diff --git a/sage/.run.term-0.term b/sage/.run.term-0.term
index 2888d8e..2e31ef2 100644
--- a/sage/.run.term-0.term
+++ b/sage/.run.term-0.term
@@ -55419,4 +55419,1553 @@ aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cart
 [6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[6D[0;94msage: [0m

 

 

-[0m [3A[6C[?7h[0m[?12l[?25h[?25l[?7l[0mf[0;38;5;241mf.expansion_at_infty()[22D[?7h[0m[?12l[?25h[?25l[?7l[0mo[0;38;5;241mr i i[C lau.expo[Cents():[23D[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;28;1mfor[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[3D[0mfo[0m[K[?7h[0m[?12l[?25h
\ No newline at end of file
+[0m [3A[6C[?7h[0m[?12l[?25h[?25l[?7l[0mf[0;38;5;241mf.expansion_at_infty()[22D[?7h[0m[?12l[?25h[?25l[?7l[0mo[0;38;5;241mr i i[C lau.expo[Cents():[23D[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;28;1mfor[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[3D[0mfo[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mq[?7h[0m[?12l[?25h[?25l[?7l[0mu[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[12D[0m[J[0;94msage: [0mquit()[12D[0m

+[J[?7h[0m[?12l[?25h[?2004l[23;0t
+]0;~/Research/2021 De Rham/DeRhamComputation/sage[01;34m~/Research/2021 De Rham/DeRhamComputation/sage[00m$ cd ..
+]0;~/Research/2021 De Rham/DeRhamComputation[01;34m~/Research/2021 De Rham/DeRhamComputation[00m$ git add -u
+]0;~/Research/2021 De Rham/DeRhamComputation[01;34m~/Research/2021 De Rham/DeRhamComputation[00m$ git status
+On branch master
+Your branch is up to date with 'origin/master'.
+
+Changes to be committed:
+  (use "git restore --staged <file>..." to unstage)
+	[32mmodified:   sage/.run.term-0.term[m
+	[32mmodified:   sage/superelliptic/superelliptic_class.sage[m
+	[32mmodified:   sage/superelliptic_drw/superelliptic_drw_auxilliaries.sage[m
+	[32mmodified:   sage/superelliptic_drw/superelliptic_drw_cech.sage[m
+	[32mmodified:   sage/tests.sage[m
+
+Untracked files:
+  (use "git add <file>..." to include in what will be committed)
+	[31m.crystalline_p2.ipynb.sage-jupyter2[m
+	[31m.deRhamComputation.ipynb.sage-jupyter2[m
+	[31m.elementary_covers_of_superelliptic_curves.ipynb.sage-jupyter2[m
+	[31m.git.x11-0.term[m
+	[31m.superelliptic.ipynb.sage-jupyter2[m
+	[31m.superelliptic_alpha.ipynb.sage-jupyter2[m
+	[31m.superelliptic_arbitrary_field.ipynb.sage-jupyter2[m
+	[31mgit.x11[m
+	[31msage/auxilliaries/laurent_analytic_part.sage[m
+	[31msage/drafty/.2023-03-06-file-1.ipynb.sage-jupyter2[m
+	[31msage/drafty/2gpcovers.sage[m
+	[31msage/drafty/as_cartier.sage[m
+	[31msage/drafty/better_trace.sage[m
+	[31msage/drafty/cartier_image_representation.sage[m
+	[31msage/drafty/convert_superelliptic_into_AS.sage[m
+	[31msage/drafty/draft4.sage[m
+	[31msage/drafty/draft5.sage[m
+	[31msage/drafty/draft6.sage[m
+	[31msage/drafty/draft7.sage[m
+	[31msage/drafty/draft8.sage[m
+	[31msage/drafty/draft_klein_covers.sage[m
+	[31msage/drafty/lift_to_de_rham.sage[m
+	[31msage/drafty/pole_numbers.sage[m
+	[31msage/superelliptic/frobenius_kernel.sage[m
+	[31msage/superelliptic/tests/expansion_at_infty.sage[m
+	[31msage/superelliptic_drw/regular_form.sage[m
+	[31msage/superelliptic_drw/tests/auxilliary_decompositions_test.sage[m
+	[31msuperelliptic_arbitrary_field.ipynb[m
+
+]0;~/Research/2021 De Rham/DeRhamComputation[01;34m~/Research/2021 De Rham/DeRhamComputation[00m$ 
+]0;~/Research/2021 De Rham/DeRhamComputation[01;34m~/Research/2021 De Rham/DeRhamComputation[00m$ sage add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/superelliptic/tests/expansion_at_infty.sagesage/auxilliaries/laurent_analytic_part.sage[C[C sage/auxilliaries/laurent_analytic_part.sage
+^C
+]0;~/Research/2021 De Rham/DeRhamComputation[01;34m~/Research/2021 De Rham/DeRhamComputation[00m$ sage add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/superelliptic/tests/expansion_at_infty.sage sage/auxilliaries/laurent_analytic_part.sage[Agit status[K
+
[K[A[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[Csage add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/superelliptic/tests/expansion_at_infty.sage sage/auxilliaries/laurent_analytic_part.sage
[A[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C[C add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/su[1P[A
]0;~/Research/2021 De Rham/DeRhamComputation[01;34m~/Research/2021 De Rham/DeRhamComputation[00m$ [C[C[C add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/sup[1P[A
]0;~/Research/2021 De Rham/DeRhamComputation[01;34m~/Research/2021 De Rham/DeRhamComputation[00m$ [C[C add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/supe[1P[A
]0;~/Research/2021 De Rham/DeRhamComputation[01;34m~/Research/2021 De Rham/DeRhamComputation[00m$ [C add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/super[1P[A
]0;~/Research/2021 De Rham/DeRhamComputation[01;34m~/Research/2021 De Rham/DeRhamComputation[00m$ g add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/supe[1@r[A
]0;~/Research/2021 De Rham/DeRhamComputation[01;34m~/Research/2021 De Rham/DeRhamComputation[00m$ [Ci add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/sup[1@e[A
]0;~/Research/2021 De Rham/DeRhamComputation[01;34m~/Research/2021 De Rham/DeRhamComputation[00m$ [C[Ct add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/su[1@p[A
]0;~/Research/2021 De Rham/DeRhamComputation[01;34m~/Research/2021 De Rham/DeRhamComputation[00m$ [C[C[C
+

+]0;~/Research/2021 De Rham/DeRhamComputation[01;34m~/Research/2021 De Rham/DeRhamComputation[00m$ git commit -m ""d"z"i"a"l"a" "[1P"j"a" "w"s"p"o"l"r"z"e"d"n"e" "c"r"y"s"t"a"l"l"i"n"e" "c"o"h"o"m"o"l"o"g"y"!"!"!"!"[C
+git commit -m "dzialaja wspolrzedne crystalline cohomologygit add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/superelliptic/tests/expansion_at_infty.sage sage/auxilliaries/laurent_analytic_part.sagegit add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/superelliptic/tests/expansion_at_infty.sage sage/auxilliaries/laurent_analytic_part.sage"
+[master a9d055a] dzialaja wspolrzedne crystalline cohomologygit add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/superelliptic/tests/expansion_at_infty.sage sage/auxilliaries/laurent_analytic_part.sagegit add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/superelliptic/tests/expansion_at_infty.sage sage/auxilliaries/laurent_analytic_part.sage
+ 9 files changed, 1398 insertions(+), 27 deletions(-)
+ create mode 100644 sage/auxilliaries/laurent_analytic_part.sage
+ create mode 100644 sage/superelliptic/tests/expansion_at_infty.sage
+ create mode 100644 sage/superelliptic_drw/regular_form.sage
+ create mode 100644 sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage
+]0;~/Research/2021 De Rham/DeRhamComputation[01;34m~/Research/2021 De Rham/DeRhamComputation[00m$ git push
+Username for 'https://git.wmi.amu.edu.pl': jgarnek
+Password for 'https://jgarnek@git.wmi.amu.edu.pl': 
+Enumerating objects: 29, done.
+Counting objects:   3% (1/29)
Counting objects:   6% (2/29)
Counting objects:  10% (3/29)
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Counting objects:  96% (28/29)
Counting objects: 100% (29/29)
Counting objects: 100% (29/29), done.
+Delta compression using up to 4 threads
+Compressing objects:   5% (1/17)
Compressing objects:  11% (2/17)
Compressing objects:  17% (3/17)
Compressing objects:  23% (4/17)
Compressing objects:  29% (5/17)
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Compressing objects:  82% (14/17)
Compressing objects:  88% (15/17)
Compressing objects:  94% (16/17)
Compressing objects: 100% (17/17)
Compressing objects: 100% (17/17), done.
+Writing objects:   5% (1/17)
Writing objects:  11% (2/17)
Writing objects:  17% (3/17)
Writing objects:  23% (4/17)
Writing objects:  29% (5/17)
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Writing objects:  88% (15/17)
Writing objects:  94% (16/17)
Writing objects: 100% (17/17)
Writing objects: 100% (17/17), 11.83 KiB | 84.00 KiB/s, done.
+Total 17 (delta 11), reused 0 (delta 0)
+remote: . Processing 1 references[K
+remote: Processed 1 references in total[K
+To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git
+   995d5f0..a9d055a  master -> master
+]0;~/Research/2021 De Rham/DeRhamComputation[01;34m~/Research/2021 De Rham/DeRhamComputation[00m$ sa[K[Kcd sage/
+]0;~/Research/2021 De Rham/DeRhamComputation/sage[01;34m~/Research/2021 De Rham/DeRhamComputation/sage[00m$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+[22;0t]0;IPython: DeRhamComputation/sage[6n[?2004h[?1l[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mM[?7h[0m[?12l[?25h[?25l[?7l[7D[0m[J[0;94msage: [0mM[7D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m[4 6]
+[1 4]
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mM[?7h[0m[?12l[?25h[?25l[?7l[0m^[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m3[?7h[0m[?12l[?25h[?25l[?7l[9D[0m[J[0;94msage: [0mM^[0;38;5;20;1m3[9D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m[1 0]
+[0 1]
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m.genus()[8D[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;241m= s[Cperelliptic((x^3 - x)^3 + x^3 - x, 2)[41D[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mad[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mIndexError[0m                                Traceback (most recent call last)
+Input [0;32mIn [4][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mload[49m[43m([49m[38;5;124;43m'[39;49m[38;5;124;43minit.sage[39;49m[38;5;124;43m'[39;49m[43m)[49m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
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+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
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+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
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+File [0;32m<string>:32[0m, in [0;36m<module>[0;34m[0m
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+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:19[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m<string>:10[0m, in [0;36mcrystalline_matrix[0;34m(C)[0m
+
+File [0;32m<string>:39[0m, in [0;36mcrystalline_cohomology_basis[0;34m(self, prec)[0m
+
+File [0;32m<string>:29[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class, prec)[0m
+
+File [0;32m<string>:7[0m, in [0;36mdecomposition_g0_g8[0;34m(fct, prec)[0m
+
+File [0;32m<string>:107[0m, in [0;36mcoordinates[0;34m(self, basis, basis_holo, prec)[0m
+
+File [0;32m<string>:79[0m, in [0;36mserre_duality_pairing[0;34m(self, fct, prec)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544[0m, in [0;36msage.rings.laurent_series_ring_element.LaurentSeries.__getitem__[0;34m()[0m
+[1;32m    542[0m         return type(self)(self._parent, f, self.__n)
+[1;32m    543[0m 
+[0;32m--> 544[0m     return self.__u[i - self.__n]
+[1;32m    545[0m 
+[1;32m    546[0m def __iter__(self):
+
+File [0;32m/ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453[0m, in [0;36msage.rings.power_series_poly.PowerSeries_poly.__getitem__[0;34m()[0m
+[1;32m    451[0m         return self.base_ring().zero()
+[1;32m    452[0m     else:
+[0;32m--> 453[0m         raise IndexError("coefficient not known")
+[1;32m    454[0m return self.__f[n]
+[1;32m    455[0m 
+
+[0;31mIndexError[0m: coefficient not known
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mB[0;38;5;241m = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)[79D[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mIndexError[0m                                Traceback (most recent call last)
+Input [0;32mIn [5][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mload[49m[43m([49m[38;5;124;43m'[39;49m[38;5;124;43minit.sage[39;49m[38;5;124;43m'[39;49m[43m)[49m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:32[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:19[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m<string>:10[0m, in [0;36mcrystalline_matrix[0;34m(C)[0m
+
+File [0;32m<string>:39[0m, in [0;36mcrystalline_cohomology_basis[0;34m(self, prec)[0m
+
+File [0;32m<string>:29[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class, prec)[0m
+
+File [0;32m<string>:7[0m, in [0;36mdecomposition_g0_g8[0;34m(fct, prec)[0m
+
+File [0;32m<string>:107[0m, in [0;36mcoordinates[0;34m(self, basis, basis_holo, prec)[0m
+
+File [0;32m<string>:79[0m, in [0;36mserre_duality_pairing[0;34m(self, fct, prec)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544[0m, in [0;36msage.rings.laurent_series_ring_element.LaurentSeries.__getitem__[0;34m()[0m
+[1;32m    542[0m         return type(self)(self._parent, f, self.__n)
+[1;32m    543[0m 
+[0;32m--> 544[0m     return self.__u[i - self.__n]
+[1;32m    545[0m 
+[1;32m    546[0m def __iter__(self):
+
+File [0;32m/ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453[0m, in [0;36msage.rings.power_series_poly.PowerSeries_poly.__getitem__[0;34m()[0m
+[1;32m    451[0m         return self.base_ring().zero()
+[1;32m    452[0m     else:
+[0;32m--> 453[0m         raise IndexError("coefficient not known")
+[1;32m    454[0m return self.__f[n]
+[1;32m    455[0m 
+
+[0;31mIndexError[0m: coefficient not known
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mB[0;38;5;241m = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)[79D[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mad[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mTypeError[0m                                 Traceback (most recent call last)
+Input [0;32mIn [6][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mload[49m[43m([49m[38;5;124;43m'[39;49m[38;5;124;43minit.sage[39;49m[38;5;124;43m'[39;49m[43m)[49m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:32[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:19[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m<string>:16[0m, in [0;36mcrystalline_matrix[0;34m(C, prec)[0m
+
+[0;31mTypeError[0m: superelliptic_drw_cech.coordinates() got an unexpected keyword argument 'prec'
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m.genus()[8D[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mad[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004l[1 0 0 0 0 0 6 0]
+[1 1 0 3 0 6 6 0]
+[1 2 1 6 6 3 6 6]
+[4 3 3 1 0 0 3 0]
+[4 1 3 2 1 8 1 2]
+[8 3 3 4 0 1 7 3]
+[3 6 3 3 0 0 1 6]
+[4 1 6 7 0 3 3 1]
+[1 0 0 0 0 0 0 0]
+[0 1 0 0 0 0 0 0]
+[0 0 1 0 0 0 0 0]
+[0 0 0 1 0 0 0 0]
+[0 0 0 0 1 0 0 0]
+[0 0 0 0 0 1 0 0]
+[0 0 0 0 0 0 1 0]
+[0 0 0 0 0 0 0 1]
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage[01;34m~/Research/2021 De Rham/DeRhamComputation/sage[00m$ 
[K]0;~/Research/2021 De Rham/DeRhamComputation/sage[01;34m~/Research/2021 De Rham/DeRhamComputation/sage[00m$ 
[K]0;~/Research/2021 De Rham/DeRhamComputation/sage[01;34m~/Research/2021 De Rham/DeRhamComputation/sage[00m$ loa[K[K[Ksage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+[22;0t]0;IPython: DeRhamComputation/sage[6n[?2004h[?1l[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mad[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004l^C[0;31m---------------------------------------------------------------------------[0m
+[0;31mKeyboardInterrupt[0m                         Traceback (most recent call last)
+File [0;32m<string>:59[0m, in [0;36m__mul__[0;34m(self, other)[0m
+
+File [0;32m<string>:235[0m, in [0;36mreduction[0;34m(C, g)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/arith/misc.py:1971[0m, in [0;36mxgcd[0;34m(a, b)[0m
+[1;32m   1970[0m [38;5;28;01mtry[39;00m:
+[0;32m-> 1971[0m     [38;5;28;01mreturn[39;00m [43ma[49m[38;5;241;43m.[39;49m[43mxgcd[49m[43m([49m[43mb[49m[43m)[49m
+[1;32m   1972[0m [38;5;28;01mexcept[39;00m [38;5;167;01mAttributeError[39;00m:
+
+File [0;32msrc/cysignals/signals.pyx:310[0m, in [0;36mcysignals.signals.python_check_interrupt[0;34m()[0m
+
+[0;31mKeyboardInterrupt[0m: 
+
+During handling of the above exception, another exception occurred:
+
+[0;31mAttributeError[0m                            Traceback (most recent call last)
+Input [0;32mIn [1][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mload[49m[43m([49m[38;5;124;43m'[39;49m[38;5;124;43minit.sage[39;49m[38;5;124;43m'[39;49m[43m)[49m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:32[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:19[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m<string>:10[0m, in [0;36mcrystalline_matrix[0;34m(C, prec)[0m
+
+File [0;32m<string>:39[0m, in [0;36mcrystalline_cohomology_basis[0;34m(self, prec)[0m
+
+File [0;32m<string>:26[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class, prec)[0m
+
+File [0;32m<string>:73[0m, in [0;36mdiffn[0;34m(self, dy_w)[0m
+
+File [0;32m<string>:177[0m, in [0;36mdy_w[0;34m(C)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/rings/rational.pyx:2414[0m, in [0;36msage.rings.rational.Rational.__mul__[0;34m()[0m
+[1;32m   2412[0m         return x
+[1;32m   2413[0m 
+[0;32m-> 2414[0m     return coercion_model.bin_op(left, right, operator.mul)
+[1;32m   2415[0m 
+[1;32m   2416[0m cpdef _mul_(self, right):
+
+File [0;32m/ext/sage/9.7/src/sage/structure/coerce.pyx:1242[0m, in [0;36msage.structure.coerce.CoercionModel.bin_op[0;34m()[0m
+[1;32m   1240[0m mul_method = getattr(y, '__r%s__'%op_name, None)
+[1;32m   1241[0m if mul_method is not None:
+[0;32m-> 1242[0m     res = mul_method(x)
+[1;32m   1243[0m     if res is not None and res is not NotImplemented:
+[1;32m   1244[0m         return res
+
+File [0;32m<string>:48[0m, in [0;36m__rmul__[0;34m(self, other)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/structure/element.pyx:1528[0m, in [0;36msage.structure.element.Element.__mul__[0;34m()[0m
+[1;32m   1526[0m     if not err:
+[1;32m   1527[0m         return (<Element>right)._mul_long(value)
+[0;32m-> 1528[0m     return coercion_model.bin_op(left, right, mul)
+[1;32m   1529[0m except TypeError:
+[1;32m   1530[0m     return NotImplemented
+
+File [0;32m/ext/sage/9.7/src/sage/structure/coerce.pyx:1242[0m, in [0;36msage.structure.coerce.CoercionModel.bin_op[0;34m()[0m
+[1;32m   1240[0m mul_method = getattr(y, '__r%s__'%op_name, None)
+[1;32m   1241[0m if mul_method is not None:
+[0;32m-> 1242[0m     res = mul_method(x)
+[1;32m   1243[0m     if res is not None and res is not NotImplemented:
+[1;32m   1244[0m         return res
+
+File [0;32m<string>:43[0m, in [0;36m__rmul__[0;34m(self, other)[0m
+
+File [0;32m<string>:31[0m, in [0;36m__add__[0;34m(self, other)[0m
+
+File [0;32m<string>:63[0m, in [0;36m__mul__[0;34m(self, other)[0m
+
+[0;31mAttributeError[0m: 'superelliptic_function' object has no attribute 'form'
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mad[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m.genus()[8D[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mc[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mB[0;38;5;241m = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)[79D[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0mC.crystalline_cohomology_basis(prec = [0;38;5;20;1m100[0m); autom(B[[0;38;5;20;1m4[0m]).coordinates[0;38;5;16;48;5;152m([0mbasis=B[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[9D[0m([7C[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[7D[0;38;5;16;48;5;152m([4C)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[6D[0m([C[0;38;5;16;48;5;152m[[C][0m[K[?7h[0m[?12l[?25h[?25l[?7l[3D[0m[[C[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[13D[0;38;5;16;48;5;152m([10C)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[12D[0m([10C[0m[K[?7h[0m[?12l[?25h[?25l[?7l[11D[0;38;5;16;48;5;152m([10C)[0;38;5;241m; autom(B[4]).coordinates(basis=B)[34D[?7h[0m[?12l[?25h[?25l[?7l[52D[0m[J[0;94msage: [0mB = C.crystalline_cohomology_basis(prec = [0;38;5;20;1m100[0m)[52D[0m

