25h[?25l[?7l = matrix(R9, [[4, 4], [6, 4]])[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lid[?7h[?12l[?25h[?25l[?7lide[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM - iden[?7h[?12l[?25h[?25l[?7l1M - iden[?7h[?12l[?25h[?25l[?7l M - iden[?7h[?12l[?25h[?25l[?7l=M - iden[?7h[?12l[?25h[?25l[?7l M - iden[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: M1 = M - identity_matrix(3)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [58], in <cell line: 1>()
+----> 1 M1 = M - identity_matrix(Integer(3))
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1358, in sage.structure.element.Element.__sub__()
+   1356     return (<Element>left)._sub_(right)
+   1357 if BOTH_ARE_ELEMENT(cl):
+-> 1358     return coercion_model.bin_op(left, right, sub)
+   1359 
+   1360 try:
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op()
+   1246     # We should really include the underlying error.
+   1247     # This causes so much headache.
+-> 1248     raise bin_op_exception(op, x, y)
+   1249 
+   1250 cpdef canonical_coercion(self, x, y):
+
+TypeError: unsupported operand parent(s) for -: 'Full MatrixSpace of 2 by 2 dense matrices over Ring of integers modulo 9' and 'Full MatrixSpace of 3 by 3 dense matrices over Integer Ring'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM1 = M - identity_matrix(3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lG3)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7lR3)[?7h[?12l[?25h[?25l[?7l93)[?7h[?12l[?25h[?25l[?7l,3)[?7h[?12l[?25h[?25l[?7l 3)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: M1 = M - identity_matrix(R9, 3)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [59], in <cell line: 1>()
+----> 1 M1 = M - identity_matrix(R9, Integer(3))
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1358, in sage.structure.element.Element.__sub__()
+   1356     return (<Element>left)._sub_(right)
+   1357 if BOTH_ARE_ELEMENT(cl):
+-> 1358     return coercion_model.bin_op(left, right, sub)
+   1359 
+   1360 try:
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op()
+   1246     # We should really include the underlying error.
+   1247     # This causes so much headache.
+-> 1248     raise bin_op_exception(op, x, y)
+   1249 
+   1250 cpdef canonical_coercion(self, x, y):
+
+TypeError: unsupported operand parent(s) for -: 'Full MatrixSpace of 2 by 2 dense matrices over Ring of integers modulo 9' and 'Full MatrixSpace of 3 by 3 dense matrices over Ring of integers modulo 9'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM1 = M - identity_matrix(R9, 3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7lsage: M1 = M - identity_matrix(R9, 2)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM1 = M - identity_matrix(R9, 2)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: M1.kernel()

+[?7h[?12l[?25h[?2004lsage/matrix/matrix_modn_dense_template.pxi:1: DeprecationWarning: invalid escape sequence '\Z'
+  """
+sage/matrix/matrix_modn_dense_template.pxi:1: DeprecationWarning: invalid escape sequence '\Z'
+  """
+---------------------------------------------------------------------------
+NotImplementedError                       Traceback (most recent call last)
+Input In [61], in <cell line: 1>()
+----> 1 M1.kernel()
+
+File /ext/sage/9.7/src/sage/matrix/matrix2.pyx:5032, in sage.matrix.matrix2.Matrix.left_kernel()
+   5030 
+   5031         tm = verbose("computing left kernel for %sx%s matrix" % (self.nrows(), self.ncols()),level=1)
+-> 5032         K = self.transpose().right_kernel(*args, **kwds)
+   5033         self.cache('left_kernel', K)
+   5034         verbose("done computing left kernel for %sx%s matrix" % (self.nrows(), self.ncols()),level=1,t=tm)
+
+File /ext/sage/9.7/src/sage/matrix/matrix2.pyx:4870, in sage.matrix.matrix2.Matrix.right_kernel()
+   4868 
+   4869         # Go get the kernel matrix, this is where it all happens
+-> 4870         M = self.right_kernel_matrix(*args, **kwds)
+   4871 
+   4872         ambient = R**self.ncols()
+
+File /ext/sage/9.7/src/sage/matrix/matrix_modn_dense_template.pxi:1897, in sage.matrix.matrix_modn_dense_float.Matrix_modn_dense_template.right_kernel_matrix()
+   1895 """
+   1896 if self.fetch('in_echelon_form') is None:
+-> 1897     self = self.echelon_form(algorithm=algorithm)
+   1898 
+   1899 cdef Py_ssize_t r = self.rank()
+
+File /ext/sage/9.7/src/sage/matrix/matrix2.pyx:7729, in sage.matrix.matrix2.Matrix.echelon_form()
+   7727     v = E.echelonize(cutoff=cutoff, **kwds)
+   7728 else:
+-> 7729     v = E.echelonize(algorithm = algorithm, cutoff=cutoff, **kwds)
+   7730 E.set_immutable()  # so we can cache the echelon form.
+   7731 self.cache('echelon_form', E)
+
+File /ext/sage/9.7/src/sage/matrix/matrix_modn_dense_template.pxi:1725, in sage.matrix.matrix_modn_dense_float.Matrix_modn_dense_template.echelonize()
+   1723 
+   1724         if not self.base_ring().is_field():
+-> 1725             raise NotImplementedError("Echelon form not implemented over '%s'."%self.base_ring())
+   1726 
+   1727         if algorithm == 'linbox':
+
+NotImplementedError: Echelon form not implemented over 'Ring of integers modulo 9'.
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM1.kernel()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: M1

+[?7h[?12l[?25h[?2004l[?7h[3 4]
+[6 3]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.kernel()[?7h[?12l[?25h[?25l[?7lsage: M1.kernel()

+  M1.C                                 M1.QR                                M1.add_multiple_of_row               M1.adjoint_classical                  

+  M1.H                                 M1.T                                 M1.add_to_entry                      M1.adjugate                           

+  M1.LLL_gram                          M1.act_on_polynomial                 M1.additive_order                    M1.anticommutator                    >

+  M1.LU                                M1.add_multiple_of_column            M1.adjoint                           M1.antitranspose                      

+ [?7h[?12l[?25h[?25l[?7lC

+ M1.C                                

+

+

+

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

+ M1.C                                 M1.QR                               [?7h[?12l[?25h[?25l[?7ladd_multiple_of_row

+ M1.QR                                M1.add_multiple_of_row              [?7h[?12l[?25h[?25l[?7ljoint_classical

+ M1.add_multiple_of_row               M1.adjoint_classical                [?7h[?12l[?25h[?25l[?7lpply_map

+ QRadd_multiple_of_rowjoint_classical  pply_map        

+ Tadd_to_entryjugat    pply_morphism

+<acton_polynomialdditive_order   ntcommutatos_bipartite_graph

+ add_multiple_of_columnjoint               ntitransposes_sum_of_permutations[?7h[?12l[?25h[?25l[?7lugment

+add_multiple_of_rowjoint_classical  pply_map        ugment  

+add_to_entryjugat    pply_morphismutomorphism_of_rows_and_columns

+dditive_order   ntcommutatos_bipartite_graphbase_extend       

+joint               ntitransposes_sum_of_permutationsbase_ring             [?7h[?12l[?25h[?25l[?7lblock_ldlt

+joint_classical  pply_map        ugment  block_ldlt

+jugat    pply_morphismutomorphism_of_rows_and_columnsblock_sum                        

+ntcommutatos_bipartite_graphbase_extend       crtesian_product

+ntitransposes_sum_of_permutationsbase_ring             ctgory [?7h[?12l[?25h[?25l[?7lchange_ring

+pply_map        ugment  block_ldltchange_ring

+pply_morphismutomorphism_of_rows_and_columnsblock_sum                        characteristic_polynomial

+s_bipartite_graphbase_extend       crtesian_productharpoly         

+s_sum_of_permutationsbase_ring             ctgory holesk[?7h[?12l[?25h[?25l[?7loefficiet

+ugment  block_ldltchange_ringoefficiet

+utomorphism_of_rows_and_columnsblock_sum                        characteristic_polynomialoefficients             

+base_extend       crtesian_productharpoly         olumn  

+base_ring             ctgory holeskolumn_ambient_module[?7h[?12l[?25h[?25l[?7lr

+

+

+

+

+[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: M1.rank()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NotImplementedError                       Traceback (most recent call last)
+Input In [63], in <cell line: 1>()
+----> 1 M1.rank()
+
+File /ext/sage/9.7/src/sage/matrix/matrix_modn_dense_template.pxi:2159, in sage.matrix.matrix_modn_dense_float.Matrix_modn_dense_template.rank()
+   2157         # linbox is very buggy for p=2, but this code should never
+   2158         # be called since p=2 is handled via M4RI
+-> 2159         return Matrix_dense.rank(self)
+   2160 
+   2161 def determinant(self):
+
+File /ext/sage/9.7/src/sage/matrix/matrix0.pyx:4643, in sage.matrix.matrix0.Matrix.rank()
+   4641 if self._nrows == 0 or self._ncols == 0:
+   4642     return 0
+-> 4643 r = len(self.pivots())
+   4644 self.cache('rank', r)
+   4645 return r
+
+File /ext/sage/9.7/src/sage/matrix/matrix0.pyx:4600, in sage.matrix.matrix0.Matrix.pivots()
+   4598 x = self.fetch('pivots')
+   4599 if not x is None: return tuple(x)
+-> 4600 self.echelon_form()
+   4601 x = self.fetch('pivots')
+   4602 if x is None:
+
+File /ext/sage/9.7/src/sage/matrix/matrix2.pyx:7727, in sage.matrix.matrix2.Matrix.echelon_form()
+   7725 E = self.__copy__()
+   7726 if algorithm == 'default':
+-> 7727     v = E.echelonize(cutoff=cutoff, **kwds)
+   7728 else:
+   7729     v = E.echelonize(algorithm = algorithm, cutoff=cutoff, **kwds)
+
+File /ext/sage/9.7/src/sage/matrix/matrix_modn_dense_template.pxi:1725, in sage.matrix.matrix_modn_dense_float.Matrix_modn_dense_template.echelonize()
+   1723 
+   1724         if not self.base_ring().is_field():
+-> 1725             raise NotImplementedError("Echelon form not implemented over '%s'."%self.base_ring())
+   1726 
+   1727         if algorithm == 'linbox':
+
+NotImplementedError: Echelon form not implemented over 'Ring of integers modulo 9'.
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM1.rank()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: M1

+[?7h[?12l[?25h[?2004l[?7h[3 4]
+[6 3]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lorma.expansionat_infty(prec=30)[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l m in range(1, p^2):[?7h[?12l[?25h[?25l[?7lalista2:[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lrange(0, 10):[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lrange[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: for a in range(3):

+....: [?7h[?12l[?25h[?25l[?7lf += a[i]*x^i[?7h[?12l[?25h[?25l[?7lor B in range(-10, 30):[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lb0, 10):[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lrange[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7l....:     for b in range(3):

+....: [?7h[?12l[?25h[?25l[?7lfor k in range(1, p-1):[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lrange[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7l....:         for c in range(3):

+....: [?7h[?12l[?25h[?25l[?7lpass[?7h[?12l[?25h[?25l[?7lrint(e, f, g)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lif not(LHS == RHS):[?7h[?12l[?25h[?25l[?7lif[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l....:             if 0 == 1:

+....: [?7h[?12l[?25h[?25l[?7lprint(m, k)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l....:                 print(1)

+....: [?7h[?12l[?25h[?25l[?7lsage: for a in range(3):

+....:     for b in range(3):

+....:         for c in range(3):

+....:             if 0 == 1:

+....:                 print(1)

+....: 

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

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7list_of_m = [m for m in list_of_m if m%p != 0][?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7llist[?7h[?12l[?25h[?25l[?7llista = ['a', 'b','c'][?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: lista = []

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llista = [][?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: licznik = 0

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llicznik = 0[?7h[?12l[?25h[?25l[?7lsta =[][?7h[?12l[?25h[?25l[?7lsage: for a in range(3):

+....:     for b in range(3):

+....:         for c in range(3):

+....:             if 0 == 1:

+....:                 print(1)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = d/(e*g)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lrange[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7l

+....: [?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1 + 3*a[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[],[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l....:                 M = matrix(R9, [[1 + 3*a, 1+3*b], [3*c, 1+3*d]])

+....: [?7h[?12l[?25h[?25l[?7lif e == 3:[?7h[?12l[?25h[?25l[?7lif[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lind[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldetity_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lntity_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7l....:                 if M^3 == identity_matrix(R9, 2):

+....: [?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l....:                     licznik += 1

+....: [?7h[?12l[?25h[?25l[?7lsage: for a in range(3):

+....:     for b in range(3):

+....:         for c in range(3):

+....:             for d in range(3):

+....:                 M = matrix(R9, [[1 + 3*a, 1+3*b], [3*c, 1+3*d]])

+....:                 if M^3 == identity_matrix(R9, 2):

+....:                     licznik += 1

+....: 

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7lsage: 3^4

+[?7h[?12l[?25h[?2004l[?7h81
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llicznik = 0[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lnik = 0[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7lsage: licznik

+[?7h[?12l[?25h[?2004l[?7h27
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM1[?7h[?12l[?25h[?25l[?7lsage: M

+[?7h[?12l[?25h[?2004l[?7h[7 7]
+[6 7]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg[?7h[?12l[?25h[?25l[?7l = yy^3/xx^3[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l2*x^4 + x^3 + x^2 + 2*x - x^3* (x^3 - x)[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l+ x^3 + x^2 + 2*x - x^3* (x^3 - x)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*x^2 + 2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx^2 + 2[?7h[?12l[?25h[?25l[?7lsage: g = 2*x^4 + 2*x^2 + 2

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = 2*x^4 + 2*x^2 + 2[?7h[?12l[?25h[?25l[?7l(x+1) - g[?7h[?12l[?25h[?25l[?7lx+1) - g[?7h[?12l[?25h[?25l[?7lsage: g(x+1) - g

+[?7h[?12l[?25h[?2004l[?7h2*x^3 + 1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy/xx[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: v = yy/xx^2

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy/xx[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7lsage: yy*v^2 - yy^2*v

+[?7h[?12l[?25h[?2004l[?7h((2*x^4 + 2*x^2 + 2)/x^3)*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy*v^2 - yy^2*v[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lhy*v^2 - y^2*v[?7h[?12l[?25h[?25l[?7l y*v^2 - y^2*v[?7h[?12l[?25h[?25l[?7l=y*v^2 - y^2*v[?7h[?12l[?25h[?25l[?7l y*v^2 - y^2*v[?7h[?12l[?25h[?25l[?7lsage: h = yy*v^2 - yy^2*v

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh = yy*v^2 - yy^2*v[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ldinates[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: h.coordinates()

+[?7h[?12l[?25h[?2004l[?7h[1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy*v^2 - yy^2*v[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: yx = yy/xx

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyx = yy/xx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: yx^8*yx.diffn()

+[?7h[?12l[?25h[?2004l[?7h((-x^10 + x^6 + x^4 - 1)/(x^5*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh.coordinates()[?7h[?12l[?25h[?25l[?7lsage: h

+[?7h[?12l[?25h[?2004l[?7h((2*x^4 + 2*x^2 + 2)/x^3)*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(x+1) - g[?7h[?12l[?25h[?25l[?7l = 2*x^4 + 2*x^2 + 2[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lyy^3/xx^3[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2(x+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7l/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7lsage: g = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g

+[?7h[?12l[?25h[?2004l[?7h((2*x + 1)/(x^2 + x))*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/xx - yy/(xx+C.one)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: g = yy/xx

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy/xx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7lsage: g = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = yy^2/(xx+C.one)^2 * yy/xx - yy/(xx+C.one) * yy^2/xx^2[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: g1 = g + yy/xx

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg1 = g + yy/xx[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: g1

+[?7h[?12l[?25h[?2004l[?7h(2/(x^2 + x))*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lansion_at_infty[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g1.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7h2*t + t^3 + 2*t^5 + t^9 + t^13 + 2*t^17 + O(t^21)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ M = msasage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l = matrix(R9, [[4, 4], [6, 4]])[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lmatrix(R9, [[4, 4], [6, 4]])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, [4, 4], [6, 4])[?7h[?12l[?25h[?25l[?7l, [4, 4], [6, 4])[?7h[?12l[?25h[?25l[?7lQ, [4, 4], [6, 4])[?7h[?12l[?25h[?25l[?7lQ, [4, 4], [6, 4])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l], [6, 4])[?7h[?12l[?25h[?25l[?7l], [6, 4])[?7h[?12l[?25h[?25l[?7l], [6, 4])[?7h[?12l[?25h[?25l[?7l], [6, 4])[?7h[?12l[?25h[?25l[?7l-], [6, 4])[?7h[?12l[?25h[?25l[?7l1], [6, 4])[?7h[?12l[?25h[?25l[?7l,], [6, 4])[?7h[?12l[?25h[?25l[?7l ], [6, 4])[?7h[?12l[?25h[?25l[?7l-], [6, 4])[?7h[?12l[?25h[?25l[?7l1], [6, 4])[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l]])[?7h[?12l[?25h[?25l[?7l1]])[?7h[?12l[?25h[?25l[?7l,]])[?7h[?12l[?25h[?25l[?7l ]])[?7h[?12l[?25h[?25l[?7l0]])[?7h[?12l[?25h[?25l[?7l[[]][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: M = matrix(QQ, [[-1, -1], [1, 0]])

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM = matrix(QQ, [[-1, -1], [1, 0]])[?7h[?12l[?25h[?25l[?7l^3[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: M^3

+[?7h[?12l[?25h[?2004l[?7h[1 0]
+[0 1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM^3[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l = M - identity_matrix(R9, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l - identity_matrix(R9, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7lQ, 2)[?7h[?12l[?25h[?25l[?7lQ, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: M1 = M - identity_matrix(QQ, 2)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM1 = M - identity_matrix(QQ, 2)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.rank()[?7h[?12l[?25h[?25l[?7lkernel()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: M1.kernel()

+[?7h[?12l[?25h[?2004l[?7hVector space of degree 2 and dimension 0 over Rational Field
+Basis matrix:
+[]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l11/3-4[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llicznik[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0 dx
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+f2 ((-x^6 - 1)/(x^2*y - y)) dx
+((x^4 + x^2 + 1)/(x^6*y)) dx
+[0]
+[0]
+t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
+((x^10 - x^6 + 1)/(x^2*y - y)) dx
+(x^7 + x, 0)
+((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+((-x^6 - 1)/(x^2*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cartier_matrix()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7las[?7h[?12l[?25h[?25l[?7las_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l1y)[?7h[?12l[?25h[?25l[?7l/y)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, superelliptic_function(C, 1/y))

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [6], in <cell line: 1>()
+----> 1 AS = as_cover(C, superelliptic_function(C, Integer(1)/y))
+
+NameError: name 'y' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, superelliptic_function(C, 1/y))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCy)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsuper)[?7h[?12l[?25h[?25l[?7lsupe)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7ly)[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y)^(-1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, (C.y)^(-1))

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [7], in <cell line: 1>()
+----> 1 AS = as_cover(C, (C.y)**(-Integer(1)))
+
+File <string>:6, in __init__(self, C, list_of_fcts, prec)
+
+TypeError: object of type 'superelliptic_function' has no len()
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, (C.y)^(-1))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[(C.y)^(-1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [(C.y)^(-1)])

+[?7h[?12l[?25h[?2004lno  0 -th root; divide by 1
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [8], in <cell line: 1>()
+----> 1 AS = as_cover(C, [(C.y)**(-Integer(1))])
+
+File <string>:44, in __init__(self, C, list_of_fcts, prec)
+
+ValueError: not enough values to unpack (expected 4, got 2)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x+1)^5 - x^5[?7h[?12l[?25h[?25l[?7lC.x/C.y).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly)^3/(C.)^4[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l(-1)[?7h[?12l[?25h[?25l[?7l(-1)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 - x, 2)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0 dx
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+f2 ((-x^6 - 1)/(x^2*y - y)) dx
+((x^4 + x^2 + 1)/(x^6*y)) dx
+[0]
+[0]
+t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
+((x^10 - x^6 + 1)/(x^2*y - y)) dx
+(x^7 + x, 0)
+((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+((-x^6 - 1)/(x^2*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.p_rank()

