From eda1cca0c29f1d4c90bc9513f30c4fcc363934d4 Mon Sep 17 00:00:00 2001 From: jgarnek Date: Wed, 29 Mar 2023 10:01:56 +0000 Subject: [PATCH] przed zmiana w expansion at infty w superelliptic --- sage/.run.term-0.term | 1551 ++++++++++++++++- sage/drafty/draft.sage | 41 +- sage/superelliptic_drw/de_rham_witt_lift.sage | 31 +- sage/superelliptic_drw/regular_form.sage | 12 +- .../superelliptic_drw_auxilliaries.sage | 9 - .../superelliptic_drw_cech.sage | 5 +- 6 files changed, 1593 insertions(+), 56 deletions(-) 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 [?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  - [?7h[?12l[?25h[?25l[?7lff.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lor i i lau.expoents():[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h \ No newline at end of file + [?7h[?12l[?25h[?25l[?7lff.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lor i i lau.expoents():[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit() +[?7h[?12l[?25h[?2004l +]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd .. +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -u +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git status +On branch master +Your branch is up to date with 'origin/master'. + +Changes to be committed: + (use "git restore --staged ..." to unstage) + modified: sage/.run.term-0.term + modified: sage/superelliptic/superelliptic_class.sage + modified: sage/superelliptic_drw/superelliptic_drw_auxilliaries.sage + modified: sage/superelliptic_drw/superelliptic_drw_cech.sage + modified: sage/tests.sage + +Untracked files: + (use "git add ..." to include in what will be committed) + .crystalline_p2.ipynb.sage-jupyter2 + .deRhamComputation.ipynb.sage-jupyter2 + .elementary_covers_of_superelliptic_curves.ipynb.sage-jupyter2 + .git.x11-0.term + .superelliptic.ipynb.sage-jupyter2 + .superelliptic_alpha.ipynb.sage-jupyter2 + .superelliptic_arbitrary_field.ipynb.sage-jupyter2 + git.x11 + sage/auxilliaries/laurent_analytic_part.sage + sage/drafty/.2023-03-06-file-1.ipynb.sage-jupyter2 + sage/drafty/2gpcovers.sage + sage/drafty/as_cartier.sage + sage/drafty/better_trace.sage + sage/drafty/cartier_image_representation.sage + sage/drafty/convert_superelliptic_into_AS.sage + sage/drafty/draft4.sage + sage/drafty/draft5.sage + sage/drafty/draft6.sage + sage/drafty/draft7.sage + sage/drafty/draft8.sage + sage/drafty/draft_klein_covers.sage + sage/drafty/lift_to_de_rham.sage + sage/drafty/pole_numbers.sage + sage/superelliptic/frobenius_kernel.sage + sage/superelliptic/tests/expansion_at_infty.sage + sage/superelliptic_drw/regular_form.sage + sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage + superelliptic_arbitrary_field.ipynb + +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ 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 sage/auxilliaries/laurent_analytic_part.sage +^C +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ 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.sagegit status + 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  add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/su ]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$  add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/sup ]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$  add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/supe ]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$  add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/super ]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ g add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/supe[1@r ]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ i add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/sup[1@e ]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ t add sage/superelliptic_drw/tests/auxilliary_decompositions_test.sage sage/superelliptic_drw/regular_form.sage sage/su[1@p ]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$  + +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git commit -m ""d"z"i"a"l"a" ""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"!"!"!"!" +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~/Research/2021 De Rham/DeRhamComputation$ git push +Username for 'https://git.wmi.amu.edu.pl': jgarnek +Password for 'https://jgarnek@git.wmi.amu.edu.pl': +Enumerating objects: 29, done. +Counting objects: 3% (1/29) Counting objects: 6% (2/29) Counting objects: 10% (3/29) Counting objects: 13% (4/29) Counting objects: 17% (5/29) Counting objects: 20% (6/29) Counting objects: 24% (7/29) Counting objects: 27% (8/29) Counting objects: 31% (9/29) Counting objects: 34% (10/29) Counting objects: 37% (11/29) Counting objects: 41% (12/29) Counting objects: 44% (13/29) Counting objects: 48% (14/29) Counting objects: 51% (15/29) Counting objects: 55% (16/29) Counting objects: 58% (17/29) Counting objects: 62% (18/29) Counting objects: 65% (19/29) Counting objects: 68% (20/29) Counting objects: 72% (21/29) Counting