+[J[?7h[0m[?12l[?25h[?2004l^C[0;31m---------------------------------------------------------------------------[0m
+[0;31mKeyboardInterrupt[0m                         Traceback (most recent call last)
+Input [0;32mIn [3][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m B [38;5;241m=[39m [43mC[49m[38;5;241;43m.[39;49m[43mcrystalline_cohomology_basis[49m[43m([49m[43mprec[49m[43m [49m[38;5;241;43m=[39;49m[43m [49m[43mInteger[49m[43m([49m[38;5;241;43m100[39;49m[43m)[49m[43m)[49m
+
+File [0;32m<string>:39[0m, in [0;36mcrystalline_cohomology_basis[0;34m(self, prec)[0m
+
+File [0;32m<string>:24[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class, prec)[0m
+
+File [0;32m<string>:6[0m, in [0;36mde_rham_witt_lift_form0[0;34m(omega)[0m
+
+File [0;32m<string>:73[0m, in [0;36mdiffn[0;34m(self, dy_w)[0m
+
+File [0;32m<string>:177[0m, in [0;36mdy_w[0;34m(C)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/rings/rational.pyx:2414[0m, in [0;36msage.rings.rational.Rational.__mul__[0;34m()[0m
+[1;32m   2412[0m         return x
+[1;32m   2413[0m 
+[0;32m-> 2414[0m     return coercion_model.bin_op(left, right, operator.mul)
+[1;32m   2415[0m 
+[1;32m   2416[0m cpdef _mul_(self, right):
+
+File [0;32m/ext/sage/9.7/src/sage/structure/coerce.pyx:1242[0m, in [0;36msage.structure.coerce.CoercionModel.bin_op[0;34m()[0m
+[1;32m   1240[0m mul_method = getattr(y, '__r%s__'%op_name, None)
+[1;32m   1241[0m if mul_method is not None:
+[0;32m-> 1242[0m     res = mul_method(x)
+[1;32m   1243[0m     if res is not None and res is not NotImplemented:
+[1;32m   1244[0m         return res
+
+File [0;32m<string>:48[0m, in [0;36m__rmul__[0;34m(self, other)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/structure/element.pyx:1528[0m, in [0;36msage.structure.element.Element.__mul__[0;34m()[0m
+[1;32m   1526[0m     if not err:
+[1;32m   1527[0m         return (<Element>right)._mul_long(value)
+[0;32m-> 1528[0m     return coercion_model.bin_op(left, right, mul)
+[1;32m   1529[0m except TypeError:
+[1;32m   1530[0m     return NotImplemented
+
+File [0;32m/ext/sage/9.7/src/sage/structure/coerce.pyx:1242[0m, in [0;36msage.structure.coerce.CoercionModel.bin_op[0;34m()[0m
+[1;32m   1240[0m mul_method = getattr(y, '__r%s__'%op_name, None)
+[1;32m   1241[0m if mul_method is not None:
+[0;32m-> 1242[0m     res = mul_method(x)
+[1;32m   1243[0m     if res is not None and res is not NotImplemented:
+[1;32m   1244[0m         return res
+
+File [0;32m<string>:43[0m, in [0;36m__rmul__[0;34m(self, other)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/structure/element.pyx:1528[0m, in [0;36msage.structure.element.Element.__mul__[0;34m()[0m
+[1;32m   1526[0m     if not err:
+[1;32m   1527[0m         return (<Element>right)._mul_long(value)
+[0;32m-> 1528[0m     return coercion_model.bin_op(left, right, mul)
+[1;32m   1529[0m except TypeError:
+[1;32m   1530[0m     return NotImplemented
+
+File [0;32m/ext/sage/9.7/src/sage/structure/coerce.pyx:1242[0m, in [0;36msage.structure.coerce.CoercionModel.bin_op[0;34m()[0m
+[1;32m   1240[0m mul_method = getattr(y, '__r%s__'%op_name, None)
+[1;32m   1241[0m if mul_method is not None:
+[0;32m-> 1242[0m     res = mul_method(x)
+[1;32m   1243[0m     if res is not None and res is not NotImplemented:
+[1;32m   1244[0m         return res
+
+File [0;32m<string>:43[0m, in [0;36m__rmul__[0;34m(self, other)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/structure/element.pyx:1528[0m, in [0;36msage.structure.element.Element.__mul__[0;34m()[0m
+[1;32m   1526[0m     if not err:
+[1;32m   1527[0m         return (<Element>right)._mul_long(value)
+[0;32m-> 1528[0m     return coercion_model.bin_op(left, right, mul)
+[1;32m   1529[0m except TypeError:
+[1;32m   1530[0m     return NotImplemented
+
+File [0;32m/ext/sage/9.7/src/sage/structure/coerce.pyx:1242[0m, in [0;36msage.structure.coerce.CoercionModel.bin_op[0;34m()[0m
+[1;32m   1240[0m mul_method = getattr(y, '__r%s__'%op_name, None)
+[1;32m   1241[0m if mul_method is not None:
+[0;32m-> 1242[0m     res = mul_method(x)
+[1;32m   1243[0m     if res is not None and res is not NotImplemented:
+[1;32m   1244[0m         return res
+
+File [0;32m<string>:43[0m, in [0;36m__rmul__[0;34m(self, other)[0m
+
+File [0;32m<string>:31[0m, in [0;36m__add__[0;34m(self, other)[0m
+
+File [0;32m<string>:82[0m, in [0;36m__pow__[0;34m(self, exp)[0m
+
+File [0;32m<string>:14[0m, in [0;36m__init__[0;34m(self, C, g)[0m
+
+File [0;32m<string>:228[0m, in [0;36mreduction[0;34m(C, g)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/structure/parent.pyx:897[0m, in [0;36msage.structure.parent.Parent.__call__[0;34m()[0m
+[1;32m    895[0m if mor is not None:
+[1;32m    896[0m     if no_extra_args:
+[0;32m--> 897[0m         return mor._call_(x)
+[1;32m    898[0m     else:
+[1;32m    899[0m         return mor._call_with_args(x, args, kwds)
+
+File [0;32m/ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156[0m, in [0;36msage.structure.coerce_maps.DefaultConvertMap_unique._call_[0;34m()[0m
+[1;32m    154[0m cdef Parent C = self._codomain
+[1;32m    155[0m try:
+[0;32m--> 156[0m     return C._element_constructor(x)
+[1;32m    157[0m except Exception:
+[1;32m    158[0m     if print_warnings:
+
+File [0;32m/ext/sage/9.7/src/sage/rings/fraction_field.py:638[0m, in [0;36mFractionField_generic._element_constructor_[0;34m(self, x, y, coerce)[0m
+[1;32m    636[0m ring_one [38;5;241m=[39m [38;5;28mself[39m[38;5;241m.[39mring()[38;5;241m.[39mone()
+[1;32m    637[0m [38;5;28;01mtry[39;00m:
+[0;32m--> 638[0m     [38;5;28;01mreturn[39;00m [38;5;28;43mself[39;49m[38;5;241;43m.[39;49m[43m_element_class[49m[43m([49m[38;5;28;43mself[39;49m[43m,[49m[43m [49m[43mx[49m[43m,[49m[43m [49m[43mring_one[49m[43m,[49m[43m [49m[43mcoerce[49m[38;5;241;43m=[39;49m[43mcoerce[49m[43m)[49m
+[1;32m    639[0m [38;5;28;01mexcept[39;00m ([38;5;167;01mTypeError[39;00m, [38;5;167;01mValueError[39;00m):
+[1;32m    640[0m     [38;5;28;01mpass[39;00m
+
+File [0;32m/ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114[0m, in [0;36msage.rings.fraction_field_element.FractionFieldElement.__init__[0;34m()[0m
+[1;32m    112[0m FieldElement.__init__(self, parent)
+[1;32m    113[0m if coerce:
+[0;32m--> 114[0m     self.__numerator   = parent.ring()(numerator)
+[1;32m    115[0m     self.__denominator = parent.ring()(denominator)
+[1;32m    116[0m else:
+
+File [0;32m/ext/sage/9.7/src/sage/structure/parent.pyx:897[0m, in [0;36msage.structure.parent.Parent.__call__[0;34m()[0m
+[1;32m    895[0m if mor is not None:
+[1;32m    896[0m     if no_extra_args:
+[0;32m--> 897[0m         return mor._call_(x)
+[1;32m    898[0m     else:
+[1;32m    899[0m         return mor._call_with_args(x, args, kwds)
+
+File [0;32m/ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156[0m, in [0;36msage.structure.coerce_maps.DefaultConvertMap_unique._call_[0;34m()[0m
+[1;32m    154[0m cdef Parent C = self._codomain
+[1;32m    155[0m try:
+[0;32m--> 156[0m     return C._element_constructor(x)
+[1;32m    157[0m except Exception:
+[1;32m    158[0m     if print_warnings:
+
+File [0;32m/ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003[0m, in [0;36msage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_[0;34m()[0m
+[1;32m   1001[0m 
+[1;32m   1002[0m         try:
+[0;32m-> 1003[0m             return self(str(element))
+[1;32m   1004[0m         except TypeError:
+[1;32m   1005[0m             pass
+
+File [0;32m/ext/sage/9.7/src/sage/structure/sage_object.pyx:194[0m, in [0;36msage.structure.sage_object.SageObject.__repr__[0;34m()[0m
+[1;32m    192[0m except AttributeError:
+[1;32m    193[0m     return super().__repr__()
+[0;32m--> 194[0m result = reprfunc()
+[1;32m    195[0m if isinstance(result, str):
+[1;32m    196[0m     return result
+
+File [0;32m/ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690[0m, in [0;36msage.rings.polynomial.polynomial_element.Polynomial._repr_[0;34m()[0m
+[1;32m   2688[0m         NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3
+[1;32m   2689[0m     """
+[0;32m-> 2690[0m     return self._repr()
+[1;32m   2691[0m 
+[1;32m   2692[0m def _latex_(self, name=None):
+
+File [0;32m/ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2656[0m, in [0;36msage.rings.polynomial.polynomial_element.Polynomial._repr[0;34m()[0m
+[1;32m   2654[0m if n != m-1:
+[1;32m   2655[0m     s += " + "
+[0;32m-> 2656[0m x = y = repr(x)
+[1;32m   2657[0m if y.find("-") == 0:
+[1;32m   2658[0m     y = y[1:]
+
+File [0;32m/ext/sage/9.7/src/sage/structure/sage_object.pyx:194[0m, in [0;36msage.structure.sage_object.SageObject.__repr__[0;34m()[0m
+[1;32m    192[0m except AttributeError:
+[1;32m    193[0m     return super().__repr__()
+[0;32m--> 194[0m result = reprfunc()
+[1;32m    195[0m if isinstance(result, str):
+[1;32m    196[0m     return result
+
+File [0;32m/ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:340[0m, in [0;36msage.rings.fraction_field_FpT.FpTElement._repr_[0;34m()[0m
+[1;32m    338[0m     return repr(self.numer())
+[1;32m    339[0m else:
+[0;32m--> 340[0m     numer_s = repr(self.numer())
+[1;32m    341[0m     denom_s = repr(self.denom())
+[1;32m    342[0m     if '-' in numer_s or '+' in numer_s:
+
+File [0;32m/ext/sage/9.7/src/sage/structure/sage_object.pyx:194[0m, in [0;36msage.structure.sage_object.SageObject.__repr__[0;34m()[0m
+[1;32m    192[0m except AttributeError:
+[1;32m    193[0m     return super().__repr__()
+[0;32m--> 194[0m result = reprfunc()
+[1;32m    195[0m if isinstance(result, str):
+[1;32m    196[0m     return result
+
+File [0;32m/ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690[0m, in [0;36msage.rings.polynomial.polynomial_element.Polynomial._repr_[0;34m()[0m
+[1;32m   2688[0m         NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3
+[1;32m   2689[0m     """
+[0;32m-> 2690[0m     return self._repr()
+[1;32m   2691[0m 
+[1;32m   2692[0m def _latex_(self, name=None):
+
+File [0;32m/ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2656[0m, in [0;36msage.rings.polynomial.polynomial_element.Polynomial._repr[0;34m()[0m
+[1;32m   2654[0m if n != m-1:
+[1;32m   2655[0m     s += " + "
+[0;32m-> 2656[0m x = y = repr(x)
+[1;32m   2657[0m if y.find("-") == 0:
+[1;32m   2658[0m     y = y[1:]
+
+File [0;32msrc/cysignals/signals.pyx:310[0m, in [0;36mcysignals.signals.python_check_interrupt[0;34m()[0m
+
+[0;31mKeyboardInterrupt[0m: 
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m.genus()[8D[?7h[0m[?12l[?25h[?25l[?7l[7D[0m[J[0;94msage: [0mC[7D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;241mgenus()[7D[?7h[0m[?12l[?25h[?25l[?7l[0mc[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0my[?7h[0m[?12l[?25h[?25l[?7l[0ms[?7h[0m[?12l[?25h[?25l[?7l[0mtalline_cohomology_basis[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0mp[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m1[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[?7h[0m[?12l[?25h[?25l[?7l[11D[0;38;5;16;48;5;152m([10C)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[11D[0m([10C)[4D[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[5D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([10C[0;38;5;16;48;5;152m)[12D[?7h[0m[?12l[?25h[?25l[?7l[0m([10C)[40D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mBC.crysta[Cline_cohomology_basis(prec = [0;38;5;20;1m1[C0[0m)[42D[?7h[0m[?12l[?25h[?25l[?7l[0m C.crysta[Cline_cohomology_basis(prec = [0;38;5;20;1m1[C0[0m)[42D[?7h[0m[?12l[?25h[?25l[?7l[0m=C.crysta[Cline_cohomology_basis(prec = [0;38;5;20;1m1[C0[0m)[42D[?7h[0m[?12l[?25h[?25l[?7l[0m C.crysta[Cline_cohomology_basis(prec = [0;38;5;20;1m1[C0[0m)[42D[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[28C[0;38;5;210;48;5;88m([10C[0;38;5;16;48;5;152m)[12D[?7h[0m[?12l[?25h[?25l[?7l[0m([10C)[7D[?7h[0m[?12l[?25h[?25l[?7l[5D[0;38;5;16;48;5;152m([10C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[52D[0m[J[0;94msage: [0mB = C.crystalline_cohomology_basis(prec = [0;38;5;20;1m100[0m)[52D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mB[0;38;5;241m = C.crystalline_cohomology_basis(prec = 100)[45D[?7h[0m[?12l[?25h[?25l[?7l[7D[0m[J[0;94msage: [0mB[7D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m[([(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), V(((x^2 + 1)/x)*y), [(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y])),
+ ([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))]
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mB[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[[0;38;5;241m1].omega8 + u.teichmuller()*v.teichmuller().diffn()[51D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m[][0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;16;48;5;152m[[C][?7h[0m[?12l[?25h[?25l[?7l[3D[0m[[C].[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0mg[?7h[0m[?12l[?25h[?25l[?7l[0mu[?7h[0m[?12l[?25h[?25l[?7l[0ml[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0m_[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0mm[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[25D[0m[J[0;94msage: [0mB[[0;38;5;20;1m0[0m].reguler_form()[25D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mAttributeError[0m                            Traceback (most recent call last)
+Input [0;32mIn [7][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mB[49m[43m[[49m[43mInteger[49m[43m([49m[38;5;241;43m0[39;49m[43m)[49m[43m][49m[38;5;241;43m.[39;49m[43mreguler_form[49m()
+
+[0;31mAttributeError[0m: 'superelliptic_drw_cech' object has no attribute 'reguler_form'
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mB[[0;38;5;20;1m0[0m].reguler_form[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([0;38;5;16;48;5;152m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0m()[3D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mr_form()[0m[K[8D[?7h[0m[?12l[?25h[?25l[?7l[0mar_form()[8D[?7h[0m[?12l[?25h[?25l[?7l[6C[0;38;5;210;48;5;88m([0;38;5;16;48;5;152m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m([C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[25D[0m[J[0;94msage: [0mB[[0;38;5;20;1m0[0m].regular_form()[25D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mAttributeError[0m                            Traceback (most recent call last)
+Input [0;32mIn [8][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mB[49m[43m[[49m[43mInteger[49m[43m([49m[38;5;241;43m0[39;49m[43m)[49m[43m][49m[38;5;241;43m.[39;49m[43mregular_form[49m()
+
+[0;31mAttributeError[0m: 'superelliptic_drw_cech' object has no attribute 'regular_form'
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mB[0;38;5;241m[0].regular_form()[18D[?7h[0m[?12l[?25h[?25l[?7l[0m[[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mB[0;38;5;241m[0].regular_form()[18D[?7h[0m[?12l[?25h[?25l[?7l[0m0[0m[K[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mB[?7h[0m[?12l[?25h[?25l[?7l[0m[[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;16;48;5;152m[[C][?7h[0m[?12l[?25h[?25l[?7l[15D[0m[J[0;94msage: [0mB0 = B[[0;38;5;20;1m0[0m][15D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mB[0;38;5;241m0 = B[0][8D[?7h[0m[?12l[?25h[?25l[?7l[0m0[?7h[0m[?12l[?25h[?25l[?7l[0m.[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0mg[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[9D[0;94msage: [0mB0.[0m