+[?7h[?12l[?25h[?2004lHyperelliptic Curve over Finite Field of size 3 defined by y^2 = x^3 + 2*x
+[?7h0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR.<u,v> = QQ[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 1)))". Alternatively, "R.<u,v> = QQ[]; WeierstrassForm(v^2 - (u^4 - 1), transformation=True)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lTru[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: R.<u,v> = QQ[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 1)))

+[?7h[?12l[?25h[?2004l[?7hElliptic Curve defined by y^2 = x^3 + 4*x over Multivariate Polynomial Ring in u, v over Rational Field
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR.<u,v> = QQ[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 1)))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]; ElipticCurve(WeierstrasForm(v^2 - (u^4 - 1)[?7h[?12l[?25h[?25l[?7l[]; ElipticCurve(WeierstrasForm(v^2 - (u^4 - 1)[?7h[?12l[?25h[?25l[?7lG[]; ElipticCurve(WeierstrasForm(v^2 - (u^4 - 1)[?7h[?12l[?25h[?25l[?7lF[]; ElipticCurve(WeierstrasForm(v^2 - (u^4 - 1)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[; ElipticCurve(WeierstrasForm(v^2 - (u^4 - 1)[?7h[?12l[?25h[?25l[?7l; ElipticCurve(WeierstrasForm(v^2 - (u^4 - 1)[?7h[?12l[?25h[?25l[?7l(; ElipticCurve(WeierstrasForm(v^2 - (u^4 - 1)[?7h[?12l[?25h[?25l[?7l3; ElipticCurve(WeierstrasForm(v^2 - (u^4 - 1)[?7h[?12l[?25h[?25l[?7l(); ElipticCurve(WeierstrasForm(v^2 - (u^4 - 1)[?7h[?12l[?25h[?25l[?7l()[; ElipticCurve(WeierstrasForm(v^2 - (u^4 - 1)[?7h[?12l[?25h[?25l[?7l[]; ElipticCurve(WeierstrasForm(v^2 - (u^4 - 1)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: R.<u,v> = GF(3)[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 1)))

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+ZeroDivisionError                         Traceback (most recent call last)
+Input In [13], in <cell line: 1>()
+----> 1 R = GF(Integer(3))['u, v']; (u, v,) = R._first_ngens(2); EllipticCurve(WeierstrassForm(v**Integer(2) - (u**Integer(4) - Integer(1))))
+
+File /ext/sage/9.7/src/sage/misc/lazy_import.pyx:391, in sage.misc.lazy_import.LazyImport.__call__()
+    389         True
+    390     """
+--> 391     return self.get_object()(*args, **kwds)
+    392 
+    393 def __repr__(self):
+
+File /ext/sage/9.7/src/sage/schemes/toric/weierstrass.py:499, in WeierstrassForm(polynomial, variables, transformation)
+    497     return WeierstrassForm_P1xP1(polynomial, variables)
+    498 if polygon is polar_P2_112_polytope():
+--> 499     return WeierstrassForm_P2_112(polynomial, variables)
+    500 raise ValueError('Newton polytope is not contained in a reflexive polygon')
+
+File /ext/sage/9.7/src/sage/schemes/toric/weierstrass.py:1078, in WeierstrassForm_P2_112(polynomial, variables)
+   1076 delta = _partial_discriminant(polynomial, y, t)
+   1077 Q = invariant_theory.binary_quartic(delta, x, z)
+-> 1078 g2 = Q.EisensteinD()
+   1079 g3 = -Q.EisensteinE()
+   1080 return (-g2/4, -g3/4)
+
+File /ext/sage/9.7/src/sage/misc/cachefunc.pyx:2299, in sage.misc.cachefunc.CachedMethodCallerNoArgs.__call__()
+   2297 if self.cache is None:
+   2298     f = self.f
+-> 2299     self.cache = f(self._instance)
+   2300 return self.cache
+   2301 
+
+File /ext/sage/9.7/src/sage/rings/invariants/invariant_theory.py:1480, in BinaryQuartic.EisensteinD(self)
+   1455 @cached_method
+   1456 def EisensteinD(self):
+   1457     r"""
+   1458     One of the Eisenstein invariants of a binary quartic.
+   1459 
+   (...)
+   1478         3*a2^2 - 4*a1*a3 + a0*a4
+   1479     """
+-> 1480     a = self.scaled_coeffs()
+   1481     assert len(a) == 5
+   1482     return a[0]*a[4]+3*a[2]**2-4*a[1]*a[3]
+
+File /ext/sage/9.7/src/sage/rings/invariants/invariant_theory.py:1452, in BinaryQuartic.scaled_coeffs(self)
+   1425 """
+   1426 The coefficients of a binary quartic.
+   1427 
+   (...)
+   1449     (a0, a1, a2, a3, a4)
+   1450 """
+   1451 coeff = self.coeffs()
+-> 1452 return (coeff[0], coeff[1]/4, coeff[2]/6, coeff[3]/4, coeff[4])
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__()
+   1740 
+   1741         try:
+-> 1742             return coercion_model.bin_op(left, right, truediv)
+   1743         except TypeError:
+   1744             return NotImplemented
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1196, in sage.structure.coerce.CoercionModel.bin_op()
+   1194         return (<Action>action)._act_(x, y)
+   1195     else:
+-> 1196         return (<Action>action)._act_(y, x)
+   1197 
+   1198 # Now coerce to a common parent and do the operation there
+
+File /ext/sage/9.7/src/sage/categories/action.pyx:494, in sage.categories.action.PrecomposedAction._act_()
+    492     if self.S_precomposition is not None:
+    493         x = self.S_precomposition._call_(x)
+--> 494     return self._action._act_(g, x)
+    495 
+    496 def domain(self):
+
+File /ext/sage/9.7/src/sage/categories/action.pyx:494, in sage.categories.action.PrecomposedAction._act_()
+    492     if self.S_precomposition is not None:
+    493         x = self.S_precomposition._call_(x)
+--> 494     return self._action._act_(g, x)
+    495 
+    496 def domain(self):
+
+File /ext/sage/9.7/src/sage/categories/action.pyx:407, in sage.categories.action.InverseAction._act_()
+    405     if self.S_precomposition is not None:
+    406         x = self.S_precomposition(x)
+--> 407     return self._action._act_(~g, x)
+    408 
+    409 def codomain(self):
+
+File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2821, in sage.rings.finite_rings.integer_mod.IntegerMod_int.__invert__()
+   2819 x = self.__modulus.inverses[self.ivalue]
+   2820 if x is None:
+-> 2821     raise ZeroDivisionError(f"inverse of Mod({self}, {self.__modulus.sageInteger}) does not exist")
+   2822 else:
+   2823     return x
+
+ZeroDivisionError: inverse of Mod(0, 3) does not exist
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR.<u,v> = GF(3)[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 1)))[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR.<u,v> = GF(3)[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 1)))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l 1)[?7h[?12l[?25h[?25l[?7l+ 1)[?7h[?12l[?25h[?25l[?7lsage: R.<u,v> = GF(3)[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 + 1)))

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+ZeroDivisionError                         Traceback (most recent call last)
+Input In [14], in <cell line: 1>()
+----> 1 R = GF(Integer(3))['u, v']; (u, v,) = R._first_ngens(2); EllipticCurve(WeierstrassForm(v**Integer(2) - (u**Integer(4) + Integer(1))))
+
+File /ext/sage/9.7/src/sage/misc/lazy_import.pyx:391, in sage.misc.lazy_import.LazyImport.__call__()
+    389         True
+    390     """
+--> 391     return self.get_object()(*args, **kwds)
+    392 
+    393 def __repr__(self):
+
+File /ext/sage/9.7/src/sage/schemes/toric/weierstrass.py:499, in WeierstrassForm(polynomial, variables, transformation)
+    497     return WeierstrassForm_P1xP1(polynomial, variables)
+    498 if polygon is polar_P2_112_polytope():
+--> 499     return WeierstrassForm_P2_112(polynomial, variables)
+    500 raise ValueError('Newton polytope is not contained in a reflexive polygon')
+
+File /ext/sage/9.7/src/sage/schemes/toric/weierstrass.py:1078, in WeierstrassForm_P2_112(polynomial, variables)
+   1076 delta = _partial_discriminant(polynomial, y, t)
+   1077 Q = invariant_theory.binary_quartic(delta, x, z)
+-> 1078 g2 = Q.EisensteinD()
+   1079 g3 = -Q.EisensteinE()
+   1080 return (-g2/4, -g3/4)
+
+File /ext/sage/9.7/src/sage/misc/cachefunc.pyx:2299, in sage.misc.cachefunc.CachedMethodCallerNoArgs.__call__()
+   2297 if self.cache is None:
+   2298     f = self.f
+-> 2299     self.cache = f(self._instance)
+   2300 return self.cache
+   2301 
+
+File /ext/sage/9.7/src/sage/rings/invariants/invariant_theory.py:1480, in BinaryQuartic.EisensteinD(self)
+   1455 @cached_method
+   1456 def EisensteinD(self):
+   1457     r"""
+   1458     One of the Eisenstein invariants of a binary quartic.
+   1459 
+   (...)
+   1478         3*a2^2 - 4*a1*a3 + a0*a4
+   1479     """
+-> 1480     a = self.scaled_coeffs()
+   1481     assert len(a) == 5
+   1482     return a[0]*a[4]+3*a[2]**2-4*a[1]*a[3]
+
+File /ext/sage/9.7/src/sage/rings/invariants/invariant_theory.py:1452, in BinaryQuartic.scaled_coeffs(self)
+   1425 """
+   1426 The coefficients of a binary quartic.
+   1427 
+   (...)
+   1449     (a0, a1, a2, a3, a4)
+   1450 """
+   1451 coeff = self.coeffs()
+-> 1452 return (coeff[0], coeff[1]/4, coeff[2]/6, coeff[3]/4, coeff[4])
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__()
+   1740 
+   1741         try:
+-> 1742             return coercion_model.bin_op(left, right, truediv)
+   1743         except TypeError:
+   1744             return NotImplemented
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1196, in sage.structure.coerce.CoercionModel.bin_op()
+   1194         return (<Action>action)._act_(x, y)
+   1195     else:
+-> 1196         return (<Action>action)._act_(y, x)
+   1197 
+   1198 # Now coerce to a common parent and do the operation there
+
+File /ext/sage/9.7/src/sage/categories/action.pyx:494, in sage.categories.action.PrecomposedAction._act_()
+    492     if self.S_precomposition is not None:
+    493         x = self.S_precomposition._call_(x)
+--> 494     return self._action._act_(g, x)
+    495 
+    496 def domain(self):
+
+File /ext/sage/9.7/src/sage/categories/action.pyx:494, in sage.categories.action.PrecomposedAction._act_()
+    492     if self.S_precomposition is not None:
+    493         x = self.S_precomposition._call_(x)
+--> 494     return self._action._act_(g, x)
+    495 
+    496 def domain(self):
+
+File /ext/sage/9.7/src/sage/categories/action.pyx:407, in sage.categories.action.InverseAction._act_()
+    405     if self.S_precomposition is not None:
+    406         x = self.S_precomposition(x)
+--> 407     return self._action._act_(~g, x)
+    408 
+    409 def codomain(self):
+
+File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2821, in sage.rings.finite_rings.integer_mod.IntegerMod_int.__invert__()
+   2819 x = self.__modulus.inverses[self.ivalue]
+   2820 if x is None:
+-> 2821     raise ZeroDivisionError(f"inverse of Mod({self}, {self.__modulus.sageInteger}) does not exist")
+   2822 else:
+   2823     return x
+
+ZeroDivisionError: inverse of Mod(0, 3) does not exist
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR.<u,v> = GF(3)[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 + 1)))[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7lQQ[]; ElliptcCurve(WierstassForm(v^2 - (u^4 - 1)))[?7h[?12l[?25h[?25l[?7lsage: R.<u,v> = QQ[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 1)))

+[?7h[?12l[?25h[?2004l[?7hElliptic Curve defined by y^2 = x^3 + 4*x over Multivariate Polynomial Ring in u, v over Rational Field
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR.<u,v> = QQ[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 1)))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l2))[?7h[?12l[?25h[?25l[?7lsage: R.<u,v> = QQ[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 2)))

+[?7h[?12l[?25h[?2004l[?7hElliptic Curve defined by y^2 = x^3 + 8*x over Multivariate Polynomial Ring in u, v over Rational Field
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR.<u,v> = QQ[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 2)))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l1))[?7h[?12l[?25h[?25l[?7l/))[?7h[?12l[?25h[?25l[?7l2))[?7h[?12l[?25h[?25l[?7lsage: R.<u,v> = QQ[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 1/2)))

+[?7h[?12l[?25h[?2004l[?7hElliptic Curve defined by y^2 = x^3 + 2*x over Multivariate Polynomial Ring in u, v over Rational Field
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR.<u,v> = QQ[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 - 1/2)))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l+))[?7h[?12l[?25h[?25l[?7l1))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l 1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: R.<u,v> = QQ[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 + 1)))

+[?7h[?12l[?25h[?2004l[?7hElliptic Curve defined by y^2 = x^3 + (-4)*x over Multivariate Polynomial Ring in u, v over Rational Field
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR.<u,v> = QQ[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 + 1)))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]; ElipticCurve(WeierstrasForm(v^2 - (u^4 + 1)[?7h[?12l[?25h[?25l[?7l[]; ElipticCurve(WeierstrasForm(v^2 - (u^4 + 1)[?7h[?12l[?25h[?25l[?7lG[]; ElipticCurve(WeierstrasForm(v^2 - (u^4 + 1)[?7h[?12l[?25h[?25l[?7lF[]; ElipticCurve(WeierstrasForm(v^2 - (u^4 + 1)[?7h[?12l[?25h[?25l[?7l([]; ElipticCurve(WeierstrasForm(v^2 - (u^4 + 1)[?7h[?12l[?25h[?25l[?7l3[]; ElipticCurve(WeierstrasForm(v^2 - (u^4 + 1)[?7h[?12l[?25h[?25l[?7l)[]; ElipticCurve(WeierstrasForm(v^2 - (u^4 + 1)[?7h[?12l[?25h[?25l[?7lsage: R.<u,v> = GF(3)[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 + 1)))

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+ZeroDivisionError                         Traceback (most recent call last)
+Input In [19], in <cell line: 1>()
+----> 1 R = GF(Integer(3))['u, v']; (u, v,) = R._first_ngens(2); EllipticCurve(WeierstrassForm(v**Integer(2) - (u**Integer(4) + Integer(1))))
+
+File /ext/sage/9.7/src/sage/misc/lazy_import.pyx:391, in sage.misc.lazy_import.LazyImport.__call__()
+    389         True
+    390     """
+--> 391     return self.get_object()(*args, **kwds)
+    392 
+    393 def __repr__(self):
+
+File /ext/sage/9.7/src/sage/schemes/toric/weierstrass.py:499, in WeierstrassForm(polynomial, variables, transformation)
+    497     return WeierstrassForm_P1xP1(polynomial, variables)
+    498 if polygon is polar_P2_112_polytope():
+--> 499     return WeierstrassForm_P2_112(polynomial, variables)
+    500 raise ValueError('Newton polytope is not contained in a reflexive polygon')
+
+File /ext/sage/9.7/src/sage/schemes/toric/weierstrass.py:1078, in WeierstrassForm_P2_112(polynomial, variables)
+   1076 delta = _partial_discriminant(polynomial, y, t)
+   1077 Q = invariant_theory.binary_quartic(delta, x, z)
+-> 1078 g2 = Q.EisensteinD()
+   1079 g3 = -Q.EisensteinE()
+   1080 return (-g2/4, -g3/4)
+
+File /ext/sage/9.7/src/sage/misc/cachefunc.pyx:2299, in sage.misc.cachefunc.CachedMethodCallerNoArgs.__call__()
+   2297 if self.cache is None:
+   2298     f = self.f
+-> 2299     self.cache = f(self._instance)
+   2300 return self.cache
+   2301 
+
+File /ext/sage/9.7/src/sage/rings/invariants/invariant_theory.py:1480, in BinaryQuartic.EisensteinD(self)
+   1455 @cached_method
+   1456 def EisensteinD(self):
+   1457     r"""
+   1458     One of the Eisenstein invariants of a binary quartic.
+   1459 
+   (...)
+   1478         3*a2^2 - 4*a1*a3 + a0*a4
+   1479     """
+-> 1480     a = self.scaled_coeffs()
+   1481     assert len(a) == 5
+   1482     return a[0]*a[4]+3*a[2]**2-4*a[1]*a[3]
+
+File /ext/sage/9.7/src/sage/rings/invariants/invariant_theory.py:1452, in BinaryQuartic.scaled_coeffs(self)
+   1425 """
+   1426 The coefficients of a binary quartic.
+   1427 
+   (...)
+   1449     (a0, a1, a2, a3, a4)
+   1450 """
+   1451 coeff = self.coeffs()
+-> 1452 return (coeff[0], coeff[1]/4, coeff[2]/6, coeff[3]/4, coeff[4])
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__()
+   1740 
+   1741         try:
+-> 1742             return coercion_model.bin_op(left, right, truediv)
+   1743         except TypeError:
+   1744             return NotImplemented
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1196, in sage.structure.coerce.CoercionModel.bin_op()
+   1194         return (<Action>action)._act_(x, y)
+   1195     else:
+-> 1196         return (<Action>action)._act_(y, x)
+   1197 
+   1198 # Now coerce to a common parent and do the operation there
+
+File /ext/sage/9.7/src/sage/categories/action.pyx:494, in sage.categories.action.PrecomposedAction._act_()
+    492     if self.S_precomposition is not None:
+    493         x = self.S_precomposition._call_(x)
+--> 494     return self._action._act_(g, x)
+    495 
+    496 def domain(self):
+
+File /ext/sage/9.7/src/sage/categories/action.pyx:494, in sage.categories.action.PrecomposedAction._act_()
+    492     if self.S_precomposition is not None:
+    493         x = self.S_precomposition._call_(x)
+--> 494     return self._action._act_(g, x)
+    495 
+    496 def domain(self):
+
+File /ext/sage/9.7/src/sage/categories/action.pyx:407, in sage.categories.action.InverseAction._act_()
+    405     if self.S_precomposition is not None:
+    406         x = self.S_precomposition(x)
+--> 407     return self._action._act_(~g, x)
+    408 
+    409 def codomain(self):
+
+File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2821, in sage.rings.finite_rings.integer_mod.IntegerMod_int.__invert__()
+   2819 x = self.__modulus.inverses[self.ivalue]
+   2820 if x is None:
+-> 2821     raise ZeroDivisionError(f"inverse of Mod({self}, {self.__modulus.sageInteger}) does not exist")
+   2822 else:
+   2823     return x
+
+ZeroDivisionError: inverse of Mod(0, 3) does not exist
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR.<u,v> = GF(3)[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 + 1)))[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0 dx
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+f2 ((-x^6 - 1)/(x^2*y - y)) dx
+((x^4 + x^2 + 1)/(x^6*y)) dx
+[0]
+[0]
+t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
+((x^10 - x^6 + 1)/(x^2*y - y)) dx
+(x^7 + x, 0)
+((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+((-x^6 - 1)/(x^2*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.p_rank()[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l4, 2)[?7h[?12l[?25h[?25l[?7l , 2)[?7h[?12l[?25h[?25l[?7l-, 2)[?7h[?12l[?25h[?25l[?7l , 2)[?7h[?12l[?25h[?25l[?7lx, 2)[?7h[?12l[?25h[?25l[?7l^, 2)[?7h[?12l[?25h[?25l[?7l3, 2)[?7h[?12l[?25h[?25l[?7l , 2)[?7h[?12l[?25h[?25l[?7l+, 2)[?7h[?12l[?25h[?25l[?7l , 2)[?7h[?12l[?25h[?25l[?7lx, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^4 - x^3 + x, 2)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^4 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l.p_rank()[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l_rank()[?7h[?12l[?25h[?25l[?7lsage: C.p_rank()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [3], in <cell line: 1>()
+----> 1 C.p_rank()
+
+File <string>:176, in p_rank(self)
+
+File /ext/sage/9.7/src/sage/schemes/hyperelliptic_curves/hyperelliptic_finite_field.py:1889, in HyperellipticCurve_finite_field.p_rank(self)
+   1855 r"""
+   1856 INPUT:
+   1857 
+   (...)
+   1880     0
+   1881 """
+   1882 #We use caching here since Hasse Witt is needed to compute p_rank. So if the Hasse Witt
+   1883 #is already computed it is stored in list A. If it was not cached (i.e. A is empty), we simply
+   1884 #compute it. If it is cached then we need to make sure that we have the correct one. So check
+   (...)
+   1887 # However, it seems a waste of time to manually analyse the cache
+   1888 # -- See Trac Ticket #11115
+-> 1889 N, E = self._Hasse_Witt_cached()
+   1890 if E != self:
+   1891     self._Hasse_Witt_cached.clear_cache()
+
+File /ext/sage/9.7/src/sage/misc/cachefunc.pyx:2299, in sage.misc.cachefunc.CachedMethodCallerNoArgs.__call__()
+   2297 if self.cache is None:
+   2298     f = self.f
+-> 2299     self.cache = f(self._instance)
+   2300 return self.cache
+   2301 
+
+File /ext/sage/9.7/src/sage/schemes/hyperelliptic_curves/hyperelliptic_finite_field.py:1727, in HyperellipticCurve_finite_field._Hasse_Witt_cached(self)
+   1647 r"""
+   1648 This is where Hasse_Witt is actually computed.
+   1649 
+   (...)
+   1712     0
+   1713 """
+   1714 # If Cartier Matrix is already cached for this curve, use that or evaluate it to get M,
+   1715 #Coeffs, genus, Fq=base field of self, p=char(Fq). This is so we have one less matrix to
+   1716 #compute.
+   (...)
+   1725 #that don't  accept arguments. Anyway, the easiest is to call
+   1726 #the cached method and simply see whether the data belong to self.
+-> 1727 M, Coeffs, g, Fq, p, E = self._Cartier_matrix_cached()
+   1728 if E != self:
+   1729     self._Cartier_matrix_cached.clear_cache()
+
+File /ext/sage/9.7/src/sage/misc/cachefunc.pyx:2299, in sage.misc.cachefunc.CachedMethodCallerNoArgs.__call__()
+   2297 if self.cache is None:
+   2298     f = self.f
+-> 2299     self.cache = f(self._instance)
+   2300 return self.cache
+   2301 
+
+File /ext/sage/9.7/src/sage/schemes/hyperelliptic_curves/hyperelliptic_finite_field.py:1523, in HyperellipticCurve_finite_field._Cartier_matrix_cached(self)
+   1521 #this implementation is for odd degree only, even degree will be handled later.
+   1522 if d%2 == 0:
+-> 1523     raise ValueError("In this implementation the degree of f must be odd")
+   1524 #Compute resultant to make sure no repeated roots
+   1525 df=f.derivative()
+
+ValueError: In this implementation the degree of f must be odd
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.p_rank()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcatier_matrix()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrtier_matrix()[?7h[?12l[?25h[?25l[?7lsage: C.cartier_matrix()