objects: 75% (22/29) Counting objects: 79% (23/29) Counting objects: 82% (24/29) Counting objects: 86% (25/29) Counting objects: 89% (26/29) Counting objects: 93% (27/29) 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) Compressing objects: 35% (6/17) Compressing objects: 41% (7/17) Compressing objects: 47% (8/17) Compressing objects: 52% (9/17) Compressing objects: 58% (10/17) Compressing objects: 64% (11/17) Compressing objects: 70% (12/17) Compressing objects: 76% (13/17) 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) Writing objects: 35% (6/17) Writing objects: 41% (7/17) Writing objects: 47% (8/17) Writing objects: 52% (9/17) Writing objects: 58% (10/17) Writing objects: 64% (11/17) Writing objects: 70% (12/17) Writing objects: 76% (13/17) Writing objects: 82% (14/17) 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 +remote: Processed 1 references in total +To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git + 995d5f0..a9d055a master -> master +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ sacd sage/ +]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.7, Release Date: 2022-09-19 │ +│ Using Python 3.10.5. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7lsage: M +[?7h[?12l[?25h[?2004l[?7h[4 6] +[1 4] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: M^3 +[?7h[?12l[?25h[?2004l[?7h[1 0] +[0 1] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7l = sperelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +IndexError Traceback (most recent call last) +Input In [4], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :19, in  + +File :10, in crystalline_matrix(C) + +File :39, in crystalline_cohomology_basis(self, prec) + +File :29, in de_rham_witt_lift(cech_class, prec) + +File :7, in decomposition_g0_g8(fct, prec) + +File :107, in coordinates(self, basis, basis_holo, prec) + +File :79, in serre_duality_pairing(self, fct, prec) + +File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__() + 542 return type(self)(self._parent, f, self.__n) + 543 +--> 544 return self.__u[i - self.__n] + 545 + 546 def __iter__(self): + +File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__() + 451 return self.base_ring().zero() + 452 else: +--> 453 raise IndexError("coefficient not known") + 454 return self.__f[n] + 455 + +IndexError: coefficient not known +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +IndexError Traceback (most recent call last) +Input In [5], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :19, in  + +File :10, in crystalline_matrix(C) + +File :39, in crystalline_cohomology_basis(self, prec) + +File :29, in de_rham_witt_lift(cech_class, prec) + +File :7, in decomposition_g0_g8(fct, prec) + +File :107, in coordinates(self, basis, basis_holo, prec) + +File :79, in serre_duality_pairing(self, fct, prec) + +File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__() + 542 return type(self)(self._parent, f, self.__n) + 543 +--> 544 return self.__u[i - self.__n] + 545 + 546 def __iter__(self): + +File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__() + 451 return self.base_ring().zero() + 452 else: +--> 453 raise IndexError("coefficient not known") + 454 return self.__f[n] + 455 + +IndexError: coefficient not known +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [6], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :19, in  + +File :16, in crystalline_matrix(C, prec) + +TypeError: superelliptic_drw_cech.coordinates() got an unexpected keyword argument 'prec' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1 0 0 0 0 0 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] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ loasage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.7, Release Date: 2022-09-19 │ +│ Using Python 3.10.5. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l^C--------------------------------------------------------------------------- +KeyboardInterrupt Traceback (most recent call last) +File :59, in __mul__(self, other) + +File :235, in reduction(C, g) + +File /ext/sage/9.7/src/sage/arith/misc.py:1971, in xgcd(a, b) + 1970 try: +-> 1971 return a.xgcd(b) + 1972 except AttributeError: + +File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() + +KeyboardInterrupt: + +During handling of the above exception, another exception occurred: + +AttributeError Traceback (most recent call last) +Input In [1], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :19, in  + +File :10, in crystalline_matrix(C, prec) + +File :39, in crystalline_cohomology_basis(self, prec) + +File :26, in de_rham_witt_lift(cech_class, prec) + +File :73, in diffn(self, dy_w) + +File :177, in dy_w(C) + +File /ext/sage/9.7/src/sage/rings/rational.pyx:2414, in sage.rings.rational.Rational.