+[9C[0;38;5;16;48;5;250m B0.coordinates B0.f           B0.omega8     [0m

+[9C[0;38;5;16;48;5;250m B0.curve       B0.is_regular  B0.r          [0m

+[9C[0;38;5;16;48;5;250m B0.div_by_p    B0.omega0      B0.reduce     [0m

+

+[0m [5A[9C[?7h[0m[?12l[?25h[?25l[?7l[0m[K[0m

+[C[0m[K[0m

+[C[0m[K[0m

+[C[0m[K[3A[7C[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mm[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0mg[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0m0[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0mg[?7h[0m[?12l[?25h[?25l[?7l[0mu[?7h[0m[?12l[?25h[?25l[?7l[0ml[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0m_[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0mm[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[30D[0m[J[0;94msage: [0mB0.omega0.regular_form()[30D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m[0] d[x] + [1] d[y] + V(((x^5 + x^3)/y) dx) + dV(0)
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[6D[0;94msage: [0m

+

+

+[0m [3A[6C[?7h[0m[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage[01;34m~/Research/2021 De Rham/DeRhamComputation/sage[00m$ 
[K]0;~/Research/2021 De Rham/DeRhamComputation/sage[01;34m~/Research/2021 De Rham/DeRhamComputation/sage[00m$ 
[K]0;~/Research/2021 De Rham/DeRhamComputation/sage[01;34m~/Research/2021 De Rham/DeRhamComputation/sage[00m$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+[22;0t]0;IPython: DeRhamComputation/sage[6n[?2004h[?1l[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[6D[0;94msage: [0m

+

+

+

+[0m [4A[6C[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[6D[0;94msage: [0m

+

+

+[0m [3A[6C[?7h[0m[?12l[?25h[?25l[?7l[0mC[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;241m= superelliptic((x^3 - x)^3 + x^3 - x, 2)[41D[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[7D[0m[J[0;94msage: [0mC[7D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[6D[0;94msage: [0m

+[0m [A[6C[?7h[0m[?12l[?25h[?25l[?7l[0mC[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;241mgenus()[7D[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mB[0;38;5;241m0.omega0.regular_form()[23D[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;241m= C.crystalline[Cc[Chomology_basis(prec = 100)[44D[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0mC.crystalline_cohomology_basis[0;38;5;16;48;5;152m([0mprec = [0;38;5;20;1m100[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0m,[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0mi[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;28min[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[2D[0minf[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0mo[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0m=[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m1[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[62D[0m[J[0;94msage: [0mB = C.crystalline_cohomology_basis(prec = [0;38;5;20;1m100[0m, info = [0;38;5;20;1m1[0m)[62D[0m

+[J[?7h[0m[?12l[?25h[?2004lComputing 0. basis element
+Computing 1. basis element
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mB[0;38;5;241m = C.crystalline_cohomology_basis(prec = 100, info = 1)[55D[?7h[0m[?12l[?25h[?25l[?7l[7D[0m[J[0;94msage: [0mB[7D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m[([(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), V(((x^2 + 1)/x)*y), [(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y])),
+ ([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))]
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mB[?7h[0m[?12l[?25h[?25l[?7l[0m[[0;38;5;241m0].regular_form()[17D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m[][0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m][0;38;5;241m.regular_form()[15D[?7h[0m[?12l[?25h[?25l[?7l[3D[0m[[C].regular_form[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[2D[0m().[?7h[0m[?12l[?25h[?25l[?7l[3D[0;38;5;16;48;5;152m()[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m([0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mm[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0mg[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0m0[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0mg[?7h[0m[?12l[?25h[?25l[?7l[0mu[?7h[0m[?12l[?25h[?25l[?7l[0ml[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0m_[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0mm[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[32D[0m[J[0;94msage: [0mB[[0;38;5;20;1m0[0m].omega0.regular_form()[32D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mAttributeError[0m                            Traceback (most recent call last)
+Input [0;32mIn [5][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mB[49m[43m[[49m[43mInteger[49m[43m([49m[38;5;241;43m0[39;49m[43m)[49m[43m][49m[38;5;241;43m.[39;49m[43momega0[49m[38;5;241;43m.[39;49m[43mregular_form[49m[43m([49m[43m)[49m
+
+File [0;32m<string>:81[0m, in [0;36mregular_drw_form[0;34m(omega)[0m
+
+[0;31mAttributeError[0m: 'superelliptic_drw_form' object has no attribute 'omega0'
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mB[[0;38;5;20;1m0[0m].omega0.regular_form[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([0;38;5;16;48;5;152m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0m()[3D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[13C[0;38;5;210;48;5;88m([0;38;5;16;48;5;152m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m([C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[0m([0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m[[C][0m[K[?7h[0m[?12l[?25h[?25l[?7l[3D[0m[[C[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;241m= superelliptic((x^3 - x)^3 + x^3 - x, 2)[41D[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0msuperelliptic[0;38;5;16;48;5;152m([0m(x^[0;38;5;20;1m3[0m - x)^[0;38;5;20;1m3[0m + x^[0;38;5;20;1m3[0m - x, [0;38;5;20;1m2[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[26D[0m([24C[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[10D[0;38;5;16;48;5;152m([7C)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[9D[0m([7C[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[6D[0;38;5;24msuper[0m[K[?7h[0m[?12l[?25h[?25l[?7l[5D[0msupe[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mB[0;38;5;241m[0].omega0.regular_form()[25D[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;241m= C.crystalline_coh[Cmology_basis(prec = 100, info = 1)[54D[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0mC.crystalline_cohomology_basis[0;38;5;16;48;5;152m([0mprec = [0;38;5;20;1m100[0m, info = [0;38;5;20;1m1[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[62D[0m[J[0;94msage: [0mB = C.crystalline_cohomology_basis(prec = [0;38;5;20;1m100[0m, info = [0;38;5;20;1m1[0m)[62D[0m

+[J[?7h[0m[?12l[?25h[?2004lComputing 0. basis element
+Computing 1. basis element
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mB[0;38;5;241m = C.crystalline_cohomology_basis(prec = 100, info = 1)[55D[?7h[0m[?12l[?25h[?25l[?7l[0m[[0;38;5;241m0].omega0.regular_f[Crm()[0m[K[24D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[0m].omega0.regular_form[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[32D[0m[J[0;94msage: [0mB[[0;38;5;20;1m0[0m].omega0.regular_form()[32D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m[0] d[x] + [1] d[y] + V((x^21 + 2*x^19 + 2*x^15 + x^13) dy) + dV((2*x^15 + x^13 + 2*x^9 + x^7)*y)
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mB[[0;38;5;20;1m0[0m].omega0.regular_form[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([0;38;5;16;48;5;152m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0m()[3D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[6D[0;38;5;16;48;5;152m[[C][?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[2D[0m[[C][2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m[[C[0;38;5;16;48;5;152m][3D[?7h[0m[?12l[?25h[?25l[?7l[0m[[C][4D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[C[0;38;5;210;48;5;88m[[C[0;38;5;16;48;5;152m][3D[?7h[0m[?12l[?25h[?25l[?7l[0m[[C][2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m[[C[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m][0m.omega0.regular_form()[0m[K[23D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m1[0;38;5;210;48;5;88m][0m.omega0.regular_form()[23D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m][?7h[0m[?12l[?25h[?25l[?7l[3D[0m[[C][7C[?7h[0m[?12l[?25h[?25l[?7l[13C[0;38;5;210;48;5;88m([0;38;5;16;48;5;152m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m([C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[32D[0m[J[0;94msage: [0mB[[0;38;5;20;1m1[0m].omega0.regular_form()[32D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m[0] d[x] + [x] d[y] + V((0) dy) + dV((x^6 + 2*x^4)*y)
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;241m= superelliptic((x^3 - x)^3 + x^3 - x, 2)[41D[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0msuperelliptic[0;38;5;16;48;5;152m([0m(x^[0;38;5;20;1m3[0m - x)^[0;38;5;20;1m3[0m + x^[0;38;5;20;1m3[0m - x, [0;38;5;20;1m2[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[49D[0m[J[0;94msage: [0mC = superelliptic((x^[0;38;5;20;1m3[0m - x)^[0;38;5;20;1m3[0m + x^[0;38;5;20;1m3[0m - x, [0;38;5;20;1m2[0m)[49D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mB[0;38;5;241m[1].omega0.regular_form()[25D[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;241m= C.crystalline_coh[Cmology_basis(prec = 100, info = 1)[54D[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0mC.crystalline_cohomology_basis[0;38;5;16;48;5;152m([0mprec = [0;38;5;20;1m100[0m, info = [0;38;5;20;1m1[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[62D[0m[J[0;94msage: [0mB = C.crystalline_cohomology_basis(prec = [0;38;5;20;1m100[0m, info = [0;38;5;20;1m1[0m)[62D[0m

+[J[?7h[0m[?12l[?25h[?2004lComputing 0. basis element
+Computing 1. basis element
+Computing 2. basis element
+Computing 3. basis element
+Computing 4. basis element
+Computing 5. basis element
+Computing 6. basis element
+Computing 7. basis element
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mB[0;38;5;241m = C.crystalline_cohomology_basis(prec = 100, info = 1)[55D[?7h[0m[?12l[?25h[?25l[?7l[0m[[0;38;5;241m1].omega0.regular_f[Crm()[0m[K[24D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;16;48;5;152m[[C][?7h[0m[?12l[?25h[?25l[?7l[3D[0m[[C].[?7h[0m[?12l[?25h[?25l[?7l[0mr[0;38;5;241megular_form()[0m[K[13D[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0mg[?7h[0m[?12l[?25h[?25l[?7l[0mu[?7h[0m[?12l[?25h[?25l[?7l[0ml[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0m_[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0mm[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[25D[0m[J[0;94msage: [0mB[[0;38;5;20;1m0[0m].regular_form()[25D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mTypeError[0m                                 Traceback (most recent call last)
+Input [0;32mIn [13][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mB[49m[43m[[49m[43mInteger[49m[43m([49m[38;5;241;43m0[39;49m[43m)[49m[43m][49m[38;5;241;43m.[39;49m[43mregular_form[49m[43m([49m[43m)[49m
+
+File [0;32m<string>:90[0m, in [0;36mregular_drw_cech[0;34m(cocycle)[0m
+
+[0;31mTypeError[0m: can only concatenate str (not "superelliptic_regular_drw_form") to str
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mB[0;38;5;241m[0].regular_form()[18D[?7h[0m[?12l[?25h[?25l[?7l[0m[[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;16;48;5;152m[[C][?7h[0m[?12l[?25h[?25l[?7l[3D[0m[[C].[?7h[0m[?12l[?25h[?25l[?7l[0mo[0;38;5;241mmega0.regular_form()[20D[?7h[0m[?12l[?25h[?25l[?7l[0mm[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0mg[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0m0.regular_form[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[32D[0m[J[0;94msage: [0mB[[0;38;5;20;1m0[0m].omega0.regular_form()[32D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m[0] d[x] + [1] d[y] + V((0) dy) + dV((x^9 + 2*x)*y)
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mB[[0;38;5;20;1m0[0m].omega0.regular_form[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([0;38;5;16;48;5;152m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0m()[3D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m[[C][?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[2D[0m[[C][2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m[[C[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m][0m.omega0.regular_form()[0m[K[23D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m7[0;38;5;210;48;5;88m][0m.omega0.regular_form()[23D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m][?7h[0m[?12l[?25h[?25l[?7l[3D[0m[[C][C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[0;38;5;210;48;5;88m([0;38;5;16;48;5;152m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m([0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[32D[0m[J[0;94msage: [0mB[[0;38;5;20;1m7[0m].omega0.regular_form()[32D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m[0] d[x] + [x^4] d[y] + V((0) dy) + dV(0)
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[6D[0;94msage: [0;38;5;28;1mdef[0m [0;38;5;25;1mregular_drw_cech[0m(cocycle):[0m

+[0;94m....: [0m    [0;38;5;24mprint[0m([0;38;5;160;48;5;231m"( "[0m + [0;38;5;24mstr[0m(cocycle.omega0.regular_form()) + [0;38;5;160;48;5;231m", "[0m + [0;38;5;24mstr[0m(cocycle.f) + [0;38;5;160;48;5;231m" )"[0m)[0m

+[0;94m....: [0m

+[0;94m....: [0msuperelliptic_drw_cech.regular_form = regular_drw_cech[60D[60C[?7h[0m[?12l[?25h[?25l[?7l[3A[60D[0m[J[0;94msage: [0;38;5;28;1mdef[0m [0;38;5;25;1mregular_drw_cech[0m(cocycle):[0m

+[0;94m....: [0m    [0;38;5;24mprint[0m([0;38;5;160;48;5;231m"( "[0m + [0;38;5;24mstr[0m(cocycle.omega0.regular_form()) + [0;38;5;160;48;5;231m", "[0m + [0;38;5;24mstr[0m(cocycle.f) + [0;38;5;160;48;5;231m" )"[0m)[0m

+[0;94m....: [0m

+[0;94m....: [0msuperelliptic_drw_cech.regular_form = regular_drw_cech[60D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[6D[0m[J[0;94msage: [6D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mB[0;38;5;241m[7].omega0.regular_form()[25D[?7h[0m[?12l[?25h[?25l[?7l[0m[[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;16;48;5;152m[[C][?7h[0m[?12l[?25h[?25l[?7l[3D[0m[[C].[?7h[0m[?12l[?25h[?25l[?7l[0mr[0;38;5;241megular_form()[0m[K[13D[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0mgular_form[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[25D[0m[J[0;94msage: [0mB[[0;38;5;20;1m0[0m].regular_form()[25D[0m

+[J[?7h[0m[?12l[?25h[?2004l( [0] d[x] + [1] d[y] + V((0) dy) + dV((x^9 + 2*x)*y), V(x*y) )
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mf[0;38;5;241mf.expansion_at_infty()[22D[?7h[0m[?12l[?25h[?25l[?7l[0mo[0;38;5;241mr i i[C lau.expo[Cents():[23D[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;28;1mfor[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;28min[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0mr[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0mg[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;24mrange[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m8[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;16;48;5;152m([C)[?7h[0m[?12l[?25h[?25l[?7l[3D[0m([C):[?7h[0m[?12l[?25h[?25l[?7l[24D[0;94msage: [0;38;5;28;1mfor[0m i [0;38;5;28min[0m [0;38;5;24mrange[0m([0;38;5;20;1m8[0m):[0m

+[0;94m....: [6D[10C[?7h[0m[?12l[?25h[?25l[?7l[0mp[0;38;5;241mrint("( " + str(cocycle.omega0.regular_form()) + ", " + str(cocycle.f) + " )")[78D[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;24mprint[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0mB[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0m[[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m[][?7h[0m[?12l[?25h[?25l[?7l[2D[0m[[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;16;48;5;152m[[C][?7h[0m[?12l[?25h[?25l[?7l[3D[0m[[C].[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0mg[?7h[0m[?12l[?25h[?25l[?7l[0mu[?7h[0m[?12l[?25h[?25l[?7l[0ml[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0m_[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0mm[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[20D[0;38;5;16;48;5;152m([17C[0m()[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[36D[0;94m....: [0m    [0;38;5;24mprint[0m(B[i].regular_form())[0m

+[0;94m....: [6D[10C[?7h[0m[?12l[?25h[?25l[?7l[2A[10D[0m[J[0;94msage: [0;38;5;28;1mfor[0m i [0;38;5;28min[0m [0;38;5;24mrange[0m([0;38;5;20;1m8[0m):[0m