+[?7h[?12l[?25h[?2004l[?7h[0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cartier_matrix()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cartier_matrix()[?7h[?12l[?25h[?25l[?7lsage: C

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^4 + 2*x^3 + x over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0 dx
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+f2 ((-x^6 - 1)/(x^2*y - y)) dx
+((x^4 + x^2 + 1)/(x^6*y)) dx
+[0]
+[0]
+t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
+((x^10 - x^6 + 1)/(x^2*y - y)) dx
+(x^7 + x, 0)
+((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+((-x^6 - 1)/(x^2*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.cartier_matrix()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrtier_matrix()[?7h[?12l[?25h[?25l[?7lsage: C.cartier_matrix()

+[?7h[?12l[?25h[?2004l[?7h[0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cartier_matrix()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.cartier_matrix()[?7h[?12l[?25h[?25l[?7lp_ank()[?7h[?12l[?25h[?25l[?7l = superelliptic(x^4 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^4 - x^3 + x, 2)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^4 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l.carti_matrix()[?7h[?12l[?25h[?25l[?7lde_rhambsis()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

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

+[?7h[?12l[?25h[?2004l0 dx
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+f2 ((-x^6 - 1)/(x^2*y - y)) dx
+((x^4 + x^2 + 1)/(x^6*y)) dx
+[0]
+[0]
+t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
+((x^10 - x^6 + 1)/(x^2*y - y)) dx
+(x^7 + x, 0)
+((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+((-x^6 - 1)/(x^2*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx.cartier()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.dx

+[?7h[?12l[?25h[?2004l[?7h1 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7liC.dx[?7h[?12l[?25h[?25l[?7lsC.dx[?7h[?12l[?25h[?25l[?7liC.dx[?7h[?12l[?25h[?25l[?7lnC.dx[?7h[?12l[?25h[?25l[?7lsC.dx[?7h[?12l[?25h[?25l[?7ltC.dx[?7h[?12l[?25h[?25l[?7laC.dx[?7h[?12l[?25h[?25l[?7lnC.dx[?7h[?12l[?25h[?25l[?7lceC.dx[?7h[?12l[?25h[?25l[?7lisinstance(C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: isinstance(C.dx,superelliptic_form)

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

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

+[?7h[?12l[?25h[?2004l0 dx
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+f2 ((-x^6 - 1)/(x^2*y - y)) dx
+((x^4 + x^2 + 1)/(x^6*y)) dx
+[0]
+[0]
+t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
+((x^10 - x^6 + 1)/(x^2*y - y)) dx
+(x^7 + x, 0)
+((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+((-x^6 - 1)/(x^2*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprint((x^8).quo_rem(x^4 + x^2 + 1))[?7h[?12l[?25h[?25l[?7larent)[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: patch(C)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [2], in <cell line: 1>()
+----> 1 patch(C)
+
+File <string>:5, in patch(C)
+
+NameError: name 'self' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0 dx
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+f2 ((-x^6 - 1)/(x^2*y - y)) dx
+((x^4 + x^2 + 1)/(x^6*y)) dx
+[0]
+[0]
+t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
+((x^10 - x^6 + 1)/(x^2*y - y)) dx
+(x^7 + x, 0)
+((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+((-x^6 - 1)/(x^2*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lpatch(C)[?7h[?12l[?25h[?25l[?7lsage: patch(C)

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = 2*x^3 + x over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpatch(C)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: patch(C).genus()

+[?7h[?12l[?25h[?2004l[?7h1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx[?7h[?12l[?25h[?25l[?7lsage: C

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = superelliptic(x^4 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7luperelliptic(x^4 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^4 - x^3 + x, 2)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^4 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpatch(C).genus()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ltch(C).genus()[?7h[?12l[?25h[?25l[?7lsage: patch(C).genus()

+[?7h[?12l[?25h[?2004l[?7h1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpatch(C).genus()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l().genus()[?7h[?12l[?25h[?25l[?7lsage: patch(C)

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x + 1 over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpatch(C)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lstr(E.local_data(2))[?7h[?12l[?25h[?25l[?7let*list2)[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x

+....: [?7h[?12l[?25h[?25l[?7l(

+)[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x

+....: )

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [10], in <cell line: 1>()
+----> 1 second_patch(C.x
+      2 )
+
+File <string>:19, in second_patch(argument)
+
+NameError: name 'y' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x

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

+[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [11], in <cell line: 1>()
+----> 1 second_patch(C.x)
+
+File <string>:19, in second_patch(argument)
+
+NameError: name 'y' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0 dx
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+f2 ((-x^6 - 1)/(x^2*y - y)) dx
+((x^4 + x^2 + 1)/(x^6*y)) dx
+[0]
+[0]
+t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
+((x^10 - x^6 + 1)/(x^2*y - y)) dx
+(x^7 + x, 0)
+((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+((-x^6 - 1)/(x^2*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [13], in <cell line: 1>()
+----> 1 second_patch(C.x)
+
+File <string>:20, in second_patch(argument)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2411, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
+   2409 if type(exp) is not Integer:
+   2410     try:
+-> 2411         exp = Integer(exp)
+   2412     except TypeError:
+   2413         try:
+
+File /ext/sage/9.7/src/sage/rings/integer.pyx:658, in sage.rings.integer.Integer.__init__()
+    656 otmp = getattr(x, "_integer_", None)
+    657 if otmp is not None:
+--> 658     set_from_Integer(self, otmp(the_integer_ring))
+    659     return
+    660 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:1391, in sage.rings.polynomial.polynomial_element.Polynomial._scalar_conversion()
+   1389     if self.degree() > 0:
+   1390         raise TypeError("cannot convert nonconstant polynomial")
+-> 1391     return R(self.get_coeff_c(0))
+   1392 
+   1393 _real_double_ = _scalar_conversion
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/categories/map.pyx:1692, in sage.categories.map.FormalCompositeMap._call_()
+   1690 """
+   1691 for f in self.__list:
+-> 1692     x = f._call_(x)
+   1693 return x
+   1694 
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1620, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
+   1618     Section._update_slots(self, _slots)
+   1619 
+-> 1620 cpdef Element _call_(self, _x):
+   1621     """
+   1622     Applies the section.
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1654, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
+   1652         raise ValueError("not integral")
+   1653     if nmod_poly_degree(x._numer) > 0:
+-> 1654         raise ValueError("not constant")
+   1655 ans = IntegerMod_int.__new__(IntegerMod_int)
+   1656 ans._parent = self.codomain()
+
+ValueError: not constant
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^4 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l.dx[?7h[?12l[?25h[?25l[?7lsage: C.

+[?7h[?12l[?25h[?2004l  Input In [14]
+    C.
+      ^
+SyntaxError: invalid syntax
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty()[1][?7h[?12l[?25h[?25l[?7lsage: C.x

+[?7h[?12l[?25h[?2004l[?7hx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x+1)^5 - x^5[?7h[?12l[?25h[?25l[?7lC.x/C.y).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()^(11)/(C.y)^3*C.dx[?7h[?12l[?25h[?25l[?7l().pth_root([?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(C.x).function[?7h[?12l[?25h[?25l[?7l (C.x).function[?7h[?12l[?25h[?25l[?7l=(C.x).function[?7h[?12l[?25h[?25l[?7l (C.x).function[?7h[?12l[?25h[?25l[?7lsage: g = (C.x).function

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = (C.x).function[?7h[?12l[?25h[?25l[?7l(x+1) - g[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g(x = x+1, y = y+1)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [17], in <cell line: 1>()
+----> 1 g(x = x+Integer(1), y = y+Integer(1))
+
+NameError: name 'y' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y = C.fct_field[?7h[?12l[?25h[?25l[?7lsage: Fxy, Rxy, x, y = C.fct_field

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y = C.fct_field[?7h[?12l[?25h[?25l[?7lg(x = +1, y=y+1)[?7h[?12l[?25h[?25l[?7lsage: g(x = x+1, y = y+1)

+[?7h[?12l[?25h[?2004l[?7hx + 1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0 dx
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+f2 ((-x^6 - 1)/(x^2*y - y)) dx
+((x^4 + x^2 + 1)/(x^6*y)) dx
+[0]
+[0]
+t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
+((x^10 - x^6 + 1)/(x^2*y - y)) dx
+(x^7 + x, 0)
+((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+((-x^6 - 1)/(x^2*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg(x = x+1, y = y+1)[?7h[?12l[?25h[?25l[?7lFxy, Ry, x,y= C.fct_field[?7h[?12l[?25h[?25l[?7lg(x = +1, y=y+1)[?7h[?12l[?25h[?25l[?7l =(C.x).function[?7h[?12l[?25h[?25l[?7lsage: g = (C.x).function

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = (C.x).function[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = (C.x).function[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg(x = x+1, y = y+1)[?7h[?12l[?25h[?25l[?7lFxy, Ry, x,y= C.fct_field[?7h[?12l[?25h[?25l[?7lg(x = +1, y=y+1)[?7h[?12l[?25h[?25l[?7l =(C.x).function[?7h[?12l[?25h[?25l[?7lC.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lload('init.sage'[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2411, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
+   2410 try:
+-> 2411     exp = Integer(exp)
+   2412 except TypeError:
+
+File /ext/sage/9.7/src/sage/rings/integer.pyx:658, in sage.rings.integer.Integer.__init__()
+    657 if otmp is not None:
+--> 658     set_from_Integer(self, otmp(the_integer_ring))
+    659     return
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:829, in sage.rings.fraction_field_element.FractionFieldElement._conversion()
+    828 if self.__denominator.is_one():
+--> 829     return R(self.__numerator)
+    830 else:
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    896 if no_extra_args:
+--> 897     return mor._call_(x)
+    898 else:
+
+File /ext/sage/9.7/src/sage/categories/map.pyx:1692, in sage.categories.map.FormalCompositeMap._call_()
+   1691 for f in self.__list:
+-> 1692     x = f._call_(x)
+   1693 return x
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:12066, in sage.rings.polynomial.polynomial_element.ConstantPolynomialSection._call_()
+  12065 """
+> 12066 cpdef Element _call_(self, x):
+  12067     """
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:12091, in sage.rings.polynomial.polynomial_element.ConstantPolynomialSection._call_()
+  12090 else:
+> 12091     raise TypeError("not a constant polynomial")
+  12092 
+
+TypeError: not a constant polynomial
+
+During handling of the above exception, another exception occurred:
+
+TypeError                                 Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2414, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
+   2413 try:
+-> 2414     n = Rational(exp)
+   2415 except TypeError:
+
+File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__()
+    537 if x is not None:
+--> 538     self.__set_value(x, base)
+    539 
+
+File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value()
+    625 elif hasattr(x, "_rational_"):
+--> 626     set_from_Rational(self, x._rational_())
+    627 
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:784, in sage.rings.fraction_field_element.FractionFieldElement._rational_()
+    783 """
+--> 784 return self._conversion(QQ)
+    785 
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:829, in sage.rings.fraction_field_element.FractionFieldElement._conversion()
+    828 if self.__denominator.is_one():
+--> 829     return R(self.__numerator)
+    830 else:
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    896 if no_extra_args:
+--> 897     return mor._call_(x)
+    898 else:
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    160     print(type(C._element_constructor), C._element_constructor)
+--> 161 raise
+    162 
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+
+File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__()
+    537 if x is not None:
+--> 538     self.__set_value(x, base)
+    539 
+
+File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value()
+    625 elif hasattr(x, "_rational_"):
+--> 626     set_from_Rational(self, x._rational_())
+    627 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:175, in sage.rings.polynomial.multi_polynomial.MPolynomial._rational_()
+    174 from sage.rings.rational_field import QQ
+--> 175 return self._scalar_conversion(QQ)
+    176 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:105, in sage.rings.polynomial.multi_polynomial.MPolynomial._scalar_conversion()
+    104     return R(self.constant_coefficient())
+--> 105 raise TypeError(f"unable to convert non-constant polynomial {self} to {R}")
+    106 
+
+TypeError: unable to convert non-constant polynomial x + 1 to Rational Field
+
+During handling of the above exception, another exception occurred:
+
+TypeError                                 Traceback (most recent call last)
+Input In [22], in <cell line: 1>()
+----> 1 second_patch(C.x)
+
+File <string>:20, in second_patch(argument)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2416, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
+   2414     n = Rational(exp)
+   2415 except TypeError:
+-> 2416     raise TypeError("{} is neither an integer nor a rational".format(exp))
+   2417 num = n.numerator()
+   2418 den = n.denominator()
+
+TypeError: x + 1 is neither an integer nor a rational
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0 dx
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+f2 ((-x^6 - 1)/(x^2*y - y)) dx
+((x^4 + x^2 + 1)/(x^6*y)) dx
+[0]
+[0]
+t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
+((x^10 - x^6 + 1)/(x^2*y - y)) dx
+(x^7 + x, 0)
+((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+((-x^6 - 1)/(x^2*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2411, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
+   2410 try:
+-> 2411     exp = Integer(exp)
+   2412 except TypeError:
+
+File /ext/sage/9.7/src/sage/rings/integer.pyx:658, in sage.rings.integer.Integer.__init__()
+    657 if otmp is not None:
+--> 658     set_from_Integer(self, otmp(the_integer_ring))
+    659     return
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:105, in sage.rings.polynomial.multi_polynomial.MPolynomial._scalar_conversion()
+    104     return R(self.constant_coefficient())
+--> 105 raise TypeError(f"unable to convert non-constant polynomial {self} to {R}")
+    106 
+
+TypeError: unable to convert non-constant polynomial x + 1 to Integer Ring
+
+During handling of the above exception, another exception occurred:
+
+TypeError                                 Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2414, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
+   2413 try:
+-> 2414     n = Rational(exp)
+   2415 except TypeError:
+
+File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__()
+    537 if x is not None:
+--> 538     self.__set_value(x, base)
+    539 
+
+File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value()
+    625 elif hasattr(x, "_rational_"):
+--> 626     set_from_Rational(self, x._rational_())
+    627 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:175, in sage.rings.polynomial.multi_polynomial.MPolynomial._rational_()
+    174 from sage.rings.rational_field import QQ
+--> 175 return self._scalar_conversion(QQ)
+    176 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:105, in sage.rings.polynomial.multi_polynomial.MPolynomial._scalar_conversion()
+    104     return R(self.constant_coefficient())
+--> 105 raise TypeError(f"unable to convert non-constant polynomial {self} to {R}")
+    106 
+
+TypeError: unable to convert non-constant polynomial x + 1 to Rational Field
+
+During handling of the above exception, another exception occurred:
+
+TypeError                                 Traceback (most recent call last)
+Input In [24], in <cell line: 1>()
+----> 1 second_patch(C.x)
+
+File <string>:20, in second_patch(argument)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2416, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
+   2414     n = Rational(exp)
+   2415 except TypeError:
+-> 2416     raise TypeError("{} is neither an integer nor a rational".format(exp))
+   2417 num = n.numerator()
+   2418 den = n.denominator()
+
+TypeError: x + 1 is neither an integer nor a rational
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: x+1

+[?7h[?12l[?25h[?2004l[?7hx + 1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()x[?7h[?12l[?25h[?25l[?7l(x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()^(11)/(C.y)^3*C.dx[?7h[?12l[?25h[?25l[?7l().pth_root([?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(C.x).function[?7h[?12l[?25h[?25l[?7l (C.x).function[?7h[?12l[?25h[?25l[?7l=(C.x).function[?7h[?12l[?25h[?25l[?7l (C.x).function[?7h[?12l[?25h[?25l[?7lsage: g = (C.x).function

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = (C.x).function[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g = Rxy(g)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = Rxy(g)[?7h[?12l[?25h[?25l[?7l(x= x+1, y = y+1)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+1) - g[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g(x+1, y+1)