__mul__() + 2412 return x + 2413 +-> 2414 return coercion_model.bin_op(left, right, operator.mul) + 2415 + 2416 cpdef _mul_(self, right): + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op() + 1240 mul_method = getattr(y, '__r%s__'%op_name, None) + 1241 if mul_method is not None: +-> 1242 res = mul_method(x) + 1243 if res is not None and res is not NotImplemented: + 1244 return res + +File :48, in __rmul__(self, other) + +File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__() + 1526 if not err: + 1527 return (right)._mul_long(value) +-> 1528 return coercion_model.bin_op(left, right, mul) + 1529 except TypeError: + 1530 return NotImplemented + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op() + 1240 mul_method = getattr(y, '__r%s__'%op_name, None) + 1241 if mul_method is not None: +-> 1242 res = mul_method(x) + 1243 if res is not None and res is not NotImplemented: + 1244 return res + +File :43, in __rmul__(self, other) + +File :31, in __add__(self, other) + +File :63, in __mul__(self, other) + +AttributeError: 'superelliptic_function' object has no attribute 'form' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l(); autom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis(prec = 100) +[?7h[?12l[?25h[?2004l^C--------------------------------------------------------------------------- +KeyboardInterrupt Traceback (most recent call last) +Input In [3], in () +----> 1 B = C.crystalline_cohomology_basis(prec = Integer(100)) + +File :39, in crystalline_cohomology_basis(self, prec) + +File :24, in de_rham_witt_lift(cech_class, prec) + +File :6, in de_rham_witt_lift_form0(omega) + +File :73, in diffn(self, dy_w) + +File :177, in dy_w(C) + +File /ext/sage/9.7/src/sage/rings/rational.pyx:2414, in sage.rings.rational.Rational.__mul__() + 2412 return x + 2413 +-> 2414 return coercion_model.bin_op(left, right, operator.mul) + 2415 + 2416 cpdef _mul_(self, right): + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op() + 1240 mul_method = getattr(y, '__r%s__'%op_name, None) + 1241 if mul_method is not None: +-> 1242 res = mul_method(x) + 1243 if res is not None and res is not NotImplemented: + 1244 return res + +File :48, in __rmul__(self, other) + +File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__() + 1526 if not err: + 1527 return (right)._mul_long(value) +-> 1528 return coercion_model.bin_op(left, right, mul) + 1529 except TypeError: + 1530 return NotImplemented + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op() + 1240 mul_method = getattr(y, '__r%s__'%op_name, None) + 1241 if mul_method is not None: +-> 1242 res = mul_method(x) + 1243 if res is not None and res is not NotImplemented: + 1244 return res + +File :43, in __rmul__(self, other) + +File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__() + 1526 if not err: + 1527 return (right)._mul_long(value) +-> 1528 return coercion_model.bin_op(left, right, mul) + 1529 except TypeError: + 1530 return NotImplemented + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op() + 1240 mul_method = getattr(y, '__r%s__'%op_name, None) + 1241 if mul_method is not None: +-> 1242 res = mul_method(x) + 1243 if res is not None and res is not NotImplemented: + 1244 return res + +File :43, in __rmul__(self, other) + +File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__() + 1526 if not err: + 1527 return (right)._mul_long(value) +-> 1528 return coercion_model.bin_op(left, right, mul) + 1529 except TypeError: + 1530 return NotImplemented + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op() + 1240 mul_method = getattr(y, '__r%s__'%op_name, None) + 1241 if mul_method is not None: +-> 1242 res = mul_method(x) + 1243 if res is not None and res is not NotImplemented: + 1244 return res + +File :43, in __rmul__(self, other) + +File :31, in __add__(self, other) + +File :82, in __pow__(self, exp) + +File :14, in __init__(self, C, g) + +File :228, in reduction(C, g) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce) + 636 ring_one = self.ring().one() + 637 try: +--> 638 return self._element_class(self, x, ring_one, coerce=coerce) + 639 except (TypeError, ValueError): + 640 pass + +File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__() + 112 FieldElement.__init__(self, parent) + 113 if coerce: +--> 114 self.__numerator = parent.ring()(numerator) + 115 self.__denominator = parent.ring()(denominator) + 116 else: + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() + 1001 + 1002 try: +-> 1003 return self(str(element)) + 1004 except TypeError: + 1005 pass + +File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__() + 192 except AttributeError: + 193 return super().__repr__() +--> 194 result = reprfunc() + 195 if isinstance(result, str): + 196 return result + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_() + 2688 NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3 + 2689 """ +-> 2690 return self._repr() + 2691 + 2692 def _latex_(self, name=None): + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2656, in sage.rings.polynomial.polynomial_element.Polynomial._repr() + 2654 if n != m-1: + 2655 s += " + " +-> 2656 x = y = repr(x) + 2657 if y.find("-") == 0: + 2658 y = y[1:] + +File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__() + 192 except AttributeError: + 193 return super().