+[0;94m....: [0m    [0;38;5;24mprint[0m(B[i].regular_form())[0m

+[0;94m....: [6D[0m

+[J[?7h[0m[?12l[?25h[?2004l( [0] d[x] + [1] d[y] + V((0) dy) + dV((x^9 + 2*x)*y), V(x*y) )
+None
+( [0] d[x] + [x] d[y] + V((2*x^36 + x^28 + x^12 + 2*x^4) dy) + dV((x^12 + 2*x^4)*y), V(((x^8 + 1)/x^4)*y) )
+None
+( [0] d[x] + [x^2] d[y] + V((x^63 + 2*x^55 + 2*x^39 + x^31) dy) + dV((2*x^39 + x^31 + 2*x^15 + x^7)*y), V(((x^8 + 1)/x)*y) )
+None
+^C[0;31m---------------------------------------------------------------------------[0m
+[0;31mKeyboardInterrupt[0m                         Traceback (most recent call last)
+Input [0;32mIn [18][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[1;32m      1[0m [38;5;28;01mfor[39;00m i [38;5;129;01min[39;00m [38;5;28mrange[39m(Integer([38;5;241m8[39m)):
+[0;32m----> 2[0m     [38;5;28mprint[39m([43mB[49m[43m[[49m[43mi[49m[43m][49m[38;5;241;43m.[39;49m[43mregular_form[49m[43m([49m[43m)[49m)
+
+Input [0;32mIn [16][0m, in [0;36mregular_drw_cech[0;34m(cocycle)[0m
+[1;32m      1[0m [38;5;28;01mdef[39;00m [38;5;21mregular_drw_cech[39m(cocycle):
+[0;32m----> 2[0m     [38;5;28mprint[39m([38;5;124m"[39m[38;5;124m( [39m[38;5;124m"[39m [38;5;241m+[39m [38;5;28mstr[39m([43mcocycle[49m[38;5;241;43m.[39;49m[43momega0[49m[38;5;241;43m.[39;49m[43mregular_form[49m[43m([49m[43m)[49m) [38;5;241m+[39m [38;5;124m"[39m[38;5;124m, [39m[38;5;124m"[39m [38;5;241m+[39m [38;5;28mstr[39m(cocycle[38;5;241m.[39mf) [38;5;241m+[39m [38;5;124m"[39m[38;5;124m )[39m[38;5;124m"[39m)
+
+File [0;32m<string>:80[0m, in [0;36mregular_drw_form[0;34m(omega)[0m
+
+File [0;32m<string>:73[0m, in [0;36mdiffn[0;34m(self, dy_w)[0m
+
+File [0;32m<string>:177[0m, in [0;36mdy_w[0;34m(C)[0m
+
+File [0;32m<string>:149[0m, in [0;36mauxilliary_derivative[0;34m(P)[0m
+
+File [0;32m<string>:84[0m, in [0;36m__add__[0;34m(self, other)[0m
+
+File [0;32m<string>:65[0m, in [0;36m__mul__[0;34m(self, other)[0m
+
+File [0;32m<string>:28[0m, in [0;36m__sub__[0;34m(self, other)[0m
+
+File [0;32m<string>:7[0m, in [0;36m__init__[0;34m(self, C, g)[0m
+
+File [0;32m<string>:252[0m, in [0;36mreduction_form[0;34m(C, g)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:647[0m, in [0;36mPolynomialRing[0;34m(base_ring, *args, **kwds)[0m
+[1;32m    644[0m         [38;5;28;01mraise[39;00m [38;5;167;01mTypeError[39;00m([38;5;124m"[39m[38;5;124mvariable names specified twice inconsistently: [39m[38;5;132;01m%r[39;00m[38;5;124m and [39m[38;5;132;01m%r[39;00m[38;5;124m"[39m [38;5;241m%[39m (names, kwnames))
+[1;32m    646[0m [38;5;28;01mif[39;00m multivariate [38;5;129;01mor[39;00m [38;5;28mlen[39m(names) [38;5;241m!=[39m [38;5;241m1[39m:
+[0;32m--> 647[0m     [38;5;28;01mreturn[39;00m [43m_multi_variate[49m[43m([49m[43mbase_ring[49m[43m,[49m[43m [49m[43mnames[49m[43m,[49m[43m [49m[38;5;241;43m*[39;49m[38;5;241;43m*[39;49m[43mkwds[49m[43m)[49m
+[1;32m    648[0m [38;5;28;01melse[39;00m:
+[1;32m    649[0m     [38;5;28;01mreturn[39;00m _single_variate(base_ring, names, [38;5;241m*[39m[38;5;241m*[39mkwds)
+
+File [0;32m/ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:762[0m, in [0;36m_multi_variate[0;34m(base_ring, names, sparse, order, implementation)[0m
+[1;32m    760[0m [38;5;28;01mfrom[39;00m [38;5;21;01msage[39;00m[38;5;21;01m.[39;00m[38;5;21;01mrings[39;00m[38;5;21;01m.[39;00m[38;5;21;01mpolynomial[39;00m[38;5;21;01m.[39;00m[38;5;21;01mterm_order[39;00m [38;5;28;01mimport[39;00m TermOrder
+[1;32m    761[0m n [38;5;241m=[39m [38;5;28mlen[39m(names)
+[0;32m--> 762[0m order [38;5;241m=[39m [43mTermOrder[49m[43m([49m[43morder[49m[43m,[49m[43m [49m[43mn[49m[43m)[49m
+[1;32m    764[0m [38;5;66;03m# "implementation" must be last[39;00m
+[1;32m    765[0m key [38;5;241m=[39m [base_ring, names, n, order, implementation]
+
+File [0;32msrc/cysignals/signals.pyx:310[0m, in [0;36mcysignals.signals.python_check_interrupt[0;34m()[0m
+
+[0;31mKeyboardInterrupt[0m: 
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[6D[0;94msage: [0;38;5;28;1mfor[0m i [0;38;5;28min[0m [0;38;5;24mrange[0m([0;38;5;20;1m8[0m):[0m

+[0;94m....: [0m    [0;38;5;24mprint[0;38;5;16;48;5;152m([0mB[i].regular_form()[0;38;5;16;48;5;152m)[36D[36C[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[21D[0m([17C[0;38;5;16;48;5;152m()[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;210;48;5;88m([?7h[0m[?12l[?25h[?25l[?7l[0m()[14D[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m[[C[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[2D[0m[[C][2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m[[C[0;38;5;16;48;5;152m][3D[?7h[0m[?12l[?25h[?25l[?7l[0m[[C][4D[?7h[0m[?12l[?25h[?25l[?7l[6D[0mprintB[i].regular_form()[0m[K[19D[?7h[0m[?12l[?25h[?25l[?7l[0mB[i].regular_form()[0m[K[19D[?7h[0m[?12l[?25h[?25l[?7l[0mB[i].regular_form()[0m[K[19D[?7h[0m[?12l[?25h[?25l[?7l[0mB[i].regular_form()[0m[K[19D[?7h[0m[?12l[?25h[?25l[?7l[0mB[i].regular_form()[0m[K[19D[?7h[0m[?12l[?25h[?25l[?7l[0mB[i].regular_form()[0m[K[19D[?7h[0m[?12l[?25h[?25l[?7l[10D[0;94m....: [0m[K[0m

+[0;94m....: [0m    B[i].regular_form()[29D[10C[?7h[0m[?12l[?25h[?25l[?7l[0mB[i].regular_form()[0m[K[19D[?7h[0m[?12l[?25h[?25l[?7l[0mB[i].regular_form()[0m[K[19D[?7h[0m[?12l[?25h[?25l[?7l[0mB[i].regular_form()[0m[K[19D[?7h[0m[?12l[?25h[?25l[?7l[0mB[i].regular_form()[0m[K[19D[?7h[0m[?12l[?25h[?25l[?7l[A[4C[0mB[i].regular_form()[0m

+[0m [0m[K[A[9C[?7h[0m[?12l[?25h[?25l[?7l[0mB[i].regular_form()[0m[K[19D[?7h[0m[?12l[?25h[?25l[?7l[0m B[i].regular_form()[19D[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[3C[?7h[0m[?12l[?25h[?25l[?7l[12C[0;38;5;210;48;5;88m([0;38;5;16;48;5;152m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m([C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[0m()[0m

+[0;94m....: [4C[?7h[0m[?12l[?25h[?25l[?7l[2A[10D[0m[J[0;94msage: [0;38;5;28;1mfor[0m i [0;38;5;28min[0m [0;38;5;24mrange[0m([0;38;5;20;1m8[0m):[0m

+[0;94m....: [0m    B[i].regular_form()[0m

+[0;94m....: [6D[0m

+[J[?7h[0m[?12l[?25h[?2004l( [0] d[x] + [1] d[y] + V((0) dy) + dV((x^9 + 2*x)*y), V(x*y) )
+( [0] d[x] + [x] d[y] + V((2*x^36 + x^28 + x^12 + 2*x^4) dy) + dV((x^12 + 2*x^4)*y), V(((x^8 + 1)/x^4)*y) )
+( [0] d[x] + [x^2] d[y] + V((x^63 + 2*x^55 + 2*x^39 + x^31) dy) + dV((2*x^39 + x^31 + 2*x^15 + x^7)*y), V(((x^8 + 1)/x)*y) )
+( [0] d[x] + [x^3] d[y] + V((0) dy) + dV(0), V((x^10 + x^2)*y) )
+( [0] d[x] + [x^7] d[y] + V((x^54 + 2*x^46 + 2*x^30 + x^22) dy) + dV((2*x^30 + x^22)*y), [2/x*y] + V(((x^24 + x^16 + x^8 + 2)/x^2)*y) )
+( [0] d[x] + [2*x^6] d[y] + V((0) dy) + dV((2*x^27 + x^19)*y), [2/x^2*y] + V((2*x^19 + 2*x^11 + 2*x^3)*y) )
+( [0] d[x] + [0] d[y] + V((x^72 + 2*x^64 + 2*x^48 + x^40) dy) + dV((2*x^48 + x^40 + 2*x^24 + x^16)*y), [2/x^3*y] )
+( [0] d[x] + [x^4] d[y] + V((0) dy) + dV(0), [2/x^4*y] + V(((x^16 + x^8 + 1)/x^3)*y) )
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m = superelliptic((x^3 - x)^3 + x^3 - x, 2)[42D[?7h[0m[?12l[?25h[?25l[?7l[7D[0m[J[0;94msage: [0mC[7D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mSuperelliptic curve with the equation y^2 = x^9 + 2*x over Finite Field of size 3
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;241m= superelliptic((x^3 - x)^3 + x^3 - x, 2)[41D[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[?7h[0m[?12l[?25h[?25l[?7l[0m1[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0ms[?7h[0m[?12l[?25h[?25l[?7l[0mu[?7h[0m[?12l[?25h[?25l[?7l[0mp[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;24msuper[?7h[0m[?12l[?25h[?25l[?7l[5D[0msupere[?7h[0m[?12l[?25h[?25l[?7l[0ml[?7h[0m[?12l[?25h[?25l[?7l[0ml[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mp[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[0m^[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m3[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0m+[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[0m,[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m2[?7h[0m[?12l[?25h[?25l[?7l[11D[0;38;5;16;48;5;152m([10C)[?7h[0m[?12l[?25h[?25l[?7l[36D[0m[J[0;94msage: [0mC1 = superelliptic(x^[0;38;5;20;1m3[0m + x, [0;38;5;20;1m2[0m)[36D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mB[0;38;5;241m[0].regular_form()[18D[?7h[0m[?12l[?25h[?25l[?7l[0m1[0m[K[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mC[?7h[0m[?12l[?25h[?25l[?7l[0m1.[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0my[?7h[0m[?12l[?25h[?25l[?7l[0ms[?7h[0m[?12l[?25h[?25l[?7l[0mtalline_cohomology_basis[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0mp[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m1[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[?7h[0m[?12l[?25h[?25l[?7l[0m,[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;28min[?7h[0m[?12l[?25h[?25l[?7l[2D[0minf[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m1[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;124;48;5;188m`[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[21D[0;38;5;16;48;5;152m([20C)[?7h[0m[?12l[?25h[?25l[?7l[64D[0m[J[0;94msage: [0mB1 = C1.crystalline_cohomology_basis(prec = [0;38;5;20;1m100[0m, info = [0;38;5;20;1m1[0m)[64D[0m

+[J[?7h[0m[?12l[?25h[?2004lComputing 0. basis element
+Computing 1. basis element
+^C[0;31m---------------------------------------------------------------------------[0m
+[0;31mAttributeError[0m                            Traceback (most recent call last)
+File [0;32m<string>:58[0m, in [0;36m__mul__[0;34m(self, other)[0m
+
+[0;31mAttributeError[0m: 'superelliptic_form' object has no attribute 'function'
+
+During handling of the above exception, another exception occurred:
+
+[0;31mKeyboardInterrupt[0m                         Traceback (most recent call last)
+Input [0;32mIn [22][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m B1 [38;5;241m=[39m [43mC1[49m[38;5;241;43m.[39;49m[43mcrystalline_cohomology_basis[49m[43m([49m[43mprec[49m[43m [49m[38;5;241;43m=[39;49m[43m [49m[43mInteger[49m[43m([49m[38;5;241;43m100[39;49m[43m)[49m[43m,[49m[43m [49m[43minfo[49m[43m [49m[38;5;241;43m=[39;49m[43m [49m[43mInteger[49m[43m([49m[38;5;241;43m1[39;49m[43m)[49m[43m)[49m
+
+File [0;32m<string>:41[0m, in [0;36mcrystalline_cohomology_basis[0;34m(self, prec, info)[0m
+
+File [0;32m<string>:33[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class, prec)[0m
+
+File [0;32m<string>:6[0m, in [0;36m__init__[0;34m(self, omega0, f)[0m
+
+File [0;32m<string>:90[0m, in [0;36mdiffn[0;34m(self, dy_w)[0m
+
+File [0;32m<string>:73[0m, in [0;36mdiffn[0;34m(self, dy_w)[0m
+
+File [0;32m<string>:177[0m, in [0;36mdy_w[0;34m(C)[0m
+
+File [0;32m<string>:65[0m, in [0;36m__mul__[0;34m(self, other)[0m
+
+File [0;32m<string>:65[0m, in [0;36m__mul__[0;34m(self, other)[0m
+
+File [0;32m<string>:7[0m, in [0;36m__init__[0;34m(self, C, g)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/structure/parent.pyx:897[0m, in [0;36msage.structure.parent.Parent.__call__[0;34m()[0m
+[1;32m    895[0m if mor is not None:
+[1;32m    896[0m     if no_extra_args:
+[0;32m--> 897[0m         return mor._call_(x)
+[1;32m    898[0m     else:
+[1;32m    899[0m         return mor._call_with_args(x, args, kwds)
+
+File [0;32m/ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156[0m, in [0;36msage.structure.coerce_maps.DefaultConvertMap_unique._call_[0;34m()[0m
+[1;32m    154[0m cdef Parent C = self._codomain
+[1;32m    155[0m try:
+[0;32m--> 156[0m     return C._element_constructor(x)
+[1;32m    157[0m except Exception:
+[1;32m    158[0m     if print_warnings:
+
+File [0;32m/ext/sage/9.7/src/sage/rings/fraction_field.py:706[0m, in [0;36mFractionField_generic._element_constructor_[0;34m(self, x, y, coerce)[0m
+[1;32m    704[0m x0, y0 [38;5;241m=[39m x, y
+[1;32m    705[0m [38;5;28;01mtry[39;00m:
+[0;32m--> 706[0m     x, y [38;5;241m=[39m [43mresolve_fractions[49m[43m([49m[43mx0[49m[43m,[49m[43m [49m[43my0[49m[43m)[49m
+[1;32m    707[0m [38;5;28;01mexcept[39;00m ([38;5;167;01mAttributeError[39;00m, [38;5;167;01mTypeError[39;00m):
+[1;32m    708[0m     [38;5;28;01mraise[39;00m [38;5;167;01mTypeError[39;00m([38;5;124m"[39m[38;5;124mcannot convert [39m[38;5;132;01m{!r}[39;00m[38;5;124m/[39m[38;5;132;01m{!r}[39;00m[38;5;124m to an element of [39m[38;5;132;01m{}[39;00m[38;5;124m"[39m[38;5;241m.[39mformat(
+[1;32m    709[0m                     x0, y0, [38;5;28mself[39m))
+
+File [0;32m/ext/sage/9.7/src/sage/rings/fraction_field.py:688[0m, in [0;36mFractionField_generic._element_constructor_.<locals>.resolve_fractions[0;34m(x, y)[0m
+[1;32m    686[0m yd [38;5;241m=[39m y[38;5;241m.[39mdenominator()
+[1;32m    687[0m [38;5;28;01mtry[39;00m:
+[0;32m--> 688[0m     [38;5;28;01mreturn[39;00m (xn [38;5;241m*[39m yd, [43myn[49m[43m [49m[38;5;241;43m*[39;49m[43m [49m[43mxd[49m)
+[1;32m    689[0m [38;5;28;01mexcept[39;00m ([38;5;167;01mAttributeError[39;00m, [38;5;167;01mTypeError[39;00m, [38;5;167;01mValueError[39;00m):
+[1;32m    690[0m     [38;5;28;01mpass[39;00m
+
+File [0;32m/ext/sage/9.7/src/sage/structure/element.pyx:1516[0m, in [0;36msage.structure.element.Element.__mul__[0;34m()[0m
+[1;32m   1514[0m     return (<Element>left)._mul_(right)
+[1;32m   1515[0m if BOTH_ARE_ELEMENT(cl):
+[0;32m-> 1516[0m     return coercion_model.bin_op(left, right, mul)
+[1;32m   1517[0m 
+[1;32m   1518[0m cdef long value
+
+File [0;32m/ext/sage/9.7/src/sage/structure/coerce.pyx:1200[0m, in [0;36msage.structure.coerce.CoercionModel.bin_op[0;34m()[0m
+[1;32m   1198[0m # Now coerce to a common parent and do the operation there
+[1;32m   1199[0m try:
+[0;32m-> 1200[0m     xy = self.canonical_coercion(x, y)
+[1;32m   1201[0m except TypeError:
+[1;32m   1202[0m     self._record_exception()
+
+File [0;32m/ext/sage/9.7/src/sage/structure/coerce.pyx:1311[0m, in [0;36msage.structure.coerce.CoercionModel.canonical_coercion[0;34m()[0m
+[1;32m   1309[0m x_map, y_map = coercions
+[1;32m   1310[0m if x_map is not None:
+[0;32m-> 1311[0m     x_elt = (<Map>x_map)._call_(x)
+[1;32m   1312[0m else:
+[1;32m   1313[0m     x_elt = x
+
+File [0;32m/ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287[0m, in [0;36msage.structure.coerce_maps.NamedConvertMap._call_[0;34m()[0m
+[1;32m    285[0m     raise TypeError("Cannot coerce {} to {}".format(x, C))
+[1;32m    286[0m cdef Map m
+[0;32m--> 287[0m cdef Element e = method(C)
+[1;32m    288[0m if e is None:
+[1;32m    289[0m     raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x)))
+
+File [0;32m/ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:198[0m, in [0;36msage.rings.polynomial.multi_polynomial.MPolynomial._polynomial_[0;34m()[0m
+[1;32m    196[0m var = R.variable_name()
+[1;32m    197[0m if var in self._parent.variable_names():
+[0;32m--> 198[0m     return R(self.polynomial(self._parent(var)))
+[1;32m    199[0m else:
+[1;32m    200[0m     return R([self])
+
+File [0;32m/ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:419[0m, in [0;36msage.rings.polynomial.multi_polynomial.MPolynomial.polynomial[0;34m()[0m
+[1;32m    417[0m w = {remove_from_tuple(e, ind): val
+[1;32m    418[0m      for e, val in self.dict().iteritems() if not e[ind]}
+[0;32m--> 419[0m v = [B(w)]  # coefficients that don't involve var
+[1;32m    420[0m z = var
+[1;32m    421[0m for i in range(1,d+1):
+
+File [0;32m/ext/sage/9.7/src/sage/structure/parent.pyx:897[0m, in [0;36msage.structure.parent.Parent.__call__[0;34m()[0m
+[1;32m    895[0m if mor is not None:
+[1;32m    896[0m     if no_extra_args:
+[0;32m--> 897[0m         return mor._call_(x)
+[1;32m    898[0m     else:
+[1;32m    899[0m         return mor._call_with_args(x, args, kwds)
+
+File [0;32m/ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156[0m, in [0;36msage.structure.coerce_maps.DefaultConvertMap_unique._call_[0;34m()[0m
+[1;32m    154[0m cdef Parent C = self._codomain
+[1;32m    155[0m try:
+[0;32m--> 156[0m     return C._element_constructor(x)
+[1;32m    157[0m except Exception:
+[1;32m    158[0m     if print_warnings:
+
+File [0;32m/ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:309[0m, in [0;36mPolynomialRing_general._element_constructor_[0;34m(self, x, check, is_gen, construct, **kwds)[0m
+[1;32m    306[0m     args [38;5;241m=[39m ([38;5;28mself[39m[38;5;241m.[39mbase_ring(), [38;5;28mself[39m[38;5;241m.[39mvariable_names(), [38;5;28;01mNone[39;00m, [38;5;28mself[39m[38;5;241m.[39mis_sparse())
+[1;32m    307[0m     [38;5;28;01mreturn[39;00m unpickle_PolynomialRing, args
+[0;32m--> 309[0m [38;5;28;01mdef[39;00m [38;5;21m_element_constructor_[39m([38;5;28mself[39m, x[38;5;241m=[39m[38;5;28;01mNone[39;00m, check[38;5;241m=[39m[38;5;28;01mTrue[39;00m, is_gen[38;5;241m=[39m[38;5;28;01mFalse[39;00m,
+[1;32m    310[0m                           construct[38;5;241m=[39m[38;5;28;01mFalse[39;00m, [38;5;241m*[39m[38;5;241m*[39mkwds):
+[1;32m    311[0m     [38;5;124mr[39m[38;5;124;03m"""[39;00m
+[1;32m    312[0m [38;5;124;03m    Convert ``x`` into this univariate polynomial ring,[39;00m
+[1;32m    313[0m [38;5;124;03m    possibly non-canonically.[39;00m
+[0;32m   (...)[0m
+[1;32m    412[0m [38;5;124;03m        λ^2[39;00m
+[1;32m    413[0m [38;5;124;03m    """[39;00m
+[1;32m    414[0m     C [38;5;241m=[39m [38;5;28mself[39m[38;5;241m.[39melement_class
+
+File [0;32msrc/cysignals/signals.pyx:310[0m, in [0;36mcysignals.signals.python_check_interrupt[0;34m()[0m
+
+[0;31mKeyboardInterrupt[0m: 
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mB1 = C1.crystalline_cohomology_basis[0;38;5;16;48;5;152m([0mprec = [0;38;5;20;1m100[0m, info = [0;38;5;20;1m1[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[64D[0m[J[0;94msage: [0mB1 = C1.crystalline_cohomology_basis(prec = [0;38;5;20;1m100[0m, info = [0;38;5;20;1m1[0m)[64D[0m