+[?7h[?12l[?25h[?2004l[?7hx + 1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(x+1, y+1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lx+1, y+1)[?7h[?12l[?25h[?25l[?7l x+1, y+1)[?7h[?12l[?25h[?25l[?7l=x+1, y+1)[?7h[?12l[?25h[?25l[?7l x+1, y+1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly+1)[?7h[?12l[?25h[?25l[?7l y+1)[?7h[?12l[?25h[?25l[?7l=y+1)[?7h[?12l[?25h[?25l[?7l y+1)[?7h[?12l[?25h[?25l[?7lsage: g(x = x+1, y = y+1)

+[?7h[?12l[?25h[?2004l[?7hx + 1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0 dx
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+f2 ((-x^6 - 1)/(x^2*y - y)) dx
+((x^4 + x^2 + 1)/(x^6*y)) dx
+[0]
+[0]
+t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
+((x^10 - x^6 + 1)/(x^2*y - y)) dx
+(x^7 + x, 0)
+((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+((-x^6 - 1)/(x^2*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg(x = x+1, y = y+1)[?7h[?12l[?25h[?25l[?7l+1, y+1)[?7h[?12l[?25h[?25l[?7l = Rxy(g)[?7h[?12l[?25h[?25l[?7l(C.x).function[?7h[?12l[?25h[?25l[?7lx+1[?7h[?12l[?25h[?25l[?7lg = (C.x).function[?7h[?12l[?25h[?25l[?7lx+1[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lload('init.sage'[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x)

+[?7h[?12l[?25h[?2004lx <class 'sage.rings.polynomial.polynomial_ring.PolynomialRing_field_with_category.element_class'>
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [31], in <cell line: 1>()
+----> 1 second_patch(C.x)
+
+File <string>:21, in second_patch(argument)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2411, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
+   2409 if type(exp) is not Integer:
+   2410     try:
+-> 2411         exp = Integer(exp)
+   2412     except TypeError:
+   2413         try:
+
+File /ext/sage/9.7/src/sage/rings/integer.pyx:658, in sage.rings.integer.Integer.__init__()
+    656 otmp = getattr(x, "_integer_", None)
+    657 if otmp is not None:
+--> 658     set_from_Integer(self, otmp(the_integer_ring))
+    659     return
+    660 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:1391, in sage.rings.polynomial.polynomial_element.Polynomial._scalar_conversion()
+   1389     if self.degree() > 0:
+   1390         raise TypeError("cannot convert nonconstant polynomial")
+-> 1391     return R(self.get_coeff_c(0))
+   1392 
+   1393 _real_double_ = _scalar_conversion
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/categories/map.pyx:1692, in sage.categories.map.FormalCompositeMap._call_()
+   1690 """
+   1691 for f in self.__list:
+-> 1692     x = f._call_(x)
+   1693 return x
+   1694 
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1620, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
+   1618     Section._update_slots(self, _slots)
+   1619 
+-> 1620 cpdef Element _call_(self, _x):
+   1621     """
+   1622     Applies the section.
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1654, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
+   1652         raise ValueError("not integral")
+   1653     if nmod_poly_degree(x._numer) > 0:
+-> 1654         raise ValueError("not constant")
+   1655 ans = IntegerMod_int.__new__(IntegerMod_int)
+   1656 ans._parent = self.codomain()
+
+ValueError: not constant
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0 dx
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+f2 ((-x^6 - 1)/(x^2*y - y)) dx
+((x^4 + x^2 + 1)/(x^6*y)) dx
+[0]
+[0]
+t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
+((x^10 - x^6 + 1)/(x^2*y - y)) dx
+(x^7 + x, 0)
+((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+((-x^6 - 1)/(x^2*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x[?7h[?12l[?25h[?25l[?7lload('init.sage'[?7h[?12l[?25h[?25l[?7lg(x = x+1, y = y+1)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x)

+[?7h[?12l[?25h[?2004lx Univariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 3 <class 'sage.rings.polynomial.polynomial_ring.PolynomialRing_field_with_category.element_class'>
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [33], in <cell line: 1>()
+----> 1 second_patch(C.x)
+
+File <string>:21, in second_patch(argument)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2411, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
+   2409 if type(exp) is not Integer:
+   2410     try:
+-> 2411         exp = Integer(exp)
+   2412     except TypeError:
+   2413         try:
+
+File /ext/sage/9.7/src/sage/rings/integer.pyx:658, in sage.rings.integer.Integer.__init__()
+    656 otmp = getattr(x, "_integer_", None)
+    657 if otmp is not None:
+--> 658     set_from_Integer(self, otmp(the_integer_ring))
+    659     return
+    660 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:1391, in sage.rings.polynomial.polynomial_element.Polynomial._scalar_conversion()
+   1389     if self.degree() > 0:
+   1390         raise TypeError("cannot convert nonconstant polynomial")
+-> 1391     return R(self.get_coeff_c(0))
+   1392 
+   1393 _real_double_ = _scalar_conversion
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/categories/map.pyx:1692, in sage.categories.map.FormalCompositeMap._call_()
+   1690 """
+   1691 for f in self.__list:
+-> 1692     x = f._call_(x)
+   1693 return x
+   1694 
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1620, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
+   1618     Section._update_slots(self, _slots)
+   1619 
+-> 1620 cpdef Element _call_(self, _x):
+   1621     """
+   1622     Applies the section.
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1654, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
+   1652         raise ValueError("not integral")
+   1653     if nmod_poly_degree(x._numer) > 0:
+-> 1654         raise ValueError("not constant")
+   1655 ans = IntegerMod_int.__new__(IntegerMod_int)
+   1656 ans._parent = self.codomain()
+
+ValueError: not constant
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y = C.fct_field[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: Fxy

+[?7h[?12l[?25h[?2004l[?7hFraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lload('init.sage'[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x[?7h[?12l[?25h[?25l[?7lload('init.sage'[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x[?7h[?12l[?25h[?25l[?7lFxy[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[1][?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgC.x.function[?7h[?12l[?25h[?25l[?7l=C.x.function[?7h[?12l[?25h[?25l[?7l C.x.function[?7h[?12l[?25h[?25l[?7lC.x.function[?7h[?12l[?25h[?25l[?7l=C.x.function[?7h[?12l[?25h[?25l[?7lC.x.function[?7h[?12l[?25h[?25l[?7lC.x.function[?7h[?12l[?25h[?25l[?7l C.x.function[?7h[?12l[?25h[?25l[?7l=C.x.function[?7h[?12l[?25h[?25l[?7l C.x.function[?7h[?12l[?25h[?25l[?7lFC.x.function[?7h[?12l[?25h[?25l[?7lxC.x.function[?7h[?12l[?25h[?25l[?7lyC.x.function[?7h[?12l[?25h[?25l[?7l(C.x.function[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g = Fxy(C.x.function)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = Fxy(C.x.function)[?7h[?12l[?25h[?25l[?7l(x= x+1, y = y+1)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+1, y+1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx = x+1, y = y+1)[?7h[?12l[?25h[?25l[?7l( = x+1, y = y+1)[?7h[?12l[?25h[?25l[?7lsage: g(x = x+1, y = y+1)

+[?7h[?12l[?25h[?2004l[?7hx + 1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(x = x+1, y = y+1)[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l{[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l{}[?7h[?12l[?25h[?25l[?7l({})[?7h[?12l[?25h[?25l[?7lsage: g.subs({x:x+1, y:y+1})

+[?7h[?12l[?25h[?2004l[?7hx + 1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0 dx
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+f2 ((-x^6 - 1)/(x^2*y - y)) dx
+((x^4 + x^2 + 1)/(x^6*y)) dx
+[0]
+[0]
+t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
+((x^10 - x^6 + 1)/(x^2*y - y)) dx
+(x^7 + x, 0)
+((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+((-x^6 - 1)/(x^2*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcond_patch(C.x)[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2411, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
+   2410 try:
+-> 2411     exp = Integer(exp)
+   2412 except TypeError:
+
+File /ext/sage/9.7/src/sage/rings/integer.pyx:658, in sage.rings.integer.Integer.__init__()
+    657 if otmp is not None:
+--> 658     set_from_Integer(self, otmp(the_integer_ring))
+    659     return
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:829, in sage.rings.fraction_field_element.FractionFieldElement._conversion()
+    828 if self.__denominator.is_one():
+--> 829     return R(self.__numerator)
+    830 else:
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    896 if no_extra_args:
+--> 897     return mor._call_(x)
+    898 else:
+
+File /ext/sage/9.7/src/sage/categories/map.pyx:1692, in sage.categories.map.FormalCompositeMap._call_()
+   1691 for f in self.__list:
+-> 1692     x = f._call_(x)
+   1693 return x
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:12066, in sage.rings.polynomial.polynomial_element.ConstantPolynomialSection._call_()
+  12065 """
+> 12066 cpdef Element _call_(self, x):
+  12067     """
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:12091, in sage.rings.polynomial.polynomial_element.ConstantPolynomialSection._call_()
+  12090 else:
+> 12091     raise TypeError("not a constant polynomial")
+  12092 
+
+TypeError: not a constant polynomial
+
+During handling of the above exception, another exception occurred:
+
+TypeError                                 Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2414, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
+   2413 try:
+-> 2414     n = Rational(exp)
+   2415 except TypeError:
+
+File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__()
+    537 if x is not None:
+--> 538     self.__set_value(x, base)
+    539 
+
+File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value()
+    625 elif hasattr(x, "_rational_"):
+--> 626     set_from_Rational(self, x._rational_())
+    627 
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:784, in sage.rings.fraction_field_element.FractionFieldElement._rational_()
+    783 """
+--> 784 return self._conversion(QQ)
+    785 
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:829, in sage.rings.fraction_field_element.FractionFieldElement._conversion()
+    828 if self.__denominator.is_one():
+--> 829     return R(self.__numerator)
+    830 else:
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    896 if no_extra_args:
+--> 897     return mor._call_(x)
+    898 else:
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    160     print(type(C._element_constructor), C._element_constructor)
+--> 161 raise
+    162 
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+
+File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__()
+    537 if x is not None:
+--> 538     self.__set_value(x, base)
+    539 
+
+File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value()
+    625 elif hasattr(x, "_rational_"):
+--> 626     set_from_Rational(self, x._rational_())
+    627 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:175, in sage.rings.polynomial.multi_polynomial.MPolynomial._rational_()
+    174 from sage.rings.rational_field import QQ
+--> 175 return self._scalar_conversion(QQ)
+    176 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:105, in sage.rings.polynomial.multi_polynomial.MPolynomial._scalar_conversion()
+    104     return R(self.constant_coefficient())
+--> 105 raise TypeError(f"unable to convert non-constant polynomial {self} to {R}")
+    106 
+
+TypeError: unable to convert non-constant polynomial x + 1 to Rational Field
+
+During handling of the above exception, another exception occurred:
+
+TypeError                                 Traceback (most recent call last)
+Input In [39], in <cell line: 1>()
+----> 1 second_patch(C.x)
+
+File <string>:20, in second_patch(argument)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2416, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
+   2414     n = Rational(exp)
+   2415 except TypeError:
+-> 2416     raise TypeError("{} is neither an integer nor a rational".format(exp))
+   2417 num = n.numerator()
+   2418 den = n.denominator()
+
+TypeError: x + 1 is neither an integer nor a rational
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0 dx
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+f2 ((-x^6 - 1)/(x^2*y - y)) dx
+((x^4 + x^2 + 1)/(x^6*y)) dx
+[0]
+[0]
+t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
+((x^10 - x^6 + 1)/(x^2*y - y)) dx
+(x^7 + x, 0)
+((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+((-x^6 - 1)/(x^2*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2411, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
+   2410 try:
+-> 2411     exp = Integer(exp)
+   2412 except TypeError:
+
+File /ext/sage/9.7/src/sage/rings/integer.pyx:658, in sage.rings.integer.Integer.__init__()
+    657 if otmp is not None:
+--> 658     set_from_Integer(self, otmp(the_integer_ring))
+    659     return
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:829, in sage.rings.fraction_field_element.FractionFieldElement._conversion()
+    828 if self.__denominator.is_one():
+--> 829     return R(self.__numerator)
+    830 else:
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    896 if no_extra_args:
+--> 897     return mor._call_(x)
+    898 else:
+
+File /ext/sage/9.7/src/sage/categories/map.pyx:1692, in sage.categories.map.FormalCompositeMap._call_()
+   1691 for f in self.__list:
+-> 1692     x = f._call_(x)
+   1693 return x
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:12066, in sage.rings.polynomial.polynomial_element.ConstantPolynomialSection._call_()
+  12065 """
+> 12066 cpdef Element _call_(self, x):
+  12067     """
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:12091, in sage.rings.polynomial.polynomial_element.ConstantPolynomialSection._call_()
+  12090 else:
+> 12091     raise TypeError("not a constant polynomial")
+  12092 
+
+TypeError: not a constant polynomial
+
+During handling of the above exception, another exception occurred:
+
+TypeError                                 Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2414, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
+   2413 try:
+-> 2414     n = Rational(exp)
+   2415 except TypeError:
+
+File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__()
+    537 if x is not None:
+--> 538     self.__set_value(x, base)
+    539 
+
+File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value()
+    625 elif hasattr(x, "_rational_"):
+--> 626     set_from_Rational(self, x._rational_())
+    627 
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:784, in sage.rings.fraction_field_element.FractionFieldElement._rational_()
+    783 """
+--> 784 return self._conversion(QQ)
+    785 
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:829, in sage.rings.fraction_field_element.FractionFieldElement._conversion()
+    828 if self.__denominator.is_one():
+--> 829     return R(self.__numerator)
+    830 else:
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    896 if no_extra_args:
+--> 897     return mor._call_(x)
+    898 else:
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    160     print(type(C._element_constructor), C._element_constructor)
+--> 161 raise
+    162 
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+
+File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__()
+    537 if x is not None:
+--> 538     self.__set_value(x, base)
+    539 
+
+File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value()
+    625 elif hasattr(x, "_rational_"):
+--> 626     set_from_Rational(self, x._rational_())
+    627 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:175, in sage.rings.polynomial.multi_polynomial.MPolynomial._rational_()
+    174 from sage.rings.rational_field import QQ
+--> 175 return self._scalar_conversion(QQ)
+    176 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:105, in sage.rings.polynomial.multi_polynomial.MPolynomial._scalar_conversion()
+    104     return R(self.constant_coefficient())
+--> 105 raise TypeError(f"unable to convert non-constant polynomial {self} to {R}")
+    106 
+
+TypeError: unable to convert non-constant polynomial x + 1 to Rational Field
+
+During handling of the above exception, another exception occurred:
+
+TypeError                                 Traceback (most recent call last)
+Input In [41], in <cell line: 1>()
+----> 1 second_patch(C.x)
+
+File <string>:20, in second_patch(argument)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2416, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
+   2414     n = Rational(exp)
+   2415 except TypeError:
+-> 2416     raise TypeError("{} is neither an integer nor a rational".format(exp))
+   2417 num = n.numerator()
+   2418 den = n.denominator()
+
+TypeError: x + 1 is neither an integer nor a rational
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(z[0])[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7ltype[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: type(x+1)

+[?7h[?12l[?25h[?2004l[?7h<class 'sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint'>
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(x+1)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2411, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
+   2410 try:
+-> 2411     exp = Integer(exp)
+   2412 except TypeError:
+
+File /ext/sage/9.7/src/sage/rings/integer.pyx:658, in sage.rings.integer.Integer.__init__()
+    657 if otmp is not None:
+--> 658     set_from_Integer(self, otmp(the_integer_ring))
+    659     return
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:829, in sage.rings.fraction_field_element.FractionFieldElement._conversion()
+    828 if self.__denominator.is_one():
+--> 829     return R(self.__numerator)
+    830 else:
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    896 if no_extra_args:
+--> 897     return mor._call_(x)
+    898 else:
+
+File /ext/sage/9.7/src/sage/categories/map.pyx:1692, in sage.categories.map.FormalCompositeMap._call_()
+   1691 for f in self.__list:
+-> 1692     x = f._call_(x)
+   1693 return x
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:12066, in sage.rings.polynomial.polynomial_element.ConstantPolynomialSection._call_()
+  12065 """
+> 12066 cpdef Element _call_(self, x):
+  12067     """
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:12091, in sage.rings.polynomial.polynomial_element.ConstantPolynomialSection._call_()
+  12090 else:
+> 12091     raise TypeError("not a constant polynomial")
+  12092 
+
+TypeError: not a constant polynomial
+
+During handling of the above exception, another exception occurred:
+
+TypeError                                 Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2414, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
+   2413 try:
+-> 2414     n = Rational(exp)
+   2415 except TypeError:
+
+File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__()
+    537 if x is not None:
+--> 538     self.__set_value(x, base)
+    539 
+
+File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value()
+    625 elif hasattr(x, "_rational_"):
+--> 626     set_from_Rational(self, x._rational_())
+    627 
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:784, in sage.rings.fraction_field_element.FractionFieldElement._rational_()
+    783 """
+--> 784 return self._conversion(QQ)
+    785 
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:829, in sage.rings.fraction_field_element.FractionFieldElement._conversion()
+    828 if self.__denominator.is_one():
+--> 829     return R(self.__numerator)
+    830 else:
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    896 if no_extra_args:
+--> 897     return mor._call_(x)
+    898 else:
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    160     print(type(C._element_constructor), C._element_constructor)
+--> 161 raise
+    162 
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+
+File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__()
+    537 if x is not None:
+--> 538     self.__set_value(x, base)
+    539 
+
+File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value()
+    625 elif hasattr(x, "_rational_"):
+--> 626     set_from_Rational(self, x._rational_())
+    627 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:175, in sage.rings.polynomial.multi_polynomial.MPolynomial._rational_()
+    174 from sage.rings.rational_field import QQ
+--> 175 return self._scalar_conversion(QQ)
+    176 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:105, in sage.rings.polynomial.multi_polynomial.MPolynomial._scalar_conversion()
+    104     return R(self.constant_coefficient())
+--> 105 raise TypeError(f"unable to convert non-constant polynomial {self} to {R}")
+    106 
+
+TypeError: unable to convert non-constant polynomial x + 1 to Rational Field
+
+During handling of the above exception, another exception occurred:
+
+TypeError                                 Traceback (most recent call last)
+Input In [43], in <cell line: 1>()
+----> 1 second_patch(C.x)
+
+File <string>:20, in second_patch(argument)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2416, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.__pow__()
+   2414     n = Rational(exp)
+   2415 except TypeError:
+-> 2416     raise TypeError("{} is neither an integer nor a rational".format(exp))
+   2417 num = n.numerator()
+   2418 den = n.denominator()
+
+TypeError: x + 1 is neither an integer nor a rational
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpatch(C)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: patch(C)

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = 2*x^3 + x over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpatch(C)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: patch(patch(C))

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpatch(patch(C))[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x[?7h[?12l[?25h[?25l[?7lsage: C

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0 dx
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+f2 ((-x^6 - 1)/(x^2*y - y)) dx
+((x^4 + x^2 + 1)/(x^6*y)) dx
+[0]
+[0]
+t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
+((x^10 - x^6 + 1)/(x^2*y - y)) dx
+(x^7 + x, 0)
+((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+((-x^6 - 1)/(x^2*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lpatch(patch(C))[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x)

+[?7h[?12l[?25h[?2004l[?7h1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lload('init.sage'[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0 dx
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+f2 ((-x^6 - 1)/(x^2*y - y)) dx
+((x^4 + x^2 + 1)/(x^6*y)) dx
+[0]
+[0]
+t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
+((x^10 - x^6 + 1)/(x^2*y - y)) dx
+(x^7 + x, 0)
+((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+((-x^6 - 1)/(x^2*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x)

+[?7h[?12l[?25h[?2004l[?7h1/x
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lesecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lcsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7losecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lnsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7ldsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7l_second_patch(C.x)[?7h[?12l[?25h[?25l[?7lpsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lasecond_patch(C.x)[?7h[?12l[?25h[?25l[?7ltsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lcsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7lhsecond_patch(C.x)[?7h[?12l[?25h[?25l[?7l(second_patch(C.x)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: second_patch(second_patch(C.x))