+[J[?7h[0m[?12l[?25h[?2004lComputing 0. basis element
+Computing 1. basis element
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mf[0;38;5;241mor i in range(8):[17D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;28;1mfor[?7h[0m[?12l[?25h[?25l[?7l[0m i [0;38;5;28min[0m [0;38;5;24mrange[0m([0;38;5;20;1m8[0m):[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m([C)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m:[0m[K[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m2[0;38;5;210;48;5;88m)[0m:[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[3D[0m([C)[C[?7h[0m[?12l[?25h[?25l[?7l[24D[0;94msage: [0;38;5;28;1mfor[0m i [0;38;5;28min[0m [0;38;5;24mrange[0m([0;38;5;20;1m2[0m):[0m

+[0;94m....: [6D[10C[?7h[0m[?12l[?25h[?25l[?7l[0mp[0;38;5;241mrint(B[i].regular_form())[25D[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;24mprint[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m([0mB[i].regular_form()[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[20D[0m([17C[0;38;5;16;48;5;152m([0;38;5;210;48;5;88m)[0m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([0;38;5;16;48;5;152m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0m()[3D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m[[C][?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[2D[0m[[C][2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m[[C[0;38;5;16;48;5;152m][3D[?7h[0m[?12l[?25h[?25l[?7l[0m[[C][4D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([19C[0;38;5;16;48;5;152m)[21D[?7h[0m[?12l[?25h[?25l[?7l[0m([19C)[20D[?7h[0m[?12l[?25h[?25l[?7l[C[0;38;5;210;48;5;88m[[C[0;38;5;16;48;5;152m][3D[?7h[0m[?12l[?25h[?25l[?7l[0m1[0;38;5;210;48;5;88m[[0mi[0;38;5;16;48;5;152m][0m.regular_form([C)[19D[?7h[0m[?12l[?25h[?25l[?7l[0m[[C][2D[?7h[0m[?12l[?25h[?25l[?7l[3C[?7h[0m[?12l[?25h[?25l[?7l[12C[0;38;5;210;48;5;88m([0;38;5;16;48;5;152m)[2D[?7h[0m[?12l[?25h[?25l[?7l[19D[0;38;5;16;48;5;152m([18C[0m()[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[37D[0;94m....: [0m    [0;38;5;24mprint[0m(B1[i].regular_form())[0m

+[0;94m....: [6D[10C[?7h[0m[?12l[?25h[?25l[?7l[2A[10D[0m[J[0;94msage: [0;38;5;28;1mfor[0m i [0;38;5;28min[0m [0;38;5;24mrange[0m([0;38;5;20;1m2[0m):[0m

+[0;94m....: [0m    [0;38;5;24mprint[0m(B1[i].regular_form())[0m

+[0;94m....: [6D[0m

+[J[?7h[0m[?12l[?25h[?2004l( [0] d[x] + [2] d[y] + V((x^21 + x^19 + x^15 + x^13) dy) + dV((x^15 + x^13 + 2*x^9 + 2*x^7)*y), V(((x^2 + 2)/x)*y) )
+None
+( [0] d[x] + [2*x] d[y] + V((0) dy) + dV((2*x^6 + 2*x^4)*y), [2/x*y] + V((x^4 + 2*x^2 + 1)*y) )
+None
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ma[0;38;5;241m^(-1)[5D[?7h[0m[?12l[?25h[?25l[?7l[0md[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0m_[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0mxpansion[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m([0mx^[0;38;5;20;1m63[0m + [0;38;5;20;1m2[0m*x^[0;38;5;20;1m55[0m + [0;38;5;20;1m2[0m*x^[0;38;5;20;1m39[0m + x^[0;38;5;20;1m31[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[31D[0m([29C),[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[0m^[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m3[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0m-[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[41D[0;38;5;16;48;5;152m([40C)[?7h[0m[?12l[?25h[?25l[?7l[62D[0m[J[0;94msage: [0madic_expansion((x^[0;38;5;20;1m63[0m + [0;38;5;20;1m2[0m*x^[0;38;5;20;1m55[0m + [0;38;5;20;1m2[0m*x^[0;38;5;20;1m39[0m + x^[0;38;5;20;1m31[0m), x^[0;38;5;20;1m3[0m - x)[62D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m[0, 0, 0, 0, x, 1, x, 2, 0, 1, x, 1, x, 0, 0, 2, 0, 0, 0, 1, 0, 1]
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ma[0;38;5;241mdic_expansion((x^63 + 2*x^55 + 2*x^39 + x^31), x^3 - x)[55D[?7h[0m[?12l[?25h[?25l[?7l[0md[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0m_[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[0mp[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0ms[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0mx[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m^[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m3[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0m-[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[0m,[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[0m^[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m3[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0m-[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[17D[0;38;5;16;48;5;152m([16C)[?7h[0m[?12l[?25h[?25l[?7l[38D[0m[J[0;94msage: [0madic_expansion(x^[0;38;5;20;1m3[0m - x, x^[0;38;5;20;1m3[0m - x)[38D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m[0, 1]
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mR[0;38;5;241mt.<t> = LaurentSeriesRing(F, default_prec = 100)[48D[?7h[0m[?12l[?25h[?25l[?7l[0mx[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0m<[?7h[0m[?12l[?25h[?25l[?7l[0m>[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mt>[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mP[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0ml[?7h[0m[?12l[?25h[?25l[?7l[0my[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mm[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0ml[?7h[0m[?12l[?25h[?25l[?7l[0mR[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0mg[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0mR[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[3D[0;38;5;16;48;5;152m([2C)[?7h[0m[?12l[?25h[?25l[?7l[34D[0m[J[0;94msage: [0mRxt.<t> = PolynomialRing(Rx)[34D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mRxt.<t> = PolynomialRing[0;38;5;16;48;5;152m([0mRx[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[28D[0madic_expansion[0;38;5;16;48;5;152m([0mx^[0;38;5;20;1m3[0m - x, x^[0;38;5;20;1m3[0m - x[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[17D[0m([16C)[2D[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([16C[0;38;5;16;48;5;152m)[18D[?7h[0m[?12l[?25h[?25l[?7l[0m([16C)[32D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mcadic_expansion(x^[0;38;5;20;1m3[0m - x, x^[0;38;5;20;1m3[0m - x)[32D[?7h[0m[?12l[?25h[?25l[?7l[0moadic_expansion(x^[0;38;5;20;1m3[0m - x, x^[0;38;5;20;1m3[0m - x)[32D[?7h[0m[?12l[?25h[?25l[?7l[0moadic_expansion(x^[0;38;5;20;1m3[0m - x, x^[0;38;5;20;1m3[0m - x)[32D[?7h[0m[?12l[?25h[?25l[?7l[0m adic_expansion(x^[0;38;5;20;1m3[0m - x, x^[0;38;5;20;1m3[0m - x)[32D[?7h[0m[?12l[?25h[?25l[?7l[0m=adic_expansion(x^[0;38;5;20;1m3[0m - x, x^[0;38;5;20;1m3[0m - x)[32D[?7h[0m[?12l[?25h[?25l[?7l[0m adic_expansion(x^[0;38;5;20;1m3[0m - x, x^[0;38;5;20;1m3[0m - x)[32D[?7h[0m[?12l[?25h[?25l[?7l[14C[0;38;5;210;48;5;88m([16C[0;38;5;16;48;5;152m)[18D[?7h[0m[?12l[?25h[?25l[?7l[0m([16C)[16D[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[3C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[16D[0;38;5;16;48;5;152m([16C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[44D[0m[J[0;94msage: [0mcoo = adic_expansion(x^[0;38;5;20;1m3[0m - x, x^[0;38;5;20;1m3[0m - x)[44D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mcoo = adic_expansion[0;38;5;16;48;5;152m([0mx^[0;38;5;20;1m3[0m - x, x^[0;38;5;20;1m3[0m - x[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[38D[0mRxt.<t> = Polynom[CalRing[0;38;5;16;48;5;152m([0mRx[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[28D[0madic_expansion[0;38;5;16;48;5;152m([0mx^[0;38;5;20;1m3[0m - x, x^[0;38;5;20;1m3[0m - x[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[17D[0m(x^[0;38;5;20;1m63[C[0m+ [0;38;5;20;1m2[0m*x^[0;38;5;20;1m55[C[0m+ [0;38;5;20;1m2[0m*x^[0;38;5;20;1m39[0m + x^[0;38;5;20;1m31[0m), x^[0;38;5;20;1m3[0m - x[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[41D[0m([40C)[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[32D[0;38;5;16;48;5;152m([29C)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[30D[0m([29C)[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([29C[0;38;5;16;48;5;152m)[31D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([0m([29C)[9C[0;38;5;16;48;5;152m)[42D[?7h[0m[?12l[?25h[?25l[?7l[0m([40C)[43D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mcadic_expansion[C(x^[0;38;5;20;1m63[0m + [0;38;5;20;1m2[0m*x^[C[0;38;5;20;1m5[0m + [0;38;5;20;1m2[0m*x^[0;38;5;20;1m39[0m + x^[0;38;5;20;1m31[0m), x^[0;38;5;20;1m3[0m - x)[56D[?7h[0m[?12l[?25h[?25l[?7l[0moadic_expansion[C(x^[0;38;5;20;1m63[0m + [0;38;5;20;1m2[0m*x^[C[0;38;5;20;1m5[0m + [0;38;5;20;1m2[0m*x^[0;38;5;20;1m39[0m + x^[0;38;5;20;1m31[0m), x^[0;38;5;20;1m3[0m - x)[56D[?7h[0m[?12l[?25h[?25l[?7l[0moadic_expansion[C(x^[0;38;5;20;1m63[0m + [0;38;5;20;1m2[0m*x^[C[0;38;5;20;1m5[0m + [0;38;5;20;1m2[0m*x^[0;38;5;20;1m39[0m + x^[0;38;5;20;1m31[0m), x^[0;38;5;20;1m3[0m - x)[56D[?7h[0m[?12l[?25h[?25l[?7l[0m adic_expansion[C(x^[0;38;5;20;1m63[0m + [0;38;5;20;1m2[0m*x^[C[0;38;5;20;1m5[0m + [0;38;5;20;1m2[0m*x^[0;38;5;20;1m39[0m + x^[0;38;5;20;1m31[0m), x^[0;38;5;20;1m3[0m - x)[56D[?7h[0m[?12l[?25h[?25l[?7l[0m=adic_expansion[C(x^[0;38;5;20;1m63[0m + [0;38;5;20;1m2[0m*x^[C[0;38;5;20;1m5[0m + [0;38;5;20;1m2[0m*x^[0;38;5;20;1m39[0m + x^[0;38;5;20;1m31[0m), x^[0;38;5;20;1m3[0m - x)[56D[?7h[0m[?12l[?25h[?25l[?7l[0m adic_expansion[C(x^[0;38;5;20;1m63[0m + [0;38;5;20;1m2[0m*x^[C[0;38;5;20;1m5[0m + [0;38;5;20;1m2[0m*x^[0;38;5;20;1m39[0m + x^[0;38;5;20;1m31[0m), x^[0;38;5;20;1m3[0m - x)[56D[?7h[0m[?12l[?25h[?25l[?7l[14C[0;38;5;210;48;5;88m([40C[0;38;5;16;48;5;152m)[42D[?7h[0m[?12l[?25h[?25l[?7l[0m([40C)[40D[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[3C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[4C[?7h[0m[?12l[?25h[?25l[?7l[3C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[27D[0;38;5;16;48;5;152m([29C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[30D[0m([29C)[C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[39D[0;38;5;16;48;5;152m([40C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[68D[0m[J[0;94msage: [0mcoo = adic_expansion((x^[0;38;5;20;1m63[0m + [0;38;5;20;1m2[0m*x^[0;38;5;20;1m55[0m + [0;38;5;20;1m2[0m*x^[0;38;5;20;1m39[0m + x^[0;38;5;20;1m31[0m), x^[0;38;5;20;1m3[0m - x)[68D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mf[0;38;5;241mor i in range(2):[17D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;28;1mfor[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0ma[0m[K[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[0mi[0;38;5;241m in range(2):[13D[?7h[0m[?12l[?25h[?25l[?7l[0m,[0m[K[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;28min[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0mu[?7h[0m[?12l[?25h[?25l[?7l[0mm[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[8D[0;38;5;24menumerate[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m([3C)[?7h[0m[?12l[?25h[?25l[?7l[5D[0m([3C):[?7h[0m[?12l[?25h[?25l[?7l[33D[0;94msage: [0;38;5;28;1mfor[0m i, a [0;38;5;28min[0m [0;38;5;24menumerate[0m(coo):[0m