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

+[?7h[?12l[?25h[?2004l0 dx
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+f2 ((-x^6 - 1)/(x^2*y - y)) dx
+((x^4 + x^2 + 1)/(x^6*y)) dx
+[0]
+[0]
+t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
+((x^10 - x^6 + 1)/(x^2*y - y)) dx
+(x^7 + x, 0)
+((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+((-x^6 - 1)/(x^2*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsecond_patch(second_patch(C.x))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7ldx)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: second_patch(second_patch(C.dx))

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce)
+    705 try:
+--> 706     x, y = resolve_fractions(x0, y0)
+    707 except (AttributeError, TypeError):
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:683, in FractionField_generic._element_constructor_.<locals>.resolve_fractions(x, y)
+    682 def resolve_fractions(x, y):
+--> 683     xn = x.numerator()
+    684     xd = x.denominator()
+
+AttributeError: 'superelliptic_function' object has no attribute 'numerator'
+
+During handling of the above exception, another exception occurred:
+
+TypeError                                 Traceback (most recent call last)
+Input In [53], in <cell line: 1>()
+----> 1 second_patch(second_patch(C.dx))
+
+File <string>:26, in second_patch(argument)
+
+File <string>:7, in __init__(self, C, g)
+
+File <string>:245, in reduction_form(C, g)
+
+File <string>:216, in reduction(C, g)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    159             print(type(C), C)
+    160             print(type(C._element_constructor), C._element_constructor)
+--> 161         raise
+    162 
+    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:708, in FractionField_generic._element_constructor_(self, x, y, coerce)
+    706     x, y = resolve_fractions(x0, y0)
+    707 except (AttributeError, TypeError):
+--> 708     raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
+    709                     x0, y0, self))
+    710 try:
+    711     return self._element_class(self, x, y, coerce=coerce)
+
+TypeError: cannot convert 2/x^2/1 to an element of Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0 dx
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+f2 ((-x^6 - 1)/(x^2*y - y)) dx
+((x^4 + x^2 + 1)/(x^6*y)) dx
+[0]
+[0]
+t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
+((x^10 - x^6 + 1)/(x^2*y - y)) dx
+(x^7 + x, 0)
+((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+((-x^6 - 1)/(x^2*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsecond_patch(second_patch(C.dx))[?7h[?12l[?25h[?25l[?7lsage: second_patch(second_patch(C.dx))

+[?7h[?12l[?25h[?2004l[?7h1 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(second_patch(C.dx))[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lsecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7lecond_patch(C.dx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.dx)

+[?7h[?12l[?25h[?2004l[?7h((-1)/x^2) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l = superelliptic(x^4 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x^4 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^4 - x^3 + x, 2)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^4 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l.x[?7h[?12l[?25h[?25l[?7lheight[?7h[?12l[?25h[?25l[?7lolomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis()

+[?7h[?12l[?25h[?2004l[?7h[(1/y) dx]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l = supeelliptc(x^4 - x^3 + x, 2[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l1 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l1 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^11 - x^3 + x, 2)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^11 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l.holomophic_dfferentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis()

+[?7h[?12l[?25h[?2004l[?7h[(1/y) dx, (x/y) dx, (x^2/y) dx, (x^3/y) dx, (x^4/y) dx]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ldrafty/draft5.sage')[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l(afty/draft5.sage')[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7lr.sage')[?7h[?12l[?25h[?25l[?7le.sage')[?7h[?12l[?25h[?25l[?7lg.sage')[?7h[?12l[?25h[?25l[?7lu.sage')[?7h[?12l[?25h[?25l[?7ll.sage')[?7h[?12l[?25h[?25l[?7la.sage')[?7h[?12l[?25h[?25l[?7lr.sage')[?7h[?12l[?25h[?25l[?7l .sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l_.sage')[?7h[?12l[?25h[?25l[?7lo.sage')[?7h[?12l[?25h[?25l[?7ln.sage')[?7h[?12l[?25h[?25l[?7l_.sage')[?7h[?12l[?25h[?25l[?7lU.sage')[?7h[?12l[?25h[?25l[?7l0.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: load('drafty/regular_on_U0.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: regula

+ regular_form

+ regulator   

+

+

+ [?7h[?12l[?25h[?25l[?7lr_form

+ regular_form

+

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

+

+

+[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: regular_form((C.y)^(-1)*C.dx)

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

+

+

+

+ [?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7lsage: ((C.y)^(-1)*C.dx).form

+[?7h[?12l[?25h[?2004l[?7h1/y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+ [?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbn((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7lo((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7le((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7ln((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7lo((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7lm((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7li((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7ln((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7la((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7lt((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7lo((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7lr((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7l(((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: denominator(((C.y)^(-1)*C.dx).form) == y

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldenominator(((C.y)^(-1)*C.dx).form) == y[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/regular_on_U0.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7ldenominator(((C.y)^(-1)*C.dx).form) == y[?7h[?12l[?25h[?25l[?7l((C.y)^(-1)*C.dx).form[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lsage: regular_form((C.y)^(-1)*C.dx)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [66], in <cell line: 1>()
+----> 1 regular_form((C.y)**(-Integer(1))*C.dx)
+
+File <string>:8, in regular_form(omega)
+
+ValueError: too many values to unpack (expected 2)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/regular_on_U0.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lsage: regular_form((C.y)^(-1)*C.dx)

+[?7h[?12l[?25h[?2004l1
+[?7h((x^9 + x^7 - x^5 + x^3 - x)/y, (x^10 + x^8 - x^6 + x^4 + x^2 + 1)/y)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/regular_on_U0.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lsage: regular_form((C.y)^(-1)*C.dx)

+[?7h[?12l[?25h[?2004l1
+[?7h(x^9 + x^7 - x^5 + x^3 - x, x^10 + x^8 - x^6 + x^4 + x^2 + 1)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l = supeelliptc(x^11 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x^11 - x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx^3 + x, 2)[?7h[?12l[?25h[?25l[?7lx^3 + x, 2)[?7h[?12l[?25h[?25l[?7lx^3 + x, 2)[?7h[?12l[?25h[?25l[?7lx^3 + x, 2)[?7h[?12l[?25h[?25l[?7lx^3 + x, 2)[?7h[?12l[?25h[?25l[?7lx^3 + x, 2)[?7h[?12l[?25h[?25l[?7l^3 + x, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l x, 2)[?7h[?12l[?25h[?25l[?7l- x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 - x, 2)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7lsage: regular_form((C.y)^(-1)*C.dx)

+[?7h[?12l[?25h[?2004l1
+[?7h(0, -1)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/regular_on_U0.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lsage: regular_form((C.y)^(-1)*C.dx)

+[?7h[?12l[?25h[?2004l1 0 2
+[?7h(0, -1)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/regular_on_U0.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lsage: regular_form((C.y)^(-1)*C.dx)

+[?7h[?12l[?25h[?2004l1 0 2
+[?7h(0, 1)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/regular_on_U0.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lsage: regular_form((C.y)^(-1)*C.dx)

+[?7h[?12l[?25h[?2004l[?7h(0, 1)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/regular_on_U0.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lregular_form((C.y)^(-1)*C.dx)[?7h[?12l[?25h[?25l[?7lsage: regular_form((C.y)^(-1)*C.dx)

+[?7h[?12l[?25h[?2004l[?7h(0, 1)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in range(3):[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.subs({x:x+1, y:y+1})[?7h[?12l[?25h[?25l[?7l = Fxy(C..function)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx^4 +x^2 + 1[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: g = x^3 + 2

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = x^3 + 2[?7h[?12l[?25h[?25l[?7l.subs({x:x+1, y:y+1})[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.lift()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [82], in <cell line: 1>()
+----> 1 g.lift()
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
+    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
+    493     """
+--> 494     return self.getattr_from_category(name)
+    495 
+    496 cdef getattr_from_category(self, name):
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
+    505     else:
+    506         cls = P._abstract_element_class
+--> 507     return getattr_from_other_class(self, cls, name)
+    508 
+    509 def __dir__(self):
+
+File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
+    359     dummy_error_message.cls = type(self)
+    360     dummy_error_message.name = name
+--> 361     raise AttributeError(dummy_error_message)
+    362 attribute = <object>attr
+    363 # Check for a descriptor (__get__ in Python)
+
+AttributeError: 'sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint' object has no attribute 'lift'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.lift()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.lift()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(x+1)[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7ltype[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: type(g)

+[?7h[?12l[?25h[?2004l[?7h<class 'sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint'>
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(g)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltyp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpatch(patch(C))[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrent(x)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: parent(g)

+[?7h[?12l[?25h[?2004l[?7hUnivariate Polynomial Ring in x over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.lift()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.lift()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [85], in <cell line: 1>()
+----> 1 g.lift()
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
+    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
+    493     """
+--> 494     return self.getattr_from_category(name)
+    495 
+    496 cdef getattr_from_category(self, name):
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
+    505     else:
+    506         cls = P._abstract_element_class
+--> 507     return getattr_from_other_class(self, cls, name)
+    508 
+    509 def __dir__(self):
+
+File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
+    359     dummy_error_message.cls = type(self)
+    360     dummy_error_message.name = name
+--> 361     raise AttributeError(dummy_error_message)
+    362 attribute = <object>attr
+    363 # Check for a descriptor (__get__ in Python)
+
+AttributeError: 'sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint' object has no attribute 'lift'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.lift()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lZ[?7h[?12l[?25h[?25l[?7lZ[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.change_ring(ZZ)

+[?7h[?12l[?25h[?2004l[?7hx^3 + 2
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.change_ring(ZZ)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: g.change_ring(ZZ) + 3

+[?7h[?12l[?25h[?2004l[?7hx^3 + 5
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.change_ring(ZZ) + 3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l) + 3[?7h[?12l[?25h[?25l[?7l) + 3[?7h[?12l[?25h[?25l[?7lI) + 3[?7h[?12l[?25h[?25l[?7ln) + 3[?7h[?12l[?25h[?25l[?7lt) + 3[?7h[?12l[?25h[?25l[?7le) + 3[?7h[?12l[?25h[?25l[?7lg) + 3[?7h[?12l[?25h[?25l[?7le) + 3[?7h[?12l[?25h[?25l[?7lr) + 3[?7h[?12l[?25h[?25l[?7ls) + 3[?7h[?12l[?25h[?25l[?7l(() + 3[?7h[?12l[?25h[?25l[?7l9) + 3[?7h[?12l[?25h[?25l[?7l(()) + 3[?7h[?12l[?25h[?25l[?7lsage: g.change_ring(Integers(9)) + 3

+[?7h[?12l[?25h[?2004l[?7hx^3 + 5
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.change_ring(Integers(9)) + 3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7lsage: g.change_ring(Integers(9)) + 9

+[?7h[?12l[?25h[?2004l[?7hx^3 + 2
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.change_ring(Integers(9)) + 9[?7h[?12l[?25h[?25l[?7l = x^3 + 2[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: g = x + 2*y

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = x + 2*y[?7h[?12l[?25h[?25l[?7l.change_ring(Integers(9)) + 9[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lZZ) + 3[?7h[?12l[?25h[?25l[?7lZ[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.change_ring(ZZ)

+[?7h[?12l[?25h[?2004l[?7hx + 2*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.change_ring(ZZ)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lI)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lg)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l9))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l) + 9[?7h[?12l[?25h[?25l[?7l() + 9[?7h[?12l[?25h[?25l[?7lsage: g.change_ring(Integers(9)) + 9

+[?7h[?12l[?25h[?2004l[?7hx + 2*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.change_ring(Integers(9)) + 9[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.change_ring(Integers(9))

+[?7h[?12l[?25h[?2004l[?7hx + 2*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.change_ring(Integers(9))[?7h[?12l[?25h[?25l[?7l = x + 2*y[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx + 2*y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x + 2*y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*x+1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g = (x + 2*y)/(-8*x+1)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = (x + 2*y)/(-8*x+1)[?7h[?12l[?25h[?25l[?7l.change_ring(Integers(9))[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lge_ring(Integers(9))[?7h[?12l[?25h[?25l[?7lsage: g.change_ring(Integers(9))

+[?7h[?12l[?25h[?2004lsage/rings/polynomial/polynomial_zmod_flint.pyx:7: DeprecationWarning: invalid escape sequence '\Z'
+  """
+sage/rings/polynomial/polynomial_zmod_flint.pyx:7: DeprecationWarning: invalid escape sequence '\Z'
+  """
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:380, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
+    379 try:
+--> 380     z = integer_ring.Z(value)
+    381 except (TypeError, ValueError):
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    896 if no_extra_args:
+--> 897     return mor._call_(x)
+    898 else:
+
+File /ext/sage/9.7/src/sage/categories/map.pyx:1692, in sage.categories.map.FormalCompositeMap._call_()
+   1691 for f in self.__list:
+-> 1692     x = f._call_(x)
+   1693 return x
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1620, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
+   1619 
+-> 1620     cpdef Element _call_(self, _x):
+   1621         """
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1652, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
+   1651 if nmod_poly_degree(x._denom) != 0:
+-> 1652     raise ValueError("not integral")
+   1653 if nmod_poly_degree(x._numer) > 0:
+
+ValueError: not integral
+
+During handling of the above exception, another exception occurred:
+
+TypeError                                 Traceback (most recent call last)
+Input In [95], in <cell line: 1>()
+----> 1 g.change_ring(Integers(Integer(9)))
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:3377, in sage.rings.polynomial.polynomial_element.Polynomial.change_ring()
+   3375         return self.map_coefficients(R)
+   3376     else:
+-> 3377         return self._parent.change_ring(R)(self.list(copy=False))
+   3378 
+   3379 cpdef dict _mpoly_dict_recursive(self, tuple variables=None, base_ring=None):
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    159             print(type(C), C)
+    160             print(type(C._element_constructor), C._element_constructor)
+--> 161         raise
+    162 
+    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:416, in PolynomialRing_general._element_constructor_(self, x, check, is_gen, construct, **kwds)
+    414 C = self.element_class
+    415 if isinstance(x, (list, tuple)):
+--> 416     return C(self, x, check=check, is_gen=False, construct=construct)
+    417 if isinstance(x, range):
+    418     return C(self, list(x), check=check, is_gen=False,
+    419              construct=construct)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zmod_flint.pyx:106, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint.__init__()
+    104 k = parent._base
+    105 if check:
+--> 106     lst = [k(i) for i in x]
+    107 else:
+    108     lst = x
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    159             print(type(C), C)
+    160             print(type(C._element_constructor), C._element_constructor)
+--> 161         raise
+    162 
+    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x)
+   1143 """
+   1144 TESTS::
+   1145 
+   (...)
+   1182     True
+   1183 """
+   1184 try:
+-> 1185     return integer_mod.IntegerMod(self, x)
+   1186 except (NotImplementedError, PariError):
+   1187     raise TypeError("error coercing to finite field")
+
+File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod()
+    199         return a
+    200 t = modulus.element_class()
+--> 201 return t(parent, value)
+    202 
+    203 
+
+File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:388, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
+    386     value = py_scalar_to_element(value)
+    387 if isinstance(value, Element) and value.parent().is_exact():
+--> 388     value = sage.rings.rational_field.QQ(value)
+    389     z = value % self.__modulus.sageInteger
+    390 else:
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    159             print(type(C), C)
+    160             print(type(C._element_constructor), C._element_constructor)
+--> 161         raise
+    162 
+    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__()
+    536     """
+    537     if x is not None:
+--> 538         self.__set_value(x, base)
+    539 
+    540 def __reduce__(self):
+
+File /ext/sage/9.7/src/sage/rings/rational.pyx:691, in sage.rings.rational.Rational.__set_value()
+    689 
+    690         else:
+--> 691             raise TypeError("unable to convert {!r} to a rational".format(x))
+    692 
+    693     cdef void set_from_mpq(Rational self, mpq_t value):
+
+TypeError: unable to convert x/(x + 1) to a rational
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.change_ring(Integers(9))[?7h[?12l[?25h[?25l[?7lsage: g.change_ring(Integers(9))

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:380, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
+    379 try:
+--> 380     z = integer_ring.Z(value)
+    381 except (TypeError, ValueError):
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    896 if no_extra_args:
+--> 897     return mor._call_(x)
+    898 else:
+
+File /ext/sage/9.7/src/sage/categories/map.pyx:1692, in sage.categories.map.FormalCompositeMap._call_()
+   1691 for f in self.__list:
+-> 1692     x = f._call_(x)
+   1693 return x
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1620, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
+   1619 
+-> 1620     cpdef Element _call_(self, _x):
+   1621         """
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1652, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
+   1651 if nmod_poly_degree(x._denom) != 0:
+-> 1652     raise ValueError("not integral")
+   1653 if nmod_poly_degree(x._numer) > 0:
+
+ValueError: not integral
+
+During handling of the above exception, another exception occurred:
+
+TypeError                                 Traceback (most recent call last)
+Input In [96], in <cell line: 1>()
+----> 1 g.change_ring(Integers(Integer(9)))
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:3377, in sage.rings.polynomial.polynomial_element.Polynomial.change_ring()
+   3375         return self.map_coefficients(R)
+   3376     else:
+-> 3377         return self._parent.change_ring(R)(self.list(copy=False))
+   3378 
+   3379 cpdef dict _mpoly_dict_recursive(self, tuple variables=None, base_ring=None):
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    159             print(type(C), C)
+    160             print(type(C._element_constructor), C._element_constructor)
+--> 161         raise
+    162 
+    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:416, in PolynomialRing_general._element_constructor_(self, x, check, is_gen, construct, **kwds)
+    414 C = self.element_class
+    415 if isinstance(x, (list, tuple)):
+--> 416     return C(self, x, check=check, is_gen=False, construct=construct)
+    417 if isinstance(x, range):
+    418     return C(self, list(x), check=check, is_gen=False,
+    419              construct=construct)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zmod_flint.pyx:106, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint.__init__()
+    104 k = parent._base
+    105 if check:
+--> 106     lst = [k(i) for i in x]
+    107 else:
+    108     lst = x
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    159             print(type(C), C)
+    160             print(type(C._element_constructor), C._element_constructor)
+--> 161         raise
+    162 
+    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x)
+   1143 """
+   1144 TESTS::
+   1145 
+   (...)
+   1182     True
+   1183 """
+   1184 try:
+-> 1185     return integer_mod.IntegerMod(self, x)
+   1186 except (NotImplementedError, PariError):
+   1187     raise TypeError("error coercing to finite field")
+
+File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod()
+    199         return a
+    200 t = modulus.element_class()
+--> 201 return t(parent, value)
+    202 
+    203 
+
+File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:388, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
+    386     value = py_scalar_to_element(value)
+    387 if isinstance(value, Element) and value.parent().is_exact():
+--> 388     value = sage.rings.rational_field.QQ(value)
+    389     z = value % self.__modulus.sageInteger
+    390 else:
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    159             print(type(C), C)
+    160             print(type(C._element_constructor), C._element_constructor)
+--> 161         raise
+    162 
+    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__()
+    536     """
+    537     if x is not None:
+--> 538         self.__set_value(x, base)
+    539 
+    540 def __reduce__(self):
+
+File /ext/sage/9.7/src/sage/rings/rational.pyx:691, in sage.rings.rational.Rational.__set_value()
+    689 
+    690         else:
+--> 691             raise TypeError("unable to convert {!r} to a rational".format(x))
+    692 
+    693     cdef void set_from_mpq(Rational self, mpq_t value):
+
+TypeError: unable to convert x/(x + 1) to a rational
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7linit.sag')[?7h[?12l[?25h[?25l[?7l(nit.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0 dx
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+f2 ((-x^6 - 1)/(x^2*y - y)) dx
+((x^4 + x^2 + 1)/(x^6*y)) dx
+[0]
+[0]
+t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
+((x^10 - x^6 + 1)/(x^2*y - y)) dx
+(x^7 + x, 0)
+((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+((-x^6 - 1)/(x^2*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ldrafty/rgular_on_U0.sage')[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l(afty/regular_on_U0.sage')[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7ld.sage')[?7h[?12l[?25h[?25l[?7lr.sage')[?7h[?12l[?25h[?25l[?7la.sage')[?7h[?12l[?25h[?25l[?7lf.sage')[?7h[?12l[?25h[?25l[?7lt.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft.sage')