+[0;94m....: [6D[10C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[6D[0m [0m[K[A[32C[?7h[0m[?12l[?25h[?25l[?7l[6D[0;38;5;16;48;5;152m([3C)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[5D[0m([3C[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[9D[0menumerat[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[0mi[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[3D[0mfo[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mF[?7h[0m[?12l[?25h[?25l[?7l[0mF[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mR[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;16;48;5;152m([C)[?7h[0m[?12l[?25h[?25l[?7l[17D[0m[J[0;94msage: [0mFF = Rxt([0;38;5;20;1m0[0m)[17D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mf[0;38;5;241mor i in range(2):[17D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;28;1mfor[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0m,[0m[K[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;28min[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[0mi[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[3D[0mfo[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mF[0;38;5;241mF = Rxt(0)[10D[?7h[0m[?12l[?25h[?25l[?7l[0mF[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0ms[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mu[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;24msum[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0m*[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0m^[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;28;1mfor[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0m,[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;28min[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0mu[?7h[0m[?12l[?25h[?25l[?7l[0mm[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[8D[0;38;5;24menumerate[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m([3C)[?7h[0m[?12l[?25h[?25l[?7l[33D[0;38;5;16;48;5;152m([27C[0m([3C)[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[48D[0m[J[0;94msage: [0mFF = [0;38;5;24msum[0m(a*t^i [0;38;5;28;1mfor[0m i, a [0;38;5;28min[0m [0;38;5;24menumerate[0m(coo))[48D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mF[0;38;5;241mF = sum(a*t^i for i, a in enumerate(coo))[41D[?7h[0m[?12l[?25h[?25l[?7l[0mF[?7h[0m[?12l[?25h[?25l[?7l[8D[0m[J[0;94msage: [0mFF[8D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mt^21 + t^19 + 2*t^15 + x*t^12 + t^11 + x*t^10 + t^9 + 2*t^7 + x*t^6 + t^5 + x*t^4
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m1 = superelliptic(x^3 + x, 2)[29D[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;241mgenus()[0m[K[7D[?7h[0m[?12l[?25h[?25l[?7l[0md[C[0;38;5;241m_rham_basis()[14D[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0m_rham_basis[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mC.de_rham_basis()[23D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m[((1/y) dx, 0, (1/y) dx),
+ ((x/y) dx, 0, (x/y) dx),
+ ((x^2/y) dx, 0, (x^2/y) dx),
+ ((x^3/y) dx, 0, (x^3/y) dx),
+ ((x^7/y) dx, 2/x*y, ((-1)/(x*y)) dx),
+ (((-x^6)/y) dx, 2/x^2*y, 0 dx),
+ (0 dx, 2/x^3*y, (1/(x^3*y)) dx),
+ ((x^4/y) dx, 2/x^4*y, ((-1)/(x^4*y)) dx)]
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+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m((-x^8 - 1)/(x^7*y)) dx
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m([0;38;5;241mC.y/C.x^7).diffn()[18D[?7h[0m[?12l[?25h[?25l[?7l[0mC[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mx[0;38;5;241m - a[C(-2)).expansion_at_infty(prec = 100)[41D[?7h[0m[?12l[?25h[?25l[?7l[0m^[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m5[?7h[0m[?12l[?25h[?25l[?7l[0m*[?7h[0m[?12l[?25h[?25l[?7l[0mC[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0my[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0md[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[18D[0;38;5;16;48;5;152m([15C[0m()[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[19D[0m([17C).[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;28min[?7h[0m[?12l[?25h[?25l[?7l[2D[0mint[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[31D[0m[J[0;94msage: [0m(C.x^[0;38;5;20;1m5[0m*C.y.diffn()).int()[31D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mZeroDivisionError[0m                         Traceback (most recent call last)
+Input [0;32mIn [40][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43m([49m[43mC[49m[38;5;241;43m.[39;49m[43mx[49m[38;5;241;43m*[39;49m[38;5;241;43m*[39;49m[43mInteger[49m[43m([49m[38;5;241;43m5[39;49m[43m)[49m[38;5;241;43m*[39;49m[43mC[49m[38;5;241;43m.[39;49m[43my[49m[38;5;241;43m.[39;49m[43mdiffn[49m[43m([49m[43m)[49m[43m)[49m[38;5;241;43m.[39;49m[43mint[49m[43m([49m[43m)[49m
+
+File [0;32m<string>:198[0m, in [0;36mint[0;34m(self)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:3994[0m, in [0;36msage.rings.polynomial.polynomial_element.Polynomial.integral[0;34m()[0m
+[1;32m   3992[0m cdef Py_ssize_t n
+[1;32m   3993[0m zero = Q.zero()
+[0;32m-> 3994[0m p = [zero] + [cm.bin_op(Q(self.get_unsafe(n)), n + 1, operator.truediv)
+[1;32m   3995[0m               if self.get_unsafe(n) else zero for n in range(self.degree() + 1)]
+[1;32m   3996[0m return S(p)
+
+File [0;32m/ext/sage/9.7/src/sage/structure/coerce.pyx:1204[0m, in [0;36msage.structure.coerce.CoercionModel.bin_op[0;34m()[0m
+[1;32m   1202[0m     self._record_exception()
+[1;32m   1203[0m else:
+[0;32m-> 1204[0m     return PyObject_CallObject(op, xy)
+[1;32m   1205[0m 
+[1;32m   1206[0m if op is mul:
+
+File [0;32m/ext/sage/9.7/src/sage/structure/element.pyx:1737[0m, in [0;36msage.structure.element.Element.__truediv__[0;34m()[0m
+[1;32m   1735[0m cdef int cl = classify_elements(left, right)
+[1;32m   1736[0m if HAVE_SAME_PARENT(cl):
+[0;32m-> 1737[0m     return (<Element>left)._div_(right)
+[1;32m   1738[0m if BOTH_ARE_ELEMENT(cl):
+[1;32m   1739[0m     return coercion_model.bin_op(left, right, truediv)
+
+File [0;32m/ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623[0m, in [0;36msage.rings.finite_rings.integer_mod.IntegerMod_int._div_[0;34m()[0m
+[1;32m   2621[0m right_inverse = self.__modulus.inverses[(<IntegerMod_int>right).ivalue]
+[1;32m   2622[0m if right_inverse is None:
+[0;32m-> 2623[0m     raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist")
+[1;32m   2624[0m else:
+[1;32m   2625[0m     return self._new_c((self.ivalue * (<IntegerMod_int>right_inverse).ivalue) % self.__modulus.int32)
+
+[0;31mZeroDivisionError[0m: inverse of Mod(0, 3) does not exist
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m(C.x^[0;38;5;20;1m5[0m*C.y.diffn()).int[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[2D[0m([0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[3D[0;38;5;28min[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0mi[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[35D[0m[J[0;94msage: [0m(C.x^[0;38;5;20;1m5[0m*C.y.diffn()).cartier()[35D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m(x^4/y) dx
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+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m[x, 2*x^2 + 1, x]
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mR[0;38;5;241mxt.<t> = PolynomialRing(Rx)[27D[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[0m.[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m<[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0madic_expansion[0;38;5;16;48;5;152m([0mx^[0;38;5;20;1m7[0m, x^[0;38;5;20;1m3[0m - x[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[28D[0m((C.x^[0;38;5;20;1m5[0m - C.x^[0;38;5;20;1m3[0m)*C.y.diffn()).cartier[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[38D[0mC.x^[0;38;5;20;1m5[0m*C.y.diffn()).cartier([2Cinv_ca[Ctier[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[16D[0;38;5;16;48;5;152m()[0m[K[?7h[0m[?12l[?25h[?25l[?7l[9D[0mint[0;38;5;16;48;5;152m()[0m[K[?7h[0m[?12l[?25h[?25l[?7l[22D[0my/C.x^[0;38;5;20;1m7[0m).di[Cfn[0;38;5;16;48;5;152m()[0m[K[?7h[0m[?12l[?25h[?25l[?7l[10D[0;38;5;20;1m5[9C[?7h[0m[?12l[?25h[?25l[?7l[7D[0mexpa[Csion_at_infty[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[23D[0;38;5;20;1m4[22C[?7h[0m[?12l[?25h[?25l[?7l[24D[0m).expansion_at_infty[0;38;5;16;48;5;152m()[0m[K[?7h[0m[?12l[?25h[?25l[?7l[22D[0m^[0;38;5;20;1m3[0m).expansion_at_infty[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[32D[0mC.de_rham_basis[0;38;5;16;48;5;152m()[0m[K[?7h[0m[?12l[?25h[?25l[?7l[17D[0mFF[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m = [0;38;5;24msum[0;38;5;16;48;5;152m([0ma*t^i [0;38;5;28;1mfor[0m i, a [0;38;5;28min[0m [0;38;5;24menumerate[0m(coo)[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[37D[0mRxt[C[0;38;5;20;1m0[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[11D[0mcoo = adic_expansion[0;38;5;16;48;5;152m([0m(x^[0;38;5;20;1m63[0m + [0;38;5;20;1m2[0m*x^[0;38;5;20;1m55[0m + [0;38;5;20;1m2[0m*x^[0;38;5;20;1m39[0m + x^[0;38;5;20;1m31[0m), x^[0;38;5;20;1m3[0m - x[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[62D[0mFF = Rxt[0;38;5;16;48;5;152m([0;38;5;20;1m0[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[6D[0;38;5;24msum[C[0ma*t^i [0;38;5;28;1mfor[0m i, a [0;38;5;28min[0m [0;38;5;24menumerate[0m(coo)[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[34D[0m([27C[0;38;5;16;48;5;152m([3C)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[5D[0m([3C[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[9D[0menumerat[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[0mi[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[3D[0mfo[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[3D[0msu[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mx[0;38;5;241mx[?7h[0m[?12l[?25h[?25l[?7l[7D[0m[J[0;94msage: [0mx[7D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mx
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mp[0;38;5;241marent(parent(lau))[18D[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0mx[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;16;48;5;152m([C)[?7h[0m[?12l[?25h[?25l[?7l[15D[0m[J[0;94msage: [0mparent(x)[15D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mUnivariate Polynomial Ring in x over Finite Field of size 3
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mR[0;38;5;241mxt.<t> = PolynomialRing(Rx)[27D[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[0m.[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m<[?7h[0m[?12l[?25h[?25l[?7l[0m>[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mx>[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mP[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0ml[?7h[0m[?12l[?25h[?25l[?7l[0my[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0mm[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0ml[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004lComputing 0. basis element
+Computing 1. basis element
+Computing 0. basis element
+[0;31m---------------------------------------------------------------------------[0m
+[0;31mIndexError[0m                                Traceback (most recent call last)
+Input [0;32mIn [47][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mload[49m[43m([49m[38;5;124;43m'[39;49m[38;5;124;43minit.sage[39;49m[38;5;124;43m'[39;49m[43m)[49m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:32[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:12[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m<string>:41[0m, in [0;36mcrystalline_cohomology_basis[0;34m(self, prec, info)[0m
+
+File [0;32m<string>:29[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class, prec)[0m
+
+File [0;32m<string>:7[0m, in [0;36mdecomposition_g0_g8[0;34m(fct, prec)[0m
+
+File [0;32m<string>:107[0m, in [0;36mcoordinates[0;34m(self, basis, basis_holo, prec)[0m
+
+File [0;32m<string>:79[0m, in [0;36mserre_duality_pairing[0;34m(self, fct, prec)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544[0m, in [0;36msage.rings.laurent_series_ring_element.LaurentSeries.__getitem__[0;34m()[0m
+[1;32m    542[0m         return type(self)(self._parent, f, self.__n)
+[1;32m    543[0m 
+[0;32m--> 544[0m     return self.__u[i - self.__n]
+[1;32m    545[0m 
+[1;32m    546[0m def __iter__(self):
+
+File [0;32m/ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453[0m, in [0;36msage.rings.power_series_poly.PowerSeries_poly.__getitem__[0;34m()[0m
+[1;32m    451[0m         return self.base_ring().zero()
+[1;32m    452[0m     else:
+[0;32m--> 453[0m         raise IndexError("coefficient not known")
+[1;32m    454[0m return self.__f[n]
+[1;32m    455[0m 
+
+[0;31mIndexError[0m: coefficient not known
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mad[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004lComputing 0. basis element
+Computing 1. basis element
+Computing 0. basis element
+Computing 1. basis element
+Computing 2. basis element
+Computing 3. basis element
+[0;31m---------------------------------------------------------------------------[0m
+[0;31mIndexError[0m                                Traceback (most recent call last)
+Input [0;32mIn [48][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mload[49m[43m([49m[38;5;124;43m'[39;49m[38;5;124;43minit.sage[39;49m[38;5;124;43m'[39;49m[43m)[49m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:32[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:12[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m<string>:41[0m, in [0;36mcrystalline_cohomology_basis[0;34m(self, prec, info)[0m
+
+File [0;32m<string>:32[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class, prec)[0m
+
+File [0;32m<string>:36[0m, in [0;36mdecomposition_omega0_omega8[0;34m(omega, prec)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/functional.py:585[0m, in [0;36msymbolic_sum[0;34m(expression, *args, **kwds)[0m
+[1;32m    583[0m     [38;5;28;01mreturn[39;00m expression[38;5;241m.[39msum([38;5;241m*[39margs, [38;5;241m*[39m[38;5;241m*[39mkwds)
+[1;32m    584[0m [38;5;28;01melif[39;00m [38;5;28mmax[39m([38;5;28mlen[39m(args),[38;5;28mlen[39m(kwds)) [38;5;241m<[39m[38;5;241m=[39m [38;5;241m1[39m:
+[0;32m--> 585[0m     [38;5;28;01mreturn[39;00m [38;5;28;43msum[39;49m[43m([49m[43mexpression[49m[43m,[49m[43m [49m[38;5;241;43m*[39;49m[43margs[49m[43m,[49m[43m [49m[38;5;241;43m*[39;49m[38;5;241;43m*[39;49m[43mkwds[49m[43m)[49m
+[1;32m    586[0m [38;5;28;01melse[39;00m:
+[1;32m    587[0m     [38;5;28;01mfrom[39;00m [38;5;21;01msage[39;00m[38;5;21;01m.[39;00m[38;5;21;01msymbolic[39;00m[38;5;21;01m.[39;00m[38;5;21;01mring[39;00m [38;5;28;01mimport[39;00m SR
+
+File [0;32m<string>:36[0m, in [0;36m<genexpr>[0;34m(.0)[0m
+
+File [0;32m<string>:156[0m, in [0;36mresidue[0;34m(self, place, prec)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544[0m, in [0;36msage.rings.laurent_series_ring_element.LaurentSeries.__getitem__[0;34m()[0m
+[1;32m    542[0m         return type(self)(self._parent, f, self.__n)
+[1;32m    543[0m 
+[0;32m--> 544[0m     return self.__u[i - self.__n]
+[1;32m    545[0m 
+[1;32m    546[0m def __iter__(self):
+
+File [0;32m/ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453[0m, in [0;36msage.rings.power_series_poly.PowerSeries_poly.__getitem__[0;34m()[0m
+[1;32m    451[0m         return self.base_ring().zero()
+[1;32m    452[0m     else:
+[0;32m--> 453[0m         raise IndexError("coefficient not known")
+[1;32m    454[0m return self.__f[n]
+[1;32m    455[0m 
+
+[0;31mIndexError[0m: coefficient not known
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mad[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004lComputing 0. basis element
+^C[0;31m---------------------------------------------------------------------------[0m
+[0;31mAttributeError[0m                            Traceback (most recent call last)
+File [0;32m<string>:58[0m, in [0;36m__mul__[0;34m(self, other)[0m
+
+[0;31mAttributeError[0m: 'superelliptic_form' object has no attribute 'function'
+
+During handling of the above exception, another exception occurred:
+
+[0;31mKeyboardInterrupt[0m                         Traceback (most recent call last)
+Input [0;32mIn [49][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mload[49m[43m([49m[38;5;124;43m'[39;49m[38;5;124;43minit.sage[39;49m[38;5;124;43m'[39;49m[43m)[49m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:32[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:11[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m<string>:41[0m, in [0;36mcrystalline_cohomology_basis[0;34m(self, prec, info)[0m
+
+File [0;32m<string>:25[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class, prec)[0m
+
+File [0;32m<string>:15[0m, in [0;36mde_rham_witt_lift_form8[0;34m(omega)[0m
+
+File [0;32m<string>:90[0m, in [0;36mdiffn[0;34m(self, dy_w)[0m
+
+File [0;32m<string>:73[0m, in [0;36mdiffn[0;34m(self, dy_w)[0m
+
+File [0;32m<string>:177[0m, in [0;36mdy_w[0;34m(C)[0m
+
+File [0;32m<string>:65[0m, in [0;36m__mul__[0;34m(self, other)[0m
+
+File [0;32m<string>:65[0m, in [0;36m__mul__[0;34m(self, other)[0m
+
+File [0;32m<string>:7[0m, in [0;36m__init__[0;34m(self, C, g)[0m
+
+File [0;32m<string>:271[0m, in [0;36mreduction_form[0;34m(C, g)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/structure/parent.pyx:897[0m, in [0;36msage.structure.parent.Parent.__call__[0;34m()[0m
+[1;32m    895[0m if mor is not None:
+[1;32m    896[0m     if no_extra_args:
+[0;32m--> 897[0m         return mor._call_(x)
+[1;32m    898[0m     else:
+[1;32m    899[0m         return mor._call_with_args(x, args, kwds)
+
+File [0;32m/ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156[0m, in [0;36msage.structure.coerce_maps.DefaultConvertMap_unique._call_[0;34m()[0m
+[1;32m    154[0m cdef Parent C = self._codomain
+[1;32m    155[0m try:
+[0;32m--> 156[0m     return C._element_constructor(x)
+[1;32m    157[0m except Exception:
+[1;32m    158[0m     if print_warnings:
+
+File [0;32m/ext/sage/9.7/src/sage/rings/fraction_field.py:638[0m, in [0;36mFractionField_generic._element_constructor_[0;34m(self, x, y, coerce)[0m
+[1;32m    636[0m ring_one [38;5;241m=[39m [38;5;28mself[39m[38;5;241m.[39mring()[38;5;241m.[39mone()
+[1;32m    637[0m [38;5;28;01mtry[39;00m:
+[0;32m--> 638[0m     [38;5;28;01mreturn[39;00m [38;5;28;43mself[39;49m[38;5;241;43m.[39;49m[43m_element_class[49m[43m([49m[38;5;28;43mself[39;49m[43m,[49m[43m [49m[43mx[49m[43m,[49m[43m [49m[43mring_one[49m[43m,[49m[43m [49m[43mcoerce[49m[38;5;241;43m=[39;49m[43mcoerce[49m[43m)[49m
+[1;32m    639[0m [38;5;28;01mexcept[39;00m ([38;5;167;01mTypeError[39;00m, [38;5;167;01mValueError[39;00m):
+[1;32m    640[0m     [38;5;28;01mpass[39;00m
+
+File [0;32m/ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114[0m, in [0;36msage.rings.fraction_field_element.FractionFieldElement.__init__[0;34m()[0m
+[1;32m    112[0m FieldElement.__init__(self, parent)
+[1;32m    113[0m if coerce:
+[0;32m--> 114[0m     self.__numerator   = parent.ring()(numerator)
+[1;32m    115[0m     self.__denominator = parent.ring()(denominator)
+[1;32m    116[0m else:
+
+File [0;32m/ext/sage/9.7/src/sage/structure/parent.pyx:897[0m, in [0;36msage.structure.parent.Parent.__call__[0;34m()[0m
+[1;32m    895[0m if mor is not None:
+[1;32m    896[0m     if no_extra_args:
+[0;32m--> 897[0m         return mor._call_(x)
+[1;32m    898[0m     else:
+[1;32m    899[0m         return mor._call_with_args(x, args, kwds)
+
+File [0;32m/ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156[0m, in [0;36msage.structure.coerce_maps.DefaultConvertMap_unique._call_[0;34m()[0m
+[1;32m    154[0m cdef Parent C = self._codomain
+[1;32m    155[0m try:
+[0;32m--> 156[0m     return C._element_constructor(x)
+[1;32m    157[0m except Exception:
+[1;32m    158[0m     if print_warnings:
+
+File [0;32m/ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1009[0m, in [0;36msage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_[0;34m()[0m
+[1;32m   1007[0m try:
+[1;32m   1008[0m     # now try calling the base ring's __call__ methods
+[0;32m-> 1009[0m     element = self.base_ring()(element)
+[1;32m   1010[0m     _p = p_NSet(sa2si(element,_ring), _ring)
+[1;32m   1011[0m     return new_MP(self,_p)
+
+File [0;32m/ext/sage/9.7/src/sage/structure/parent.pyx:897[0m, in [0;36msage.structure.parent.Parent.__call__[0;34m()[0m
+[1;32m    895[0m if mor is not None:
+[1;32m    896[0m     if no_extra_args:
+[0;32m--> 897[0m         return mor._call_(x)
+[1;32m    898[0m     else:
+[1;32m    899[0m         return mor._call_with_args(x, args, kwds)
+
+File [0;32m/ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156[0m, in [0;36msage.structure.coerce_maps.DefaultConvertMap_unique._call_[0;34m()[0m
+[1;32m    154[0m cdef Parent C = self._codomain
+[1;32m    155[0m try:
+[0;32m--> 156[0m     return C._element_constructor(x)
+[1;32m    157[0m except Exception:
+[1;32m    158[0m     if print_warnings:
+
+File [0;32m/ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185[0m, in [0;36mIntegerModRing_generic._element_constructor_[0;34m(self, x)[0m
+[1;32m   1143[0m [38;5;124;03m"""[39;00m
+[1;32m   1144[0m [38;5;124;03mTESTS::[39;00m
+[1;32m   1145[0m 
+[0;32m   (...)[0m
+[1;32m   1182[0m [38;5;124;03m    True[39;00m
+[1;32m   1183[0m [38;5;124;03m"""[39;00m
+[1;32m   1184[0m [38;5;28;01mtry[39;00m:
+[0;32m-> 1185[0m     [38;5;28;01mreturn[39;00m [43minteger_mod[49m[38;5;241;43m.[39;49m[43mIntegerMod[49m[43m([49m[38;5;28;43mself[39;49m[43m,[49m[43m [49m[43mx[49m[43m)[49m
+[1;32m   1186[0m [38;5;28;01mexcept[39;00m ([38;5;167;01mNotImplementedError[39;00m, PariError):
+[1;32m   1187[0m     [38;5;28;01mraise[39;00m [38;5;167;01mTypeError[39;00m([38;5;124m"[39m[38;5;124merror coercing to finite field[39m[38;5;124m"[39m)
+
+File [0;32m/ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201[0m, in [0;36msage.rings.finite_rings.integer_mod.IntegerMod[0;34m()[0m
+[1;32m    199[0m         return a
+[1;32m    200[0m t = modulus.element_class()
+[0;32m--> 201[0m return t(parent, value)
+[1;32m    202[0m 
+[1;32m    203[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:380[0m, in [0;36msage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__[0;34m()[0m
+[1;32m    378[0m else:
+[1;32m    379[0m     try:
+[0;32m--> 380[0m         z = integer_ring.Z(value)
+[1;32m    381[0m     except (TypeError, ValueError):
+[1;32m    382[0m         from sage.structure.element import Expression
+
+File [0;32m/ext/sage/9.7/src/sage/structure/parent.pyx:897[0m, in [0;36msage.structure.parent.Parent.__call__[0;34m()[0m
+[1;32m    895[0m if mor is not None:
+[1;32m    896[0m     if no_extra_args:
+[0;32m--> 897[0m         return mor._call_(x)
+[1;32m    898[0m     else:
+[1;32m    899[0m         return mor._call_with_args(x, args, kwds)
+
+File [0;32m/ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287[0m, in [0;36msage.structure.coerce_maps.NamedConvertMap._call_[0;34m()[0m
+[1;32m    285[0m     raise TypeError("Cannot coerce {} to {}".format(x, C))
+[1;32m    286[0m cdef Map m
+[0;32m--> 287[0m cdef Element e = method(C)
+[1;32m    288[0m if e is None:
+[1;32m    289[0m     raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x)))
+
+File [0;32m/ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:831[0m, in [0;36msage.rings.fraction_field_element.FractionFieldElement._conversion[0;34m()[0m
+[1;32m    829[0m     return R(self.__numerator)
+[1;32m    830[0m else:
+[0;32m--> 831[0m     self.reduce()
+[1;32m    832[0m     num = R(self.__numerator)
+[1;32m    833[0m     inv_den = R(self.__denominator).inverse_of_unit()
+
+File [0;32m/ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:1239[0m, in [0;36msage.rings.fraction_field_element.FractionFieldElement_1poly_field.reduce[0;34m()[0m
+[1;32m   1237[0m if self._is_reduced:
+[1;32m   1238[0m     return
+[0;32m-> 1239[0m super(self.__class__, self).reduce()
+[1;32m   1240[0m self.normalize_leading_coefficients()
+[1;32m   1241[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:164[0m, in [0;36msage.rings.fraction_field_element.FractionFieldElement.reduce[0;34m()[0m
+[1;32m    162[0m     return codomain.coerce(nnum/nden)
+[1;32m    163[0m 
+[0;32m--> 164[0m cpdef reduce(self):
+[1;32m    165[0m     """
+[1;32m    166[0m     Reduce this fraction.
+
+File [0;32m/ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:197[0m, in [0;36msage.rings.fraction_field_element.FractionFieldElement.reduce[0;34m()[0m
+[1;32m    195[0m     return
+[1;32m    196[0m try:
+[0;32m--> 197[0m     g = self.__numerator.gcd(self.__denominator)
+[1;32m    198[0m     if not g.is_unit():
+[1;32m    199[0m         self.__numerator //= g
+
+File [0;32m/ext/sage/9.7/src/sage/structure/element.pyx:4494[0m, in [0;36msage.structure.element.coerce_binop.new_method[0;34m()[0m
+[1;32m   4492[0m def new_method(self, other, *args, **kwargs):
+[1;32m   4493[0m     if have_same_parent(self, other):
+[0;32m-> 4494[0m         return method(self, other, *args, **kwargs)
+[1;32m   4495[0m     else:
+[1;32m   4496[0m         a, b = coercion_model.canonical_coercion(self, other)
+
+File [0;32m/ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:4913[0m, in [0;36msage.rings.polynomial.polynomial_element.Polynomial.gcd[0;34m()[0m
+[1;32m   4911[0m         raise NotImplementedError("%s does not provide a gcd implementation for univariate polynomials"%self._parent._base)
+[1;32m   4912[0m     else:
+[0;32m-> 4913[0m         return doit(self, other)
+[1;32m   4914[0m 
+[1;32m   4915[0m @coerce_binop
+
+File [0;32m/ext/sage/9.7/src/sage/rings/fraction_field.py:944[0m, in [0;36mFractionField_generic._gcd_univariate_polynomial[0;34m(self, f, g)[0m
+[1;32m    942[0m Pol [38;5;241m=[39m f[38;5;241m.[39mparent()
+[1;32m    943[0m Num [38;5;241m=[39m Pol[38;5;241m.[39mchange_ring([38;5;28mself[39m[38;5;241m.[39mbase())
+[0;32m--> 944[0m f1 [38;5;241m=[39m [43mNum[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mnumerator[49m[43m([49m[43m)[49m[43m)[49m
+[1;32m    945[0m g1 [38;5;241m=[39m Num(g[38;5;241m.[39mnumerator())
+[1;32m    946[0m [38;5;28;01mreturn[39;00m Pol(f1[38;5;241m.[39mgcd(g1))[38;5;241m.[39mmonic()
+
+File [0;32m/ext/sage/9.7/src/sage/structure/parent.pyx:897[0m, in [0;36msage.structure.parent.Parent.__call__[0;34m()[0m
+[1;32m    895[0m if mor is not None:
+[1;32m    896[0m     if no_extra_args:
+[0;32m--> 897[0m         return mor._call_(x)
+[1;32m    898[0m     else:
+[1;32m    899[0m         return mor._call_with_args(x, args, kwds)
+
+File [0;32m/ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156[0m, in [0;36msage.structure.coerce_maps.DefaultConvertMap_unique._call_[0;34m()[0m
+[1;32m    154[0m cdef Parent C = self._codomain
+[1;32m    155[0m try:
+[0;32m--> 156[0m     return C._element_constructor(x)
+[1;32m    157[0m except Exception:
+[1;32m    158[0m     if print_warnings:
+
+File [0;32m/ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:452[0m, in [0;36mPolynomialRing_general._element_constructor_[0;34m(self, x, check, is_gen, construct, **kwds)[0m
+[1;32m    450[0m     [38;5;28;01mexcept[39;00m [38;5;167;01mNameError[39;00m:
+[1;32m    451[0m         [38;5;28;01mraise[39;00m [38;5;167;01mTypeError[39;00m([38;5;124m"[39m[38;5;124mUnable to coerce string[39m[38;5;124m"[39m)
+[0;32m--> 452[0m [38;5;28;01melif[39;00m [38;5;28;43misinstance[39;49m[43m([49m[43mx[49m[43m,[49m[43m [49m[43mFractionFieldElement[49m[43m)[49m:
+[1;32m    453[0m     [38;5;28;01mif[39;00m x[38;5;241m.[39mdenominator()[38;5;241m.[39mis_unit():
+[1;32m    454[0m         x [38;5;241m=[39m x[38;5;241m.[39mnumerator() [38;5;241m*[39m x[38;5;241m.[39mdenominator()[38;5;241m.[39minverse_of_unit()
+
+File [0;32msrc/cysignals/signals.pyx:310[0m, in [0;36mcysignals.signals.python_check_interrupt[0;34m()[0m
+
+[0;31mKeyboardInterrupt[0m: 
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mt[0;38;5;241m^(-8).integral()[16D[?7h[0m[?12l[?25h[?25l[?7l[0mr[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;28;1mtry[?7h[0m[?12l[?25h[?25l[?7l[3D[0mtryL[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;28;1mtry[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m:[?7h[0m[?12l[?25h[?25l[?7l[10D[0;94msage: [0;38;5;28;1mtry[0m:[0m

+[0;94m....: [6D[10C[?7h[0m[?12l[?25h[?25l[?7l[0mp[0;38;5;241mrint(B1[i].regular_form())[26D[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;24mprint[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m/[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m([3C)[?7h[0m[?12l[?25h[?25l[?7l[20D[0;94m....: [0m    [0;38;5;24mprint[0m([0;38;5;20;1m0[0m/[0;38;5;20;1m0[0m)[0m

+[0;94m....: [6D[10C[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[0mp[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[5D[0m[K[4C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[A[9C[0;38;5;16;48;5;152m([3C)[0m

+[0m [0m[K[A[19C[?7h[0m[?12l[?25h[?25l[?7l[5D[0m([3C)e[?7h[0m[?12l[?25h[?25l[?7l[6D[0;38;5;16;48;5;152m([3C)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[5D[0m([3C)[0m

+[0;94m....: [4C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0me[0;38;5;241mta2 - B[1][10D[?7h[0m[?12l[?25h[?25l[?7l[0mx[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0mp[?7h[0m[?12l[?25h[?25l[?7l[5D[0;38;5;28;1mexcept[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;125;1mIndexError[?7h[0m[?12l[?25h[?25l[?7l[0m:[?7h[0m[?12l[?25h[?25l[?7l[24D[0;94m....: [0;38;5;28;1mexcept[0m [0;38;5;125;1mIndexError[0m:[0m

+[0;94m....: [6D[10C[?7h[0m[?12l[?25h[?25l[?7l[0mp[0;38;5;241mrint(B1[i].regular_form())[26D[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;24mprint[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;160;48;5;231m"[0;38;5;241m( " + str(cocycle.omega0.regular_form()) + ", " + str(cocycle.f) + " )")[72D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;160;48;5;231ma[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;160;48;5;231m"[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m([3C)[?7h[0m[?12l[?25h[?25l[?7l[20D[0;94m....: [0m    [0;38;5;24mprint[0m([0;38;5;160;48;5;231m"a"[0m)[0m

+[0;94m....: [6D[10C[?7h[0m[?12l[?25h[?25l[?7l[4A[10D[0m[J[0;94msage: [0;38;5;28;1mtry[0m:[0m

+[0;94m....: [0m    [0;38;5;24mprint[0m([0;38;5;20;1m0[0m/[0;38;5;20;1m0[0m)[0m

+[0;94m....: [0;38;5;28;1mexcept[0m [0;38;5;125;1mIndexError[0m:[0m

+[0;94m....: [0m    [0;38;5;24mprint[0m([0;38;5;160;48;5;231m"a"[0m)[0m

+[0;94m....: [6D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mZeroDivisionError[0m                         Traceback (most recent call last)
+Input [0;32mIn [50][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[1;32m      1[0m [38;5;28;01mtry[39;00m:
+[0;32m----> 2[0m     [38;5;28mprint[39m([43mInteger[49m[43m([49m[38;5;241;43m0[39;49m[43m)[49m[38;5;241;43m/[39;49m[43mInteger[49m[43m([49m[38;5;241;43m0[39;49m[43m)[49m)
+[1;32m      3[0m [38;5;28;01mexcept[39;00m [38;5;167;01mIndexError[39;00m:
+[1;32m      4[0m     [38;5;28mprint[39m([38;5;124m"[39m[38;5;124ma[39m[38;5;124m"[39m)
+
+File [0;32m/ext/sage/9.7/src/sage/rings/integer.pyx:2022[0m, in [0;36msage.rings.integer.Integer.__truediv__[0;34m()[0m
+[1;32m   2020[0m if type(left) is type(right):
+[1;32m   2021[0m     if mpz_sgn((<Integer>right).value) == 0:
+[0;32m-> 2022[0m         raise ZeroDivisionError("rational division by zero")
+[1;32m   2023[0m     x = <Rational> Rational.__new__(Rational)
+[1;32m   2024[0m     mpq_div_zz(x.value, (<Integer>left).value, (<Integer>right).value)
+
+[0;31mZeroDivisionError[0m: rational division by zero
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[6D[0;94msage: [0;38;5;28;1mtry[0m:[0m

+[0;94m....: [0m    [0;38;5;24mprint[0m([0;38;5;20;1m0[0m/[0;38;5;20;1m0[0m)[0m

+[0;94m....: [0;38;5;28;1mexcept[0m [0;38;5;125;1mIndexError[0m:[0m

+[0;94m....: [0m    [0;38;5;24mprint[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m"a"[0;38;5;16;48;5;152m)[20D[20C[?7h[0m[?12l[?25h[?25l[?7l[5D[0m([3C)[A[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[5D[0mIndeError:[0m[K[6D[?7h[0m[?12l[?25h[?25l[?7l[0mEr[Cor:[0m[K[6D[?7h[0m[?12l[?25h[?25l[?7l[0mEr[Cor:[0m[K[6D[?7h[0m[?12l[?25h[?25l[?7l[0mEr[Cor:[0m[K[6D[?7h[0m[?12l[?25h[?25l[?7l[0mEr[Cor:[0m[K[6D[?7h[0m[?12l[?25h[?25l[?7l[0mZE[Cror:[6D[?7h[0m[?12l[?25h[?25l[?7l[0meE[Cror:[6D[?7h[0m[?12l[?25h[?25l[?7l[0mrE[Cror:[6D[?7h[0m[?12l[?25h[?25l[?7l[0moE[Cror:[6D[?7h[0m[?12l[?25h[?25l[?7l[0mDE[Cror:[6D[?7h[0m[?12l[?25h[?25l[?7l[0miE[Cror:[6D[?7h[0m[?12l[?25h[?25l[?7l[0mvE[Cror:[6D[?7h[0m[?12l[?25h[?25l[?7l[0miE[Cror:[6D[?7h[0m[?12l[?25h[?25l[?7l[0msE[Cror:[6D[?7h[0m[?12l[?25h[?25l[?7l[0miE[Cror:[6D[?7h[0m[?12l[?25h[?25l[?7l[0moE[Cror:[6D[?7h[0m[?12l[?25h[?25l[?7l[11D[0;38;5;125;1mZeroDivisionError[0m:[6D[?7h[0m[?12l[?25h[?25l[?7l[5C[?7h[0m[?12l[?25h[?25l[?7l[0m

+[15C[0;38;5;210;48;5;88m([3C[0;38;5;16;48;5;152m)[5D[?7h[0m[?12l[?25h[?25l[?7l[0m([3C)[3D[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;16;48;5;152m([3C)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[20D[0;94m....: [0m    [0;38;5;24mprint[0m([0;38;5;160;48;5;231m"a"[0m)[0m

+[0;94m....: [6D[10C[?7h[0m[?12l[?25h[?25l[?7l[4A[10D[0m[J[0;94msage: [0;38;5;28;1mtry[0m:[0m