+[?7h[?12l[?25h[?2004l(y, -x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('drafty/draft.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/draft.sage')

+[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
+(y, -x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.holomophic_dfferentials_basis()[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis()

+[?7h[?12l[?25h[?2004l[?7h[(1/y) dx]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsC.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7leC.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7lcC.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7loC.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7lnC.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7ldC.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7l_C.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7lpC.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7laC.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7ltC.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7lcC.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7lhC.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7l(C.holomorphic_diferentials_basis()[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.holomorphic_differentials_basis()[0])

+[?7h[?12l[?25h[?2004l[?7h((-1)/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(g)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ltch(patch(C))[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: patch(C)

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l?identity_matrix[?7h[?12l[?25h[?25l[?7lsuperelliptic[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuperelliptic[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lsage: ?second_patch

+[?7h[?12l[?25h[?2004lSignature:      second_patch(argument)
+Init docstring: Initialize self.  See help(type(self)) for accurate signature.
+File:           Dynamically generated function. No source code available.
+Type:           function
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ld_patch[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: help(second_patch)

+[?7h[?12l[?25h[?2004l[?1049h[?1h=
Help on function second_patch in module __main__:
+
+second_patch(argument)
+(END)

(END)
 ::qq
[?1l>[?1049l
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l?second_patch[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lsage: ?regula

+ regular_form

+ regulator   

+

+

+ [?7h[?12l[?25h[?25l[?7lr_form

+ regular_form

+

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

+

+

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

+[?7h[?12l[?25h[?2004lSignature:      regular_form(omega)
+Docstring:     
+Given a form omega regular on U0, present it as P(x, y) dx + Q(x, y)
+dy for some polynomial P, Q.
+   The output is A(x)*y, B(x), where omega = A(x) y dx + B(x) dy
+Init docstring: Initialize self.  See help(type(self)) for accurate signature.
+File:           Dynamically generated function. No source code available.
+Type:           function
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/draft.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7l(nit.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0 dx
+3*X^21 + 2*X^19 + 2*X^17 + 8*X^13 - 4*X^11 + 14*X^7 - 10*X^5 + 3*X^3
+f2 ((-x^6 - 1)/(x^2*y - y)) dx
+((x^4 + x^2 + 1)/(x^6*y)) dx
+[0]
+[0]
+t^5 + 2*t^11 + 2*t^15 + t^19 + O(t^25)
+((x^10 - x^6 + 1)/(x^2*y - y)) dx
+(x^7 + x, 0)
+((-x^10 - x^8 - x^6 + x^4 + x^2 + 1)/(x^6*y)) dx
+((-x^6 - 1)/(x^2*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l?regular_form[?7h[?12l[?25h[?25l[?7lhelp(second_patch)[?7h[?12l[?25h[?25l[?7l?second_patch[?7h[?12l[?25h[?25l[?7lpath(C)[?7h[?12l[?25h[?25l[?7l?seond_patch[?7h[?12l[?25h[?25l[?7lhelp(second_patch)[?7h[?12l[?25h[?25l[?7l?regular_form[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

+I-search:[?7h[?12l[?25h[?25l[?7lload('init.sage')

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

+;[?7h[?12l[?25h[?25l[?7lload('init.sage')

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

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

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

+[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
+False
+(y, -x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
+((2*x^3 + 1)/y) dx (1/y) dx
+(y, -x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
+((2*x^3 + 1)/y) dx (1/y) dx
+3*x^3 + 1 1
+(y, -x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 1 over Finite Field of size 5
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
+((2*x^3 + 1)/y) dx (1/y) dx
+1 1
+(y, -x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
+((-2*x^3 + 1)/y) dx (1/y) dx
+1 1
+(y, -x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
+(1/y) dx (1/y) dx
+1 1
+(y, x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
+False
+(y, x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7ldx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: C.dx == C.dx

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx == C.dx[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
+(1/y) dx (1/y) dx
+(y, x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx == C.dx[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C == C

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

+[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
+(1/y) dx (1/y) dx
+(y, x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7licznik[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lega[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: omega = C.de

+ C.de_rham_basis                     C.degrees_de_rham1                 

+ C.degrees_de_rham0                  C.degrees_holomorphic_differentials

+

+

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

+ C.de_rham_basis                    

+

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

+

+

+[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega = C.de_rham_basis()

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

+

+

+

+ [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7licznik[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt

+ lift            

+ lift_form_to_drw

+ lift_to_sl2z    

+ 

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

+ lift            

+

+

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

+ lift            

+ lift_form_to_drw[?7h[?12l[?25h[?25l[?7l

+

+

+

+[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: lift_form_to_drw(omega)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [24], in <cell line: 1>()
+----> 1 lift_form_to_drw(omega)
+
+File <string>:29, in lift_form_to_drw(omega)
+
+File <string>:5, in regular_form(omega)
+
+AttributeError: 'list' object has no attribute 'curve'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift_form_to_drw(omega)[?7h[?12l[?25h[?25l[?7lomega = C.derham_basis()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: omega = C.de_rham_basis()[0]

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7llift_form_todrw(omega)[?7h[?12l[?25h[?25l[?7lsage: lift_form_to_drw(omega)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [26], in <cell line: 1>()
+----> 1 lift_form_to_drw(omega)
+
+File <string>:29, in lift_form_to_drw(omega)
+
+File <string>:10, in regular_form(omega)
+
+AttributeError: 'superelliptic_cech' object has no attribute 'form'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift_form_to_drw(omega)[?7h[?12l[?25h[?25l[?7lomega = C.derham_basis()[0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: omega = C.holomorphic_differentials_basis()[0]

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega = C.holomorphic_differentials_basis()[0][?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega = C.holomorphic_differentials_basis()[0][?7h[?12l[?25h[?25l[?7llift_form_t_drw(omega)[?7h[?12l[?25h[?25l[?7lsage: lift_form_to_drw(omega)

+[?7h[?12l[?25h[?2004l(1/y) dx (1/y) dx
+y dx + x dy
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR.<u,v> = GF(3)[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 + 1)))[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: R = Integers(25)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR = Integers(25)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: R(2^5)

+[?7h[?12l[?25h[?2004l[?7h7
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR(2^5)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l%[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: R(7^5)

+[?7h[?12l[?25h[?2004l[?7h7
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR(7^5)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: R(2^25)

+[?7h[?12l[?25h[?2004l[?7h7
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in range(3):[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lin range(3):[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l):[?7h[?12l[?25h[?25l[?7l2):[?7h[?12l[?25h[?25l[?7l5):[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: for a in range(25):

+....: [?7h[?12l[?25h[?25l[?7lif m%p != 0:[?7h[?12l[?25h[?25l[?7lif[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la not in lista2:[?7h[?12l[?25h[?25l[?7l%[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7land[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l....:     if a%5 == 2 and a^5 == 1:

+....: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lan[?7h[?12l[?25h[?25l[?7land[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l%[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l

+....: [?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l....:         print(a)

+....: [?7h[?12l[?25h[?25l[?7lsage: for a in range(25):

+....:     if a%5 == 2 and a^5%25 == 1:

+....:         print(a)

+....: 

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for a in range(25):

+....:     if a%5 == 2 and a^5%25 == 1:

+....:         print(a)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a^5%25 = 1:[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()%25 = 1:[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

+....: 

+....:         print(a)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l        print(a)

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

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

+....: [?7h[?12l[?25h[?25l[?7lsage: for a in range(25):

+....:     if a%5 == 2 and (a^5)%25 == 1:

+....:         print(a)

+....: 

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for a in range(25):

+....:     if a%5 == 2 and (a^5)%25 == 1:

+....:         print(a)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7la:[?7h[?12l[?25h[?25l[?7l

+()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:         print(a)

+....: [?7h[?12l[?25h[?25l[?7lsage: for a in range(25):

+....:     if a%5 == 2 and (a^5)%25 == a:

+....:         print(a)

+....: 

+[?7h[?12l[?25h[?2004l7
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR(2^25)[?7h[?12l[?25h[?25l[?7l(2^25)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laR(2)[?7h[?12l[?25h[?25l[?7l R(2)[?7h[?12l[?25h[?25l[?7l=R(2)[?7h[?12l[?25h[?25l[?7l R(2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: a = R(2)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = R(2)[?7h[?12l[?25h[?25l[?7lsage: a

+[?7h[?12l[?25h[?2004l[?7h2
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.substitute({x:x^2, y:y, z[0]:x, z[1]:x})[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a.lift()

+[?7h[?12l[?25h[?2004l[?7h2
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift_form_to_drw(omega)[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
+(1/y) dx (1/y) dx
+(y, x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(g)[?7h[?12l[?25h[?25l[?7lextE.local_data(2))[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: teichmuller(C.x + 2*C.y)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+UnboundLocalError                         Traceback (most recent call last)
+Input In [40], in <cell line: 1>()
+----> 1 teichmuller(C.x + Integer(2)*C.y)
+
+File <string>:22, in teichmuller(fct)
+
+UnboundLocalError: local variable 'fct1' referenced before assignment
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
+(1/y) dx (1/y) dx
+(y, x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lsage: teichmuller(C.x + 2*C.y)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [42], in <cell line: 1>()
+----> 1 teichmuller(C.x + Integer(2)*C.y)
+
+File <string>:22, in teichmuller(fct)
+
+TypeError: unsupported operand type(s) for -: 'PolynomialRing_field_with_category.element_class' and 'superelliptic_function'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
+(1/y) dx (1/y) dx
+(y, x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lsage: teichmuller(C.x + 2*C.y)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [44], in <cell line: 1>()
+----> 1 teichmuller(C.x + Integer(2)*C.y)
+
+File <string>:24, in teichmuller(fct)
+
+File <string>:24, in teichmuller(fct)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
+    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
+    493     """
+--> 494     return self.getattr_from_category(name)
+    495 
+    496 cdef getattr_from_category(self, name):
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
+    505     else:
+    506         cls = P._abstract_element_class
+--> 507     return getattr_from_other_class(self, cls, name)
+    508 
+    509 def __dir__(self):
+
+File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
+    359     dummy_error_message.cls = type(self)
+    360     dummy_error_message.name = name
+--> 361     raise AttributeError(dummy_error_message)
+    362 attribute = <object>attr
+    363 # Check for a descriptor (__get__ in Python)
+
+AttributeError: 'sage.rings.fraction_field_FpT.FpTElement' object has no attribute 'lift'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
+(1/y) dx (1/y) dx
+(y, x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lsage: teichmuller(C.x + 2*C.y)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [46], in <cell line: 1>()
+----> 1 teichmuller(C.x + Integer(2)*C.y)
+
+File <string>:18, in teichmuller(fct)
+
+AttributeError: 'superelliptic' object has no attribute 'base_field'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
+(1/y) dx (1/y) dx
+(y, x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lsage: teichmuller(C.x + 2*C.y)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [48], in <cell line: 1>()
+----> 1 teichmuller(C.x + Integer(2)*C.y)
+
+File <string>:23, in teichmuller(fct)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:6094, in sage.rings.polynomial.polynomial_element.Polynomial.monomial_coefficient()
+   6092 """
+   6093 if not m.parent() is self._parent:
+-> 6094     raise TypeError("monomial must have same parent as self.")
+   6095 
+   6096 d = m.degree()
+
+TypeError: monomial must have same parent as self.
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
+(1/y) dx (1/y) dx
+(y, x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lsage: teichmuller(C.x + 2*C.y)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [50], in <cell line: 1>()
+----> 1 teichmuller(C.x + Integer(2)*C.y)
+
+File <string>:26, in teichmuller(fct)
+
+File <string>:26, in teichmuller(fct)
+
+File /ext/sage/9.7/src/sage/rings/integer.pyx:1769, in sage.rings.integer.Integer.__add__()
+   1767         return y
+   1768 
+-> 1769     return coercion_model.bin_op(left, right, operator.add)
+   1770 
+   1771 cpdef _add_(self, right):
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op()
+   1246     # We should really include the underlying error.
+   1247     # This causes so much headache.
+-> 1248     raise bin_op_exception(op, x, y)
+   1249 
+   1250 cpdef canonical_coercion(self, x, y):
+
+TypeError: unsupported operand parent(s) for +: 'Integer Ring' and '<class '__main__.superelliptic_witt'>'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
+(1/y) dx (1/y) dx
+(y, x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lsage: teichmuller(C.x + 2*C.y)

+[?7h[?12l[?25h[?2004l[?7h<repr(<__main__.superelliptic_witt at 0x7f3375d368c0>) failed: NameError: name 'f0' is not defined>
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
+(1/y) dx (1/y) dx
+(y, x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lsage: teichmuller(C.x + 2*C.y)

+[?7h[?12l[?25h[?2004l[?7hx + 32*y + V(2*x^2*y + 4*x^4 + 4*x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC == C[?7h[?12l[?25h[?25l[?7lsage: C

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 1 over Finite Field of size 5
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
+(1/y) dx (1/y) dx
+(y, x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lsage: teichmuller(C.x + 2*C.y)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [57], in <cell line: 1>()
+----> 1 teichmuller(C.x + Integer(2)*C.y)
+
+File <string>:43, in teichmuller(fct)
+
+File <string>:43, in teichmuller(fct)
+
+File <string>:38, in teichmuller(fct)
+
+File <string>:6, in __init__(self, C, f0, f1)
+
+File <string>:23, in reduce_rational_fct(fct, p)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
+    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
+    493     """
+--> 494     return self.getattr_from_category(name)
+    495 
+    496 cdef getattr_from_category(self, name):
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
+    505     else:
+    506         cls = P._abstract_element_class
+--> 507     return getattr_from_other_class(self, cls, name)
+    508 
+    509 def __dir__(self):
+
+File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
+    359     dummy_error_message.cls = type(self)
+    360     dummy_error_message.name = name
+--> 361     raise AttributeError(dummy_error_message)
+    362 attribute = <object>attr
+    363 # Check for a descriptor (__get__ in Python)
+
+AttributeError: 'sage.rings.integer.Integer' object has no attribute 'monomials'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
+(1/y) dx (1/y) dx
+(y, x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lsage: teichmuller(C.x + 2*C.y)

+[?7h[?12l[?25h[?2004l[?7hx + 7*y + V(2*x^2*y + 4*x^4 + 4*x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lSuperelliptic curve with the equation y^2 = x^4 + x over Finite Field of size 5 ((-1)/y) dx
+(1/y) dx (1/y) dx
+(y, x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l == C[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR(2^25)[?7h[?12l[?25h[?25l[?7lx.<x> = PolynomialRing(GF(3))[?7h[?12l[?25h[?25l[?7l.<x> = PolynomialRing(GF(3))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l4))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: Rx.<x> = PolynomialRing(GF(4))

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l == C[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lrelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 3)[?7h[?12l[?25h[?25l[?7l, 3)[?7h[?12l[?25h[?25l[?7l, 3)[?7h[?12l[?25h[?25l[?7l+, 3)[?7h[?12l[?25h[?25l[?7l , 3)[?7h[?12l[?25h[?25l[?7l1, 3)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 + 1, 3)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 + 1, 3)[?7h[?12l[?25h[?25l[?7l.dx == C.dx[?7h[?12l[?25h[?25l[?7lis_smooth()[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lsmooth()[?7h[?12l[?25h[?25l[?7lsage: C.is_smooth()

+[?7h[?12l[?25h[?2004l[?7h1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.is_smooth()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lp_rank()[?7h[?12l[?25h[?25l[?7lsage: C.p_rank()

+ C.p_rank    

+ C.polynomial

+

+

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

+

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

+  C.a_number                               C.basis_of_cohomology                    C.degrees_de_rham0                        

+  C.base_ring                              C.cartier_matrix                         C.degrees_de_rham1                        

+  C.basis_de_rham_degrees                  C.characteristic                         C.degrees_holomorphic_differentials      >

+  C.basis_holomorphic_differentials_degree C.de_rham_basis                          C.dr_frobenius_matrix                     [?7h[?12l[?25h[?25l[?7lgenus()

+

+

+

+[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.genus()

+[?7h[?12l[?25h[?2004l[?7h1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+ [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7lis_smooth()[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 + 1, 3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + 1, 2)[?7h[?12l[?25h[?25l[?7l4 + 1, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^4 + 1, 2)

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

+

+ [?7h[?12l[?25h[?25l[?7lC = superelliptic(x^4 + 1, 2)[?7h[?12l[?25h[?25l[?7l.gens()[?7h[?12l[?25h[?25l[?7lis_smooth()[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_smooth()[?7h[?12l[?25h[?25l[?7lsage: C.is_smooth()

+[?7h[?12l[?25h[?2004l[?7h0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.is_smooth()[?7h[?12l[?25h[?25l[?7l = superelliptic(x^4 + 1, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7lx, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^4 + x, 2)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^4 + x, 2)[?7h[?12l[?25h[?25l[?7l.is_smooth()[?7h[?12l[?25h[?25l[?7lsage: C.is_smooth()

+[?7h[?12l[?25h[?2004l[?7h1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.is_smooth()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.genus()

+[?7h[?12l[?25h[?2004l[?7h1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[x^5 + x^4 + z0*z1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [(C.y)^(-1)])[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.cartier_matrix()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in range(25):[?7h[?12l[?25h[?25l[?7l =x^3 - x[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: f = AS.magical_element()[0]

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = AS.magical_element()[0][?7h[?12l[?25h[?25l[?7lsage: f

+[?7h[?12l[?25h[?2004l[?7hx^5 + x^4 + z0*z1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f.valuation()

+[?7h[?12l[?25h[?2004l[?7h-13
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [(C.y)^(-1)])[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.cartier_matrix()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: AS.exponent_of_different

+ AS.exponent_of_different     

+ AS.exponent_of_different_prim

+

+

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

+ AS.exponent_of_different     

+

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

+ AS.exponent_of_different     

+ AS.exponent_of_different_prim[?7h[?12l[?25h[?25l[?7l

+

+

+[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.exponent_of_different_prim()

+[?7h[?12l[?25h[?2004l[?7h13
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+ [?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lf.valuation()[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.valuation()[?7h[?12l[?25h[?25l[?7l = AS.magical_element()[0][?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf + z0^2[?7h[?12l[?25h[?25l[?7l1f + z0^2[?7h[?12l[?25h[?25l[?7l f + z0^2[?7h[?12l[?25h[?25l[?7l=f + z0^2[?7h[?12l[?25h[?25l[?7l f + z0^2[?7h[?12l[?25h[?25l[?7lsage: f1 = f + z0^2

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [6], in <cell line: 1>()
+----> 1 f1 = f + z0**Integer(2)
+
+NameError: name 'z0' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = f + z0^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = f + z0^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz0^2[?7h[?12l[?25h[?25l[?7lSz0^2[?7h[?12l[?25h[?25l[?7l.z0^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: f1 = f + AS.z[0]^2

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = f + AS.z[0]^2[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f1.valuation()

+[?7h[?12l[?25h[?2004l[?7h-20
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[x^4 + z0*z1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lsage: AS.exponent_of_different_prim()

+[?7h[?12l[?25h[?2004l[?7h13
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[x^5 + x^4 + z0*z1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]*[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfAS.z[0]*AS.z[1][?7h[?12l[?25h[?25l[?7l1AS.z[0]*AS.z[1][?7h[?12l[?25h[?25l[?7l AS.z[0]*AS.z[1][?7h[?12l[?25h[?25l[?7l=AS.z[0]*AS.z[1][?7h[?12l[?25h[?25l[?7l AS.z[0]*AS.z[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]+[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[1]+x^4[?7h[?12l[?25h[?25l[?7lAS.z[1]+x^4[?7h[?12l[?25h[?25l[?7lSAS.z[1]+x^4[?7h[?12l[?25h[?25l[?7l.AS.z[1]+x^4[?7h[?12l[?25h[?25l[?7lzAS.z[1]+x^4[?7h[?12l[?25h[?25l[?7l[AS.z[1]+x^4[?7h[?12l[?25h[?25l[?7l0AS.z[1]+x^4[?7h[?12l[?25h[?25l[?7l[]AS.z[1]+x^4[?7h[?12l[?25h[?25l[?7l[] AS.z[1]+x^4[?7h[?12l[?25h[?25l[?7l+AS.z[1]+x^4[?7h[?12l[?25h[?25l[?7l AS.z[1]+x^4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])+x^4[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: f1 = AS.z[0]*(AS.z[0] + AS.z[1])+x^4

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [12], in <cell line: 1>()
+----> 1 f1 = AS.z[Integer(0)]*(AS.z[Integer(0)] + AS.z[Integer(1)])+x**Integer(4)
+
+File <string>:23, in __add__(self, other)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
+    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
+    493     """
+--> 494     return self.getattr_from_category(name)
+    495 
+    496 cdef getattr_from_category(self, name):
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
+    505     else:
+    506         cls = P._abstract_element_class
+--> 507     return getattr_from_other_class(self, cls, name)
+    508 
+    509 def __dir__(self):
+
+File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
+    359     dummy_error_message.cls = type(self)
+    360     dummy_error_message.name = name
+--> 361     raise AttributeError(dummy_error_message)
+    362 attribute = <object>attr
+    363 # Check for a descriptor (__get__ in Python)
+
+AttributeError: 'sage.rings.polynomial.polynomial_gf2x.Polynomial_GF2X' object has no attribute 'function'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = AS.z[0]*(AS.z[0] + AS.z[1])+x^4[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: f1

+[?7h[?12l[?25h[?2004l[?7hx^5 + x^4 + z0^2 + z0*z1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1[?7h[?12l[?25h[?25l[?7l = AS.z[0]*(AS.z[0] + AS.z[1])+x^4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAx^4[?7h[?12l[?25h[?25l[?7lSx^4[?7h[?12l[?25h[?25l[?7l.x^4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: f1 = AS.z[0]*(AS.z[0] + AS.z[1])+AS.x^4

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = AS.z[0]*(AS.z[0] + AS.z[1])+AS.x^4[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lluation()[?7h[?12l[?25h[?25l[?7lsage: f1.valuation()

+[?7h[?12l[?25h[?2004l[?7h-13
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx.<x> = PolynomialRing(GF(4))[?7h[?12l[?25h[?25l[?7l.<u,v> = GF(3)[]; EllipticCurve(WeierstrassForm(v^2 - (u^4 + 1)))[?7h[?12l[?25h[?25l[?7l<[?7h[?12l[?25h[?25l[?7l>[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx>[?7h[?12l[?25h[?25l[?7l = PolynomialRing(GF(3))[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l PolynomialRing(GF(3))[?7h[?12l[?25h[?25l[?7lsage: R.<x> = PolynomialRing(GF(3))

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1.valuation()[?7h[?12l[?25h[?25l[?7l = AS.magical_element()[0][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx^3 - x[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: f = x^3 + 2*x - 1

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(C.holomorphic_differentials_basis()[0])[?7h[?12l[?25h[?25l[?7ltr(E.local_data(2))[?7h[?12l[?25h[?25l[?7lstr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l"[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l"[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l"[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]"[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: str(f).replace("x", "[x]")

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

+[?7h[?12l[?25h[?2004l[x^5 + x^4 + z0*z1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lsage: teichmuller(C.x + 2*C.y)

+[?7h[?12l[?25h[?2004l[?7h[x] + V(0)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lTraceback (most recent call last):
+
+  File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
+    exec(code_obj, self.user_global_ns, self.user_ns)
+
+  Input In [6] in <cell line: 1>
+    load('init.sage')
+
+  File sage/misc/persist.pyx:175 in sage.misc.persist.load
+    sage.repl.load.load(filename, globals())
+
+  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
+    exec(preparse_file(f.read()) + "\n", globals)
+
+  File <string>:26 in <module>
+
+  File sage/misc/persist.pyx:175 in sage.misc.persist.load
+    sage.repl.load.load(filename, globals())
+
+  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
+    exec(preparse_file(f.read()) + "\n", globals)
+
+  File <string>:14
+    return "[" + str(t) "] + " + str(f0).replace("x", "[x]").replace("y", "[y]") + " + V(" + str(f1) + ")"
+                        ^
+SyntaxError: invalid syntax
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[x^5 + x^4 + z0*z1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.lift()[?7h[?12l[?25h[?25l[?7l = R(2[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lw[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a = superelliptic_witt(C, C.x, 0, C.y)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = superelliptic_witt(C, C.x, 0, C.y)[?7h[?12l[?25h[?25l[?7lsage: a

+[?7h[?12l[?25h[?2004l[?7h[x] + 0 + V(x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = superelliptic_witt(C, C.x, 0, C.y)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x, 0, C.y)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(), 0, C.y)[?7h[?12l[?25h[?25l[?7l()^, 0, C.y)[?7h[?12l[?25h[?25l[?7l2, 0, C.y)[?7h[?12l[?25h[?25l[?7l , 0, C.y)[?7h[?12l[?25h[?25l[?7l+, 0, C.y)[?7h[?12l[?25h[?25l[?7l , 0, C.y)[?7h[?12l[?25h[?25l[?7lC, 0, C.y)[?7h[?12l[?25h[?25l[?7l., 0, C.y)[?7h[?12l[?25h[?25l[?7ly, 0, C.y)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: a = superelliptic_witt(C, (C.x)^2 + C.y, 0, C.y)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = superelliptic_witt(C, (C.x)^2 + C.y, 0, C.y)[?7h[?12l[?25h[?25l[?7lsage: a

+[?7h[?12l[?25h[?2004l[?7h[x^2 + x] + 0 + V(x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

+[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd ..
+]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git status
+On branch master
+Your branch is up to date with 'origin/master'.
+
+Changes not staged for commit:
+  (use "git add <file>..." to update what will be committed)
+  (use "git restore <file>..." to discard changes in working directory)
+	modified:   sage/.run.term-0.term
+	modified:   sage/as_covers/as_cover_class.sage
+	modified:   sage/as_covers/as_form_class.sage
+	modified:   sage/drafty/draft.sage
+	modified:   sage/drafty/draft2.sage
+	modified:   sage/init.sage
+	modified:   sage/superelliptic/superelliptic_class.sage
+	modified:   sage/superelliptic/superelliptic_form_class.sage
+	modified:   sage/superelliptic/superelliptic_function_class.sage
+	modified:   sage/tests.sage
+
+Untracked files:
+  (use "git add <file>..." to include in what will be committed)
+	.crystalline_p2.ipynb.sage-jupyter2
+	.deRhamComputation.ipynb.sage-jupyter2
+	.elementary_covers_of_superelliptic_curves.ipynb.sage-jupyter2
+	.git.x11-0.term
+	.superelliptic.ipynb.sage-jupyter2
+	.superelliptic_alpha.ipynb.sage-jupyter2
+	.superelliptic_arbitrary_field.ipynb.sage-jupyter2
+	git.x11
+	sage/as_covers/tests/cartier_test.sage
+	sage/drafty/as_cartier.sage
+	sage/drafty/better_trace.sage
+	sage/drafty/cartier_image_representation.sage
+	sage/drafty/draft4.sage
+	sage/drafty/draft5.sage
+	sage/drafty/draft6.sage
+	sage/drafty/draft7.sage
+	sage/drafty/lift_to_de_rham.sage
+	sage/drafty/pole_numbers.sage
+	sage/drafty/regular_on_U0.sage
+	sage/drafty/second_patch.sage
+	sage/drafty/superelliptic_drw.sage
+	sage/superelliptic/decomposition_into_g0_g8.sage
+	sage/superelliptic/frobenius_kernel.sage
+	sage/superelliptic/tests/
+	superelliptic_arbitrary_field.ipynb
+
+no changes added to commit (use "git add" and/or "git commit -a")
+]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ add sage/drafty/addgit add sage/drafty/superelliptic_drw.sage sage/drafty/superelliptic/decomposition_into_g0_g8.sage 
+]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ g
\ No newline at end of file
diff --git a/sage/as_covers/as_cover_class.sage b/sage/as_covers/as_cover_class.sage
index 316ab5a..acadbbc 100644
--- a/sage/as_covers/as_cover_class.sage
+++ b/sage/as_covers/as_cover_class.sage
@@ -32,12 +32,12 @@ class as_cover:
         all_jumps = []
 
         for i in range(delta):
-            x_series = superelliptic_function(C, x).expansion_at_infty(i = i, prec=prec)
-            y_series = superelliptic_function(C, y).expansion_at_infty(i = i, prec=prec)
+            x_series = superelliptic_function(C, x).expansion_at_infty(place = i, prec=prec)
+            y_series = superelliptic_function(C, y).expansion_at_infty(place = i, prec=prec)
             z_series = []
             jumps = []
             n = len(list_of_fcts)
-            list_of_power_series = [g.expansion_at_infty(i = i, prec=prec) for g in list_of_fcts]
+            list_of_power_series = [g.expansion_at_infty(place = i, prec=prec) for g in list_of_fcts]
             for i in range(n):
                 power_series = list_of_power_series[i]
                 jump, correction, t_old, z = artin_schreier_transform(power_series, prec = prec)
@@ -93,19 +93,19 @@ class as_cover:
         p = self.characteristic
         return p^n*gY + (p^n - 1)*(delta - 1) + sum(p^(n-j-1)*(jumps[i][j]-1)*(p-1)/2 for j in range(n) for i in range(delta))
     
-    def exponent_of_different(self, i = 0):
+    def exponent_of_different(self, place = 0):
         jumps = self.jumps
         n = self.height
         delta = self.nb_of_pts_at_infty
         p = self.characteristic
-        return sum(p^(n-j-1)*(jumps[i][j]+1)*(p-1) for j in range(n))
+        return sum(p^(n-j-1)*(jumps[place][j]+1)*(p-1) for j in range(n))
 
-    def exponent_of_different_prim(self, i = 0):
+    def exponent_of_different_prim(self, place = 0):
         jumps = self.jumps
         n = self.height
         delta = self.nb_of_pts_at_infty
         p = self.characteristic
-        return sum(p^(n-j-1)*(jumps[i][j])*(p-1) for j in range(n))
+        return sum(p^(n-j-1)*(jumps[place][j])*(p-1) for j in range(n))
     
     def holomorphic_differentials_basis(self, threshold = 8):
         from itertools import product
@@ -136,7 +136,7 @@ class as_cover:
         forms = holomorphic_combinations(S)
         
         for i in range(1, delta):
-            forms = [(omega, omega.expansion_at_infty(i = i)) for omega in forms]
+            forms = [(omega, omega.expansion_at_infty(place = i)) for omega in forms]
             forms = holomorphic_combinations(forms)
         
         if len(forms) < self.genus():
@@ -145,6 +145,14 @@ class as_cover:
         if len(forms) > self.genus():
             print("Increase precision.")
         return forms
+    
+    def cartier_matrix(self, prec=50):
+        g = self.genus()
+        F = self.base_ring
+        M = matrix(F, g, g)
+        for i, omega in enumerate(self.holomorphic_differentials_basis()):
+            M[:, i] = vector(omega.cartier().coordinates())
+        return M
 
     def at_most_poles(self, pole_order, threshold = 8):
         """ Find fcts with pole order in infty's at most pole_order. Threshold gives a bound on powers of x in the function.
@@ -177,7 +185,7 @@ class as_cover:
         forms = holomorphic_combinations_fcts(S, pole_order)
 
         for i in range(1, delta):
-            forms = [(omega, omega.expansion_at_infty(i = i)) for omega in forms]
+            forms = [(omega, omega.expansion_at_infty(place = i)) for omega in forms]
             forms = holomorphic_combinations_fcts(forms, pole_order)
                   
         return forms
@@ -229,13 +237,13 @@ class as_cover:
         forms = holomorphic_combinations_forms(S, pole_order)
 
         for i in range(1, delta):
-            forms = [(omega, omega.expansion_at_infty(i = i)) for omega in forms]
+            forms = [(omega, omega.expansion_at_infty(place = i)) for omega in forms]
             forms = holomorphic_combinations_forms(forms, pole_order)
                   
         return forms
     
-    def uniformizer(self, i = 0):
-        '''Return uniformizer of curve self at i-th place at infinity.'''
+    def uniformizer(self, place = 0):
+        '''Return uniformizer of curve self at place-th place at infinity.'''
         p = self.characteristic
         n = self.height
         F = self.base_ring
@@ -244,8 +252,8 @@ class as_cover:
         z = [as_function(self, zi) for zi in z]
         # We create a list of functions. We add there all variables...
         list_of_fcts = [fx]+z
-        vfx = fx.valuation(i)
-        vz = [zi.valuation(i) for zi in z]
+        vfx = fx.valuation(place)
+        vz = [zi.valuation(place) for zi in z]
         
         # Then we subtract powers of variables with the same valuation (so that 1/t^(kp) cancels) and add to this list.
         for  j1 in range(n):
@@ -255,19 +263,19 @@ class as_cover:
                     vz1 = vz[j1]/a
                     vz2 = vz[j2]/a
                     for b in F:
-                        if (z[j1]^(vz2) - b*z[j2]^(vz1)).valuation(i) > (z[j2]^(vz1)).valuation(i):
+                        if (z[j1]^(vz2) - b*z[j2]^(vz1)).valuation(place) > (z[j2]^(vz1)).valuation(place):
                             list_of_fcts += [z[j1]^(vz2) - b*z[j2]^(vz1)]
         for j1 in range(n):
             a = gcd(vz[j1], vfx)
             vzj = vz[j1] /a
             vfx = vfx/a
             for b in F:
-                if (fx^(vzj) - b*z[j1]^(vfx)).valuation(i) > (z[j1]^(vfx)).valuation(i):
+                if (fx^(vzj) - b*z[j1]^(vfx)).valuation(place) > (z[j1]^(vfx)).valuation(place):
                     list_of_fcts += [fx^(vzj) - b*z[j1]^(vfx)]
         #Finally, we check if on the list there are two elements with the same valuation.
         for f1 in list_of_fcts:
             for f2 in list_of_fcts:
-                d, a, b = xgcd(f1.valuation(i), f2.valuation(i))
+                d, a, b = xgcd(f1.valuation(place), f2.valuation(place))
                 if d == 1:
                     return f1^a*f2^b
         raise ValueError("My method of generating fcts with relatively prime valuation failed.")
@@ -298,6 +306,10 @@ class as_cover:
             G = Gi
             i+=1
         return ramification_jps
+    
+    def a_number(self):
+        g = self.genus()
+        return g - self.cartier_matrix().rank()
 
     def cohomology_of_structure_sheaf_basis(self, threshold = 8):
         holo_diffs = self.holomorphic_differentials_basis(threshold = threshold)
diff --git a/sage/as_covers/as_form_class.sage b/sage/as_covers/as_form_class.sage
index 715ff84..99c1e80 100644
--- a/sage/as_covers/as_form_class.sage
+++ b/sage/as_covers/as_form_class.sage
@@ -106,6 +106,39 @@ class as_form:
     def serre_duality_pairing(self, fct):
         AS = self.curve
         return sum((fct*self).residue(place = _) for _ in range(AS.nb_of_pts_at_infty))
+
+    def cartier(self):
+        C = self.curve
+        F = C.base_ring
+        n = C.height
+        ff = C.functions
+        p = F.characteristic()
+        C_super = C.quotient
+        (RxyzQ, Rxyz, x, y, z) = C.fct_field
+        fct = self.form
+        Rxy.<x, y> = PolynomialRing(F, 2)
+        RxyQ = FractionField(Rxy)
+        x, y = Rxyz.gens()[0], Rxyz.gens()[1]
+        z = Rxyz.gens()[2:]
+        num = Rxyz(fct.numerator())
+        den = Rxyz(fct.denominator())
+        result = RxyzQ(0)
+        #return (num, den, z, fct)
+        if den in Rxy:
+            sub_list = {x : x, y : y} | {z[j] : (z[j]^p - RxyzQ(ff[j].function)) for j in range(n)}
+            num = RxyzQ(num.substitute(sub_list))
+            den1 = Rxyz(num.denominator())
+            num = Rxyz(num*den1^p)
+            for monomial in Rxyz(num).monomials():
+                degrees = [monomial.degree(z[i]) for i in range(n)]
+                product_of_z = prod(z[i]^(degrees[i]) for i in range(n))
+                monomial_divided_by_z = monomial/product_of_z
+                product_of_z_no_p = prod(z[i]^(degrees[i]/p) for i in range(n))
+                aux_form = superelliptic_form(C_super, RxyQ(monomial_divided_by_z/den))
+                aux_form = aux_form.cartier()
+                result += product_of_z_no_p * Rxyz(num).monomial_coefficient(monomial) * aux_form.form/den1
+            return as_form(C, result)
+        raise ValueError("Please present first your form as sum z^i omega_i, where omega_i are forms on quotient curve.")
     