+[0;94m....: [0m    [0;38;5;24mprint[0m([0;38;5;20;1m0[0m/[0;38;5;20;1m0[0m)[0m

+[0;94m....: [0;38;5;28;1mexcept[0m [0;38;5;125;1mZeroDivisionError[0m:[0m

+[0;94m....: [0m    [0;38;5;24mprint[0m([0;38;5;160;48;5;231m"a"[0m)[0m

+[0;94m....: [6D[0m

+[J[?7h[0m[?12l[?25h[?2004la
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004lComputing 0. basis element
+Computing 1. basis element
+Computing 0. basis element
+Computing 1. basis element
+Computing 2. basis element
+Computing 3. basis element
+Computing 4. basis element
+Computing 5. basis element
+Computing 6. basis element
+Computing 7. basis element
+^C[0;31m---------------------------------------------------------------------------[0m
+[0;31mKeyboardInterrupt[0m                         Traceback (most recent call last)
+File [0;32m<string>:60[0m, in [0;36m__mul__[0;34m(self, other)[0m
+
+File [0;32m<string>:14[0m, in [0;36m__init__[0;34m(self, C, g)[0m
+
+File [0;32m<string>:228[0m, in [0;36mreduction[0;34m(C, g)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/structure/parent.pyx:897[0m, in [0;36msage.structure.parent.Parent.__call__[0;34m()[0m
+[1;32m    896[0m if no_extra_args:
+[0;32m--> 897[0m     return mor._call_(x)
+[1;32m    898[0m else:
+
+File [0;32m/ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156[0m, in [0;36msage.structure.coerce_maps.DefaultConvertMap_unique._call_[0;34m()[0m
+[1;32m    155[0m try:
+[0;32m--> 156[0m     return C._element_constructor(x)
+[1;32m    157[0m except Exception:
+
+File [0;32m/ext/sage/9.7/src/sage/rings/fraction_field.py:638[0m, in [0;36mFractionField_generic._element_constructor_[0;34m(self, x, y, coerce)[0m
+[1;32m    637[0m [38;5;28;01mtry[39;00m:
+[0;32m--> 638[0m     [38;5;28;01mreturn[39;00m [38;5;28;43mself[39;49m[38;5;241;43m.[39;49m[43m_element_class[49m[43m([49m[38;5;28;43mself[39;49m[43m,[49m[43m [49m[43mx[49m[43m,[49m[43m [49m[43mring_one[49m[43m,[49m[43m [49m[43mcoerce[49m[38;5;241;43m=[39;49m[43mcoerce[49m[43m)[49m
+[1;32m    639[0m [38;5;28;01mexcept[39;00m ([38;5;167;01mTypeError[39;00m, [38;5;167;01mValueError[39;00m):
+
+File [0;32m/ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114[0m, in [0;36msage.rings.fraction_field_element.FractionFieldElement.__init__[0;34m()[0m
+[1;32m    113[0m if coerce:
+[0;32m--> 114[0m     self.__numerator   = parent.ring()(numerator)
+[1;32m    115[0m     self.__denominator = parent.ring()(denominator)
+
+File [0;32m/ext/sage/9.7/src/sage/structure/parent.pyx:897[0m, in [0;36msage.structure.parent.Parent.__call__[0;34m()[0m
+[1;32m    896[0m if no_extra_args:
+[0;32m--> 897[0m     return mor._call_(x)
+[1;32m    898[0m else:
+
+File [0;32m/ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156[0m, in [0;36msage.structure.coerce_maps.DefaultConvertMap_unique._call_[0;34m()[0m
+[1;32m    155[0m try:
+[0;32m--> 156[0m     return C._element_constructor(x)
+[1;32m    157[0m except Exception:
+
+File [0;32m/ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003[0m, in [0;36msage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_[0;34m()[0m
+[1;32m   1002[0m try:
+[0;32m-> 1003[0m     return self(str(element))
+[1;32m   1004[0m except TypeError:
+
+File [0;32m/ext/sage/9.7/src/sage/structure/parent.pyx:897[0m, in [0;36msage.structure.parent.Parent.__call__[0;34m()[0m
+[1;32m    896[0m if no_extra_args:
+[0;32m--> 897[0m     return mor._call_(x)
+[1;32m    898[0m else:
+
+File [0;32m/ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156[0m, in [0;36msage.structure.coerce_maps.DefaultConvertMap_unique._call_[0;34m()[0m
+[1;32m    155[0m try:
+[0;32m--> 156[0m     return C._element_constructor(x)
+[1;32m    157[0m except Exception:
+
+File [0;32m/ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:991[0m, in [0;36msage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_[0;34m()[0m
+[1;32m    990[0m         element = element.replace("^","**")
+[0;32m--> 991[0m         element = eval(element, d, {})
+[1;32m    992[0m except (SyntaxError, NameError):
+
+File [0;32m<string>:1[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32msrc/cysignals/signals.pyx:310[0m, in [0;36mcysignals.signals.python_check_interrupt[0;34m()[0m
+
+[0;31mKeyboardInterrupt[0m: 
+
+During handling of the above exception, another exception occurred:
+
+[0;31mAttributeError[0m                            Traceback (most recent call last)
+Input [0;32mIn [52][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mload[49m[43m([49m[38;5;124;43m'[39;49m[38;5;124;43minit.sage[39;49m[38;5;124;43m'[39;49m[43m)[49m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:32[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:12[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m<string>:44[0m, in [0;36mcrystalline_cohomology_basis[0;34m(self, prec, info)[0m
+
+File [0;32m<string>:26[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class, prec)[0m
+
+File [0;32m<string>:90[0m, in [0;36mdiffn[0;34m(self, dy_w)[0m
+
+File [0;32m<string>:73[0m, in [0;36mdiffn[0;34m(self, dy_w)[0m
+
+File [0;32m<string>:177[0m, in [0;36mdy_w[0;34m(C)[0m
+
+File [0;32m<string>:149[0m, in [0;36mauxilliary_derivative[0;34m(P)[0m
+
+File [0;32m<string>:149[0m, in [0;36mauxilliary_derivative[0;34m(P)[0m
+
+File [0;32m<string>:147[0m, in [0;36mauxilliary_derivative[0;34m(P)[0m
+
+File [0;32m<string>:35[0m, in [0;36m__sub__[0;34m(self, other)[0m
+
+File [0;32m<string>:31[0m, in [0;36m__add__[0;34m(self, other)[0m
+
+File [0;32m<string>:63[0m, in [0;36m__mul__[0;34m(self, other)[0m
+
+[0;31mAttributeError[0m: 'superelliptic_function' object has no attribute 'form'
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mq[?7h[0m[?12l[?25h[?25l[?7l[0mu[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[12D[0m[J[0;94msage: [0mquit()[12D[0m

+[J[?7h[0m[?12l[?25h[?2004l[23;0t
+]0;~/Research/2021 De Rham/DeRhamComputation/sage[01;34m~/Research/2021 De Rham/DeRhamComputation/sage[00m$ g[Kcd ..
+]0;~/Research/2021 De Rham/DeRhamComputation[01;34m~/Research/2021 De Rham/DeRhamComputation[00m$ git 
\ No newline at end of file
diff --git a/sage/drafty/draft.sage b/sage/drafty/draft.sage
index 2e74027..06d0e4f 100644
--- a/sage/drafty/draft.sage
+++ b/sage/drafty/draft.sage
@@ -1,28 +1,25 @@
-p = 3
+p = 5
 m = 2
 F = GF(p)
 Rx.<x> = PolynomialRing(F)
-f = x^3 - x
+#f = (x^3 - x)^3 + x^3 - x
+f = x^3 + x
+f1 = f(x = x^5 - x)
 C = superelliptic(f, m)
-#C1 = patch(C)
-#print(C1.crystalline_cohomology_basis())
-#g1 = C1.polynomial
-#g_AS = g1(x^p - x)
-#C2 = superelliptic(g_AS, 2)
-#print(convert_super_into_AS(C2))
-#converted = (C2.x)^4 - (C2.x)^2
-#print(convert_super_fct_into_AS(converted))
-#b = C.crystalline_cohomology_basis()
-#print(autom(b[0]).coordinates(basis = b))
-#eta1 = (dy + dV(2xy) + V(x^5 \, dy), V(y/x))
-#eta1 = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).verschiebung())
-#eta2 =  (  x \, dy + 3 x^3 \, dy + dV((2x^4 + 2x^2 + 2) y) + V( (x^4 + x^2 + 1) dy), -[y/x])
-#eta2 = superelliptic_drw_cech(C.x.teichmuller()*(C.y.teichmuller()).diffn() + ((2*C.x^4 + 2*C.x^2 + 2*C.one) * C.y).verschiebung().diffn(), - (C.y/C.x).teichmuller())
-#omega8_lift0, compare = de_rham_witt_lift(C.de_rham_basis()[1])
-#omega8_lift = -(C.x^(-3)).teichmuller()*C.y.teichmuller().diffn() + 2*C.y.teichmuller()*(C.x^(-4)).teichmuller()*C.x.teichmuller().diffn()
-#eta2 = de_rham_witt_lift(C.de_rham_basis()[1])
-#b = autom(eta2)
-#print(autom(C.crystalline_cohomology_basis()[1]).coordinates())
-
+C1 = superelliptic(f1, m)
+B = C.crystalline_cohomology_basis(prec = 100, info = 1)
+B1 = C1.crystalline_cohomology_basis(prec = 500, info = 1)
 
+def crystalline_matrix(C, prec = 50):
+    B = C.crystalline_cohomology_basis(prec = prec)
+    g = C.genus()
+    p = C.characteristic
+    Zp2 = Integers(p^2)
+    M = matrix(Zp2, 2*g, 2*g)
+    for i, b in enumerate(B):
+        M[i, :] = vector(autom(b).coordinates(basis = B))
+    return M
 
+#M = crystalline_matrix(C, prec = 150)
+#print(M)
+#print(M^3)
\ No newline at end of file
diff --git a/sage/superelliptic_drw/de_rham_witt_lift.sage b/sage/superelliptic_drw/de_rham_witt_lift.sage
index 22295a5..921aed3 100644
--- a/sage/superelliptic_drw/de_rham_witt_lift.sage
+++ b/sage/superelliptic_drw/de_rham_witt_lift.sage
@@ -22,9 +22,7 @@ def de_rham_witt_lift(cech_class, prec = 50):
     fct = cech_class.f
     omega0_lift = de_rham_witt_lift_form0(omega0)
     omega8_lift = de_rham_witt_lift_form8(omega8)
-    print('omega0_lift, omega8_lift', omega0_lift, omega8_lift)
     aux = omega0_lift - omega8_lift - fct.teichmuller().diffn() # now aux is of the form (V(smth) + dV(smth), V(smth))
-    #return aux
     if aux.h1.function != 0:
         raise ValueError('Something went wrong - aux is not of the form (V(smth) + dV(smth), V(smth)).')
     decom_aux_h2 = decomposition_g0_g8(aux.h2, prec=prec) #decompose dV(smth) in aux as smth regular on U0 - smth regular on U8.
@@ -32,24 +30,21 @@ def de_rham_witt_lift(cech_class, prec = 50):
     aux_f = decom_aux_h2[2]
     aux_omega0 = decomposition_omega0_omega8(aux.omega, prec=prec)[0]
     result = superelliptic_drw_cech(omega0_lift - aux_omega0.verschiebung(), fct.teichmuller() + aux_h2.verschiebung() + aux_f.verschiebung())
-    compare = omega8_lift-decom_aux_h2[1].verschiebung().diffn() - decomposition_omega0_omega8(aux.omega, prec=prec)[1].verschiebung()
-    print("result.omega8 == compare", result.omega8 == compare)
-    print("result.omega8 - compare", result.omega8 - compare)
-    
-    #print('test:', omega0_lift - omega8_lift - fct.teichmuller().diffn() == decom_aux_h2[0].verschiebung().diffn() - decom_aux_h2[1].verschiebung().diffn() + decomposition_omega0_omega8(aux.omega, prec=prec)[0].verschiebung() - decomposition_omega0_omega8(aux.omega, prec=prec)[1].verschiebung())
-    #print('test 1:', omega0_lift - decom_aux_h2[0].verschiebung().diffn() - decomposition_omega0_omega8(aux.omega, prec=prec)[0].verschiebung() - fct.teichmuller().diffn() == omega8_lift - decom_aux_h2[1].verschiebung().diffn() - decomposition_omega0_omega8(aux.omega, prec=prec)[1].verschiebung())
-    #A = omega0_lift - decomposition_omega0_omega8(aux.omega, prec=prec)[0].verschiebung()
-    #B = decom_aux_h2[0].verschiebung() + fct.teichmuller()
-    #C = omega8_lift - decom_aux_h2[1].verschiebung().diffn() - decomposition_omega0_omega8(aux.omega, prec=prec)[1].verschiebung()
-    #print('test 2:', A - B.diffn() == C)
-    #print('test 3:', result.omega0 == A, result.f == B, result.omega8 == C)
-    #print(result.omega8, '\n \n', compare, '\n \n', aux_f, '\n \n')
-    return result#.reduce()
+    return result
 
-def crystalline_cohomology_basis(self, prec = 50):
+def crystalline_cohomology_basis(self, prec = 50, info = 0):
     result = []
-    for a in self.de_rham_basis():
-        result += [de_rham_witt_lift(a, prec = prec)]
+    for i, a in enumerate(self.de_rham_basis()):
+        if info:
+            print("Computing " + str(i) +". basis element")
+        prec1 = prec
+        while True:
+            try:
+                result += [de_rham_witt_lift(a, prec = prec1)]
+                break
+            except IndexError:
+                prec1 += 100
+                result += [de_rham_witt_lift(a, prec = prec1)]
     return result
 
 superelliptic.crystalline_cohomology_basis = crystalline_cohomology_basis
\ No newline at end of file
diff --git a/sage/superelliptic_drw/regular_form.sage b/sage/superelliptic_drw/regular_form.sage
index 8603428..069bdea 100644
--- a/sage/superelliptic_drw/regular_form.sage
+++ b/sage/superelliptic_drw/regular_form.sage
@@ -66,7 +66,7 @@ class superelliptic_regular_drw_form:
         B = self.dy
         h2 = self.h2
         omega = self.omega
-        form1 = superelliptic_drw_form(A, omega, h2)
+        form1 = superelliptic_drw_form(A, omega.form(), h2)
         form2 = B.teichmuller()*C.y.teichmuller().diffn()
         
     def __repr__(self):
@@ -77,11 +77,19 @@ def regular_drw_form(omega):
     omega_aux = omega.r()
     omega_aux = omega_aux.regular_form()
     aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()
-    result = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega, aux.h2)
+    aux.omega, fct = decomposition_omega0_hpdh(aux.omega)
+    aux.h2 += fct^p
+    aux.h2 = decomposition_g0_p2th_power(aux.h2)[0]
+    result = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2)
     return result
 
 superelliptic_drw_form.regular_form = regular_drw_form
 
+def regular_drw_cech(cocycle):
+    return("( " + str(cocycle.omega0.regular_form()) + ", " + str(cocycle.f) + " )")
+
+superelliptic_drw_cech.regular_form = regular_drw_cech
+    
 def regular_form(omega):
     '''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'''
diff --git a/sage/superelliptic_drw/superelliptic_drw_auxilliaries.sage b/sage/superelliptic_drw/superelliptic_drw_auxilliaries.sage
index ed9b8da..96e11bc 100644
--- a/sage/superelliptic_drw/superelliptic_drw_auxilliaries.sage
+++ b/sage/superelliptic_drw/superelliptic_drw_auxilliaries.sage
@@ -20,7 +20,6 @@ def decomposition_omega0_hpdh(omega):
     return (omega1, fct)
 
 def decomposition_omega8_hpdh(omega, prec = 50):
-    print('decomposition_omega8_hpdh', omega)
     '''Decompose omega = (regular on U8) + h^(p-1) dh, so that Cartier(omega) = (regular on U8) + dh.
     Result: (regular on U8, h)'''
     C = omega.curve
@@ -30,23 +29,16 @@ def decomposition_omega8_hpdh(omega, prec = 50):
     p = C.characteristic
     Rt.<t> = LaurentSeriesRing(F)
     omega_analytic = Rt(laurent_analytic_part(omega.expansion_at_infty(prec = prec)))
-    print('omega_analytic', omega_analytic)
     Cv = C.uniformizer()
     v = Fxy(Cv.function)
     omega_analytic = Fxy(omega_analytic(t = v))
     omega_analytic = superelliptic_function(C, omega_analytic)*Cv.diffn()
-    print('omega_analytic.expansion_at_infty()', omega_analytic.expansion_at_infty(prec = prec))
-    print('omega_analytic', omega_analytic)
     omega8 = omega - omega_analytic
-    print('omega8', omega8)
     dh = omega.cartier() - omega8.cartier()
-    print('dh', dh)
     h = dh.int()
-    print('omega8.expansion_at_infty()', omega8.expansion_at_infty(prec = prec))
     return (omega8, h)
 
 def decomposition_g8_pth_power(fct, prec = 50):
-    print('decomposition_g8_pth_power', fct)
     '''Decompose fct as g8 + A^p, if possible. Output: (g8, A).'''
     C = fct.curve
     F = C.base_ring
@@ -62,7 +54,6 @@ def decomposition_g8_pth_power(fct, prec = 50):
     return (g8, A)
 
 def decomposition_g8_p2th_power(fct):
-    print('decomposition_g8_p2th_power', fct)
     '''Decompose fct as g8 + A^(p^2), if possible. Output: (g8, A).'''
     g0, A = decomposition_g8_pth_power(fct)
     A0, A1 = decomposition_g8_pth_power(A)
diff --git a/sage/superelliptic_drw/superelliptic_drw_cech.sage b/sage/superelliptic_drw/superelliptic_drw_cech.sage
index 3bb9a1d..7dd569d 100644
--- a/sage/superelliptic_drw/superelliptic_drw_cech.sage
+++ b/sage/superelliptic_drw/superelliptic_drw_cech.sage
@@ -84,15 +84,13 @@ class superelliptic_drw_cech:
         aux.omega8.h2 = decomposition_g8_p2th_power(aux.omega8.h2)[0]
         aux.f += aux.omega8.h2.verschiebung()
         aux.omega8.h2 = 0*C.x
-        print('aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier()', aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier())
         aux_divided_by_p = superelliptic_cech(C, aux.omega0.omega.cartier(), aux.f.f.pth_root())
         return aux_divided_by_p
         
-    def coordinates(self, basis = 0):
+    def coordinates(self, basis = 0, prec = 50):
         C = self.curve
         g = C.genus()
         coord_mod_p = self.r().coordinates()
-        print(coord_mod_p)
         coord_lifted = [lift(a) for a in coord_mod_p]
         if basis == 0:
             basis = C.crystalline_cohomology_basis()
@@ -106,7 +104,6 @@ class superelliptic_drw_cech:
         return coordinates
     
     def is_regular(self):
-        print(self.omega0.r().is_regular_on_U0(), self.omega8.r().is_regular_on_Uinfty(), self.omega0.frobenius().is_regular_on_U0(),     self.omega8.frobenius().is_regular_on_Uinfty())
         eq1 = self.omega0.r().is_regular_on_U0() and self.omega8.r().is_regular_on_Uinfty()
         eq2 = self.omega0.frobenius().is_regular_on_U0() and self.omega8.frobenius().is_regular_on_Uinfty()
         return eq1 and eq2
\ No newline at end of file