 def artin_schreier_transform(power_series, prec = 10):
     """Given a power_series, find correction such that power_series - (correction)^p +correction has valuation
diff --git a/sage/drafty/draft.sage b/sage/drafty/draft.sage
index 82a4967..120f4e9 100644
--- a/sage/drafty/draft.sage
+++ b/sage/drafty/draft.sage
@@ -1,19 +1,9 @@
-p = 5
+p = 2
 m = 1
 F = GF(p)
 Rx.<x> = PolynomialRing(F)
 f = x
-C_super = superelliptic(f, m)
-
-Rxy.<x, y> = PolynomialRing(F, 2)
-for a in range(3, 13):
-    for b in range(3, 13):
-        if a %p != 0 and b%p != 0 and a !=b:
-            try:
-                f1 = superelliptic_function(C_super, x^a+x)
-                f2 = superelliptic_function(C_super, x^b)
-                AS = as_cover(C_super, [f1, f2], prec=1000)
-                #print(AS.at_most_poles(AS.exponent_of_different_prim()))
-                print(AS.magical_element(threshold = 20))
-            except:
-                pass
\ No newline at end of file
+C = superelliptic(f, m)
+xx = C.x
+AS = as_cover(C, [xx^5, xx^5 + xx^3])
+print(AS.magical_element())
\ No newline at end of file
diff --git a/sage/drafty/draft2.sage b/sage/drafty/draft2.sage
index 36474e2..d9659ec 100644
--- a/sage/drafty/draft2.sage
+++ b/sage/drafty/draft2.sage
@@ -1,13 +1,5 @@
-p = 3
-m = 2
-F = GF(p)
-Rx.<x> = PolynomialRing(F)
-f = x^3 - x
-C = superelliptic(f, m)
-x = C.x
-y = C.y
-dx = C.dx
-om1 = x^3*y*dx
-u = (C.one)/x
-v = y/x^2
-print(om1 + u^3*v*u.diffn() - (y/x)^2*(y/x).diffn())
\ No newline at end of file
+F = GF(2)
+A = matrix(F, [[1, 1, 1], [0, 0, 1], [0, 1, 0]])
+B = matrix(F, [[0, 0, 1], [1, 1, 1], [1, 0, 0]])
+print(A^2 == identity_matrix(3), B^2 == identity_matrix(3), A*B == B*A)
+print(magmathis(A, B))
\ No newline at end of file
diff --git a/sage/drafty/superelliptic_drw.sage b/sage/drafty/superelliptic_drw.sage
new file mode 100644
index 0000000..1465dd6
--- /dev/null
+++ b/sage/drafty/superelliptic_drw.sage
@@ -0,0 +1,110 @@
+class superelliptic_witt:
+    def __init__(self, C, t, f0, f1):
+        ''' Define Witt function on C of the form [t] + f0([x], [y]) + V(f1). '''
+        self.curve = C
+        p = C.characteristic
+        self.t = t #superelliptic_function
+        self.f0 = reduce_rational_fct(f0, p) #polynomial/rational function over Z/p^2
+        self.f1 = f1 #superelliptic_function
+    
+    def __repr__(self):
+        f0 = self.f0
+        f1 = self.f1
+        t = self.t
+        return "[" + str(t) + "] + " + str(f0).replace("x", "[x]").replace("y", "[y]") + " + V(" + str(f1) + ")"
+    
+    def __add__(self, other):
+        C = self.curve
+        return superelliptic_witt(C, self.t + other.t, self.f0 + other.f0, self.f1 + other.f1)
+
+    def teichmuller_representation(self):
+        '''Represents as [f] + V(g), i.e. f0 = 0.'''
+        C = self.curve
+        Fxy, Rxy, x, y = self.fct_field
+        F = C.base_ring
+        function = Rxy(self.f0)
+        if self.f0 == 0:
+            return self
+        M = Rxy(function.monomials()[0])
+        a = F(function.monomial_coefficient(M))
+        fct1 = fct - superelliptic_function(C, a*M)
+        function1 = fct1.function
+        return teichmuller(fct1) + superelliptic_witt(C, (a.lift())^p*M.change_ring(QQ), superelliptic_function(C, function1^2*a*M + function1*(a*M)^2))
+    
+    def antiteichmuller_representation(self):
+        '''Represents as f([x], [y]) + V(g), i.e. teichmuller part is zero.'''
+        return 0
+    
+def reduce_rational_fct(fct, p):
+    Rxy.<x, y> = PolynomialRing(QQ)
+    Fxy = FractionField(Rxy)
+    fct = Fxy(fct)
+    num = Rxy(fct.numerator())
+    den = Rxy(fct.denominator())
+    num1 = Rxy(0)
+    for m in num.monomials():
+        a = num.monomial_coefficient(m)
+        num1 += (a%p^2)*m
+    den1 = Rxy(0)
+    for m in den.monomials():
+        a = den.monomial_coefficient(m)
+        den1 += (a%p^2)*m
+    return num1/den1
+
+def teichmuller(fct):
+    C = fct.curve
+    Fxy, Rxy, x, y = C.fct_field
+    F = C.base_ring
+    function = Rxy(fct.function)
+    if function == 0:
+        return superelliptic_witt(C, 0, 0*C.x)
+    M = Rxy(function.monomials()[0])
+    a = F(function.monomial_coefficient(M))
+    fct1 = fct - superelliptic_function(C, a*M)
+    function1 = fct1.function
+    return teichmuller(fct1) + superelliptic_witt(C, (a.lift())^p*M.change_ring(QQ), superelliptic_function(C, function1^2*a*M + function1*(a*M)^2))
+
+class superelliptic_drw_form:
+    def __init__(self, C, omega_x, omega_y, omega, h):
+        '''Form [omega_x] d[x] + [omega_y] d[y] + V(omega) + dV([h])'''
+        self.curve = C
+        self.omega_x = omega_x
+        self.omega_y = omega_y
+        self.omega = omega
+        self.h = h
+        
+    def __eq__(self, other):
+        eq1 = (self.omega1 == self.omega1)
+        try:
+            H = (self.h - other.h).pthroot()
+        except:
+            return False
+        eq2 = (self.omega2 - other.omega2).cartier() - H.diffn()
+        if eq1 and eq2:
+            return True
+        return False
+    
+    def __repr__(self):
+        C = self.curve
+        omega_x = self.omega_x
+        omega_y = self.omega_y
+        h = self.h
+        return  str(omega_x) + "] dx + [" + str(omega_x.form) + "] d[x] " + "+ V(" + str(omega2) + ") + dV([" + str(h) +"])"
+
+def mult_by_p(omega):
+    C = omega.curve
+    fct = omega.form
+    Fxy, Rxy, x, y = C.fct_field
+    omega2 = superelliptic_form(C, fct^p * x^(p-1))
+    result = superelliptic_drw_form(C, 0*C.dx, omega2, 0*C.x)
+    return result
+    
+def basis_W2Omega(C):
+    basis = C.holomorphic_differentials_basis()
+    result = []
+    for omega in basis:
+        result += [mult_by_p(omega)]
+        
+    image_of_cartier = []
+    
+    return result
\ No newline at end of file
diff --git a/sage/init.sage b/sage/init.sage
index 0143cbe..26843a6 100644
--- a/sage/init.sage
+++ b/sage/init.sage
@@ -2,6 +2,8 @@ load('superelliptic/superelliptic_class.sage')
 load('superelliptic/superelliptic_function_class.sage')
 load('superelliptic/superelliptic_form_class.sage')
 load('superelliptic/superelliptic_cech_class.sage')
+load('superelliptic/frobenius_kernel.sage')
+load('superelliptic/decomposition_into_g0_g8.sage')
 load('as_covers/as_cover_class.sage')
 load('as_covers/as_function_class.sage')
 load('as_covers/as_form_class.sage')
@@ -17,8 +19,10 @@ load('auxilliaries/hensel.sage')
 load('auxilliaries/linear_combination_polynomials.sage')
 ##############
 ##############
+load('drafty/second_patch.sage')
+load('drafty/regular_on_U0.sage')
 load('drafty/lift_to_de_rham.sage')
 #load('drafty/superelliptic_cohomology_class.sage')
-load('drafty/draft5.sage')
-load('drafty/pole_numbers.sage')
-#load('drafty/draft4.sage')
\ No newline at end of file
+load('drafty/superelliptic_drw.sage')
+load('drafty/draft.sage')
+load('drafty/pole_numbers.sage')
\ No newline at end of file
diff --git a/sage/superelliptic/decomposition_into_g0_g8.sage b/sage/superelliptic/decomposition_into_g0_g8.sage
new file mode 100644
index 0000000..845540d
--- /dev/null
+++ b/sage/superelliptic/decomposition_into_g0_g8.sage
@@ -0,0 +1,44 @@
+def decomposition_g0_g8(fct):
+    '''Writes fct as a difference g0 - g8, with g0 regular on the affine patch and g8 at the points in infinity.'''
+    C = fct.curve
+    g = C.genus()
+    if fct.coordinates() != g*[0]:
+        raise ValueError("The given function cannot be written as g0 - g8.")
+    
+    Fxy, Rxy, x, y = C.fct_field
+    fct = Fxy(fct.function)
+    num = fct.numerator()
+    den = fct.denominator()
+    aux_den = superelliptic_function(C, Rxy(den))
+    g0 = superelliptic_function(C, 0)
+    g8 = superelliptic_function(C, 0)
+    for monomial in num.monomials():
+        aux = superelliptic_function(C, monomial)
+        if aux.expansion_at_infty().valuation() >= aux_den.expansion_at_infty().valuation():
+            g8 += num.monomial_coefficient(monomial)*aux/aux_den
+        else:
+            g0 += num.monomial_coefficient(monomial)*aux/aux_den
+    return (g0, g8)
+    
+def decomposition_omega0_omega8(omega, prec=50):
+    '''Writes omega as a difference omega0 - omega8, with omega0 regular on the affine patch and omega8 at the points in infinity.'''
+    C = omega.curve
+    Fxy, Rxy, x, y = C.fct_field
+    fct = Fxy(omega.form)
+    num = fct.numerator()
+    den = fct.denominator()
+    aux_den = superelliptic_function(C, Rxy(den))
+    g0 = superelliptic_function(C, 0)
+    g8 = superelliptic_function(C, 0)
+    dx_valuation = C.dx.expansion_at_infty(prec=prec).valuation()
+    for monomial in num.monomials():
+        aux = superelliptic_function(C, monomial)
+        if aux.expansion_at_infty(prec=prec).valuation() + dx_valuation >= aux_den.expansion_at_infty(prec=prec).valuation():
+            g8 += num.monomial_coefficient(monomial)*aux/aux_den
+        else:
+            g0 += num.monomial_coefficient(monomial)*aux/aux_den
+    g0, g8  = g0*C.dx, g8*C.dx
+    if g0.is_regular_on_U0():
+        return (g0, g8)
+    else:
+        raise Error("Something went wrong.")
\ No newline at end of file
diff --git a/sage/superelliptic/superelliptic_class.sage b/sage/superelliptic/superelliptic_class.sage
index 2183ee4..7681157 100644
--- a/sage/superelliptic/superelliptic_class.sage
+++ b/sage/superelliptic/superelliptic_class.sage
@@ -12,7 +12,7 @@ class superelliptic:
         self.exponent = m
         self.base_ring = F
         self.characteristic = F.characteristic()
-        self.fct_field = RxyzQ, Rxyz, x, y, z
+        self.fct_field = Fxy, Rxy, x, y
         r = Rx(f).degree()
         delta = GCD(r, m)
         self.nb_of_pts_at_infty = delta
@@ -26,19 +26,6 @@ class superelliptic:
         m = self.exponent
         F = self.base_ring
         return 'Superelliptic curve with the equation y^' + str(m) + ' = ' + str(f)+' over ' + str(F)
-
-    def coordinates2(self, basis = 0):
-        """Find coordinates of the given holomorphic form self in terms of the basis forms in a list holo."""
-        C = self.curve
-        if basis == 0:
-            basis = C.holomorphic_differentials_basis()
-        RxyzQ, Rxyz, x, y, z = C.fct_field
-        # We need to have only polynomials to use monomial_coefficients in linear_representation_polynomials,
-        # and sometimes basis elements have denominators. Thus we multiply by them.
-        denom = LCM([denominator(omega.form) for omega in basis])
-        basis = [denom*omega for omega in basis]
-        self_with_no_denominator = denom*self
-        return linear_representation_polynomials(Rxyz(self_with_no_denominator.form), [Rxyz(omega.form) for omega in basis]) 
     
     #Auxilliary algorithm that returns the basis of holomorphic differentials
     #of the curve and (as a second argument) the list of pairs (i, j)
@@ -164,8 +151,8 @@ class superelliptic:
         for i in range(0, len(basis)):
             w = basis[i]
             v = w.cartier().coordinates()
-            M[i, :] = v
-        return M     
+            M[:, i] = vector(v)
+        return M
 
     def frobenius_matrix(self, prec=20):
         g = self.genus()
@@ -177,11 +164,18 @@ class superelliptic:
         M = M.transpose()
         return M
     
-#    def p_rank(self):
-#        return self.cartier_matrix().rank()
+    def p_rank(self):
+        if self.exponent != 2:
+            raise ValueError('No implemented yet.')
+        f = self.polynomial()
+        F = self.base_ring
+        Rt.<t> = PolynomialRing(F)
+        f = Rt(f)
+        H = HyperellipticCurve(f, 0)
+        return H.p_rank()
     
     def a_number(self):
-        g = C.genus()
+        g = self.genus()
         return g - self.cartier_matrix().rank()
     
     def final_type(self, test = 0):
diff --git a/sage/superelliptic/superelliptic_form_class.sage b/sage/superelliptic/superelliptic_form_class.sage
index 1ef4311..922003a 100644
--- a/sage/superelliptic/superelliptic_form_class.sage
+++ b/sage/superelliptic/superelliptic_form_class.sage
@@ -33,6 +33,8 @@ class superelliptic_form:
         return superelliptic_form(C, constant*omega)
     
     def cartier(self):
+        '''Computes Cartier operator on the form. Idea: y^m = f(x) -> y^(p^r - 1) = f(x)^M, where r = ord_p(m),
+        M = (p^r - 1)/m. Thus h(x)/y^j dx = h(x) f(x)^(M*j)/y^(p^r * j) dx. Thus C(h(x)/y^j dx) = 1/y^(p^(r-1)*j) C(h(x) f(x)^(M*j) dx).'''
         C = self.curve
         m = C.exponent
         p = C.characteristic
@@ -46,15 +48,19 @@ class superelliptic_form:
         mult_order = Integers(m)(p).multiplicative_order()
         M = Integer((p^(mult_order)-1)/m)
         
-        for j in range(1, m):
+        for j in range(0, m):
             fct_j = self.jth_component(j)
-            h = Rx(fct_j*f^(M*j))
+            h = Fx(fct_j*f^(M*j))
+            h_denom = h.denominator()
+            h *= (h_denom)^(p)
+            h = Rx(h)
             j1 = (p^(mult_order-1)*j)%m
             B = floor(p^(mult_order-1)*j/m)
-            result += superelliptic_form(C, polynomial_part(p, h)/(f^B*y^(j1)))
+            result += superelliptic_form(C, polynomial_part(p, h)/(f^B*y^(j1)*h_denom))
         return result   
 
     def serre_duality_pairing(self, fct, prec=20):
+        '''Compute Serre duality pairing of the form with a cohomology class in H1(X, OX) represented by function fct.'''
         result = 0
         C = self.curve
         delta = C.nb_of_pts_at_infty
@@ -62,31 +68,21 @@ class superelliptic_form:
             result += (fct*self).expansion_at_infty(place=i, prec=prec)[-1]
         return -result
     
-    def coordinates(self):
+    def coordinates(self, basis = 0):
+        """Find coordinates of the given holomorphic form self in terms of the basis forms in a list holo."""
         C = self.curve
-        F = C.base_ring
-        m = C.exponent
-        Rx.<x> = PolynomialRing(F)
-        Fx = FractionField(Rx)
-        FxRy.<y> = PolynomialRing(Fx)
-        g = C.genus()
-        degrees_holo = C.degrees_holomorphic_differentials()
-        degrees_holo_inv = {b:a for a, b in degrees_holo.items()}
-        basis = C.holomorphic_differentials_basis()
-        
-        for j in range(1, m):
-            omega_j = Fx(self.jth_component(j))
-            if omega_j != Fx(0):
-                d = degree_of_rational_fctn(omega_j, F)
-                index = degrees_holo_inv[(d, j)]
-                a = coeff_of_rational_fctn(omega_j, F)
-                a1 = coeff_of_rational_fctn(basis[index].jth_component(j), F)
-                elt = self - (a/a1)*basis[index]
-                return elt.coordinates() + a/a1*vector([F(i == index) for i in range(0, g)])
-            
-        return vector(g*[0])
+        if basis == 0:
+            basis = C.holomorphic_differentials_basis()
+        Fxy, Rxy, x, y = C.fct_field
+        # We need to have only polynomials to use monomial_coefficients in linear_representation_polynomials,
+        # and sometimes basis elements have denominators. Thus we multiply by them.
+        denom = LCM([denominator(omega.form) for omega in basis])
+        basis = [denom*omega.form for omega in basis]
+        self_with_no_denominator = denom*self.form
+        return linear_representation_polynomials(Rxy(self_with_no_denominator), [Rxy(omega) for omega in basis])
     
     def jth_component(self, j):
+        '''If self = sum_j h_j(x)/y^j dx, output is h_j(x).'''
         g = self.form
         C = self.curve
         F = C.base_ring
diff --git a/sage/superelliptic/superelliptic_function_class.sage b/sage/superelliptic/superelliptic_function_class.sage
index 50bfbde..80516cb 100644
--- a/sage/superelliptic/superelliptic_function_class.sage
+++ b/sage/superelliptic/superelliptic_function_class.sage
@@ -1,6 +1,6 @@
-#Class of rational functions on a superelliptic curve C. g = g(x, y) is a polynomial
-#defining the function.
 class superelliptic_function:
+    '''Class of rational functions on a superelliptic curve C. g = g(x, y) is a polynomial
+       defining the function.'''
     def __init__(self, C, g):
         F = C.base_ring
         Rxy.<x, y> = PolynomialRing(F, 2)
@@ -12,7 +12,12 @@ class superelliptic_function:
         self.curve = C
         g = reduction(C, g)
         self.function = g
-        
+    
+    def __eq__(self, other):
+        if self.function == other.function:
+            return True
+        return False
+    
     def __repr__(self):
         return str(self.function)
     
@@ -83,11 +88,11 @@ class superelliptic_function:
         B = g.derivative(y)*f.derivative(x)/(m*y^(m-1))
         return superelliptic_form(C, A+B)
 
-    def coordinates(self, basis = 0, basis_holo = 0, prec=20):
+    def coordinates(self, basis = 0, basis_holo = 0, prec=50):
         '''Find coordinates in H1(X, OX) in given basis basis with dual basis basis_holo.'''
         C = self.curve
         if basis == 0:
-            basis = basis_of_cohomology(C)
+            basis = C.basis_of_cohomology()
         if basis_holo == 0:
             basis_holo = C.holomorphic_differentials_basis()
         g = C.genus()
@@ -96,7 +101,7 @@ class superelliptic_function:
             coordinates[i] = omega.serre_duality_pairing(self, prec=prec)
         return coordinates
     
-    def expansion_at_infty(self, place = 0, prec=10):
+    def expansion_at_infty(self, place = 0, prec=20):
         C = self.curve
         f = C.polynomial
         m = C.exponent
@@ -125,3 +130,15 @@ class superelliptic_function:
         xx = Rt(1/(t^M*ww^b))
         yy = 1/(t^R*ww^a)
         return Rt(fct(x = Rt(xx), y = Rt(yy)))
+
+    def pth_root(self):
+        '''Compute p-th root of given function. This uses the following fact: if h = H^p, then C(h*dx/x) = H*dx/x.'''
+        C = self.curve
+        if self.diffn().form != 0:
+            raise ValueError("Function is not a p-th power.")
+        Fxy, Rxy, x, y = C.fct_field
+        auxilliary_form = superelliptic_form(C, self.function/x)
+        auxilliary_form = auxilliary_form.cartier()
+        auxilliary_form = C.x * auxilliary_form
+        auxilliary_form = auxilliary_form.form
+        return superelliptic_function(C, auxilliary_form)
\ No newline at end of file
diff --git a/sage/tests.sage b/sage/tests.sage
index b32bba4..8405b77 100644
--- a/sage/tests.sage
+++ b/sage/tests.sage
@@ -1,7 +1,16 @@
+load('init.sage')
+#print("superelliptic form coordinates test:")
+#load('superelliptic/tests/form_coordinates_test.sage')
+#print("p-th root test:")
+#load('superelliptic/tests/pth_root_test.sage')
+#print("not working! superelliptic p rank test:")
+#load('superelliptic/tests/p_rank_test.sage')
+print("a-number test:")
+load('superelliptic/tests/a_number_test.sage')
 #print("as_cover_test:")
 #load('as_covers/tests/as_cover_test.sage')
 #print("group_action_matrices_test:")
-load('as_covers/tests/group_action_matrices_test.sage')
+#load('as_covers/tests/group_action_matrices_test.sage')
 #print("dual_element_test:")
 #load('as_covers/tests/dual_element_test.sage')
 #print("ith_component_test:")
@@ -13,4 +22,6 @@ load('as_covers/tests/group_action_matrices_test.sage')
 #print("ramification jumps test:")
 #load('as_covers/tests/ramification_jumps_test.sage')
 #print("diffn_test:")
-#load('as_covers/tests/diffn_test.sage')
\ No newline at end of file
+#load('as_covers/tests/diffn_test.sage')
+#print("Cartier test:")
+#load('as_covers/tests/cartier_test.sage')
\ No newline at end of file