__repr__() +--> 194 result = reprfunc() + 195 if isinstance(result, str): + 196 return result + +File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:340, in sage.rings.fraction_field_FpT.FpTElement._repr_() + 338 return repr(self.numer()) + 339 else: +--> 340 numer_s = repr(self.numer()) + 341 denom_s = repr(self.denom()) + 342 if '-' in numer_s or '+' in numer_s: + +File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__() + 192 except AttributeError: + 193 return super().__repr__() +--> 194 result = reprfunc() + 195 if isinstance(result, str): + 196 return result + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_() + 2688 NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3 + 2689 """ +-> 2690 return self._repr() + 2691 + 2692 def _latex_(self, name=None): + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2656, in sage.rings.polynomial.polynomial_element.Polynomial._repr() + 2654 if n != m-1: + 2655 s += " + " +-> 2656 x = y = repr(x) + 2657 if y.find("-") == 0: + 2658 y = y[1:] + +File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() + +KeyboardInterrupt: +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.genus()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7ltalline_cohomology_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBC.crystaline_cohomology_basis(prec = 10)[?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis(prec = 10)[?7h[?12l[?25h[?25l[?7l=C.crystaline_cohomology_basis(prec = 10)[?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis(prec = 10)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis(prec = 100) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 100)[?7h[?12l[?25h[?25l[?7lsage: B +[?7h[?12l[?25h[?2004l[?7h[([(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]))] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1].omega8 + u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B[0].reguler_form() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [7], in () +----> 1 B[Integer(0)].reguler_form() + +AttributeError: 'superelliptic_drw_cech' object has no attribute 'reguler_form' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].reguler_form()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr_form()[?7h[?12l[?25h[?25l[?7lar_form()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B[0].regular_form() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [8], in () +----> 1 B[Integer(0)].regular_form() + +AttributeError: 'superelliptic_drw_cech' object has no attribute 'regular_form' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].regular_form()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].regular_form()[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: B0 = B[0] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB0 = B[0][?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B0. + B0.coordinates B0.f B0.omega8  + B0.curve B0.is_regular B0.r  + B0.div_by_p B0.omega0 B0.reduce  + + [?7h[?12l[?25h[?25l[?7l + + +[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B0.omega0.regular_form() +[?7h[?12l[?25h[?2004l[?7h[0] d[x] + [1] d[y] + V(((x^5 + x^3)/y) dx) + dV(0) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + [?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.7, Release Date: 2022-09-19 │ +│ Using Python 3.10.5. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  + [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.genus()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB0.omega0.regular_form()[?7h[?12l[?25h[?25l[?7l = C.crystallinechomology_basis(prec = 100)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis(prec = 100)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lin)[?7h[?12l[?25h[?25l[?7linf)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis(prec = 100, info = 1) +[?7h[?12l[?25h[?2004lComputing 0. basis element +Computing 1. basis element +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 100, info = 1)[?7h[?12l[?25h[?25l[?7lsage: B +[?7h[?12l[?25h[?2004l[?7h[([(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]))] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[0].regular_form()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l0][?7h[?12l[?25h[?25l[?7l].regular_form()[?7h[?12l[?25h[?25l[?7l[].regular_form()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B[0].omega0.regular_form() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [5], in () +----> 1 B[Integer(0)].omega0.regular_form() + +File :81, in regular_drw_form(omega) + +AttributeError: 'superelliptic_drw_form' object has no attribute 'omega0' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupe[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohmology_basis(prec = 100, info = 1)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis(prec = 100, info = 1)[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis(prec = 100, info = 1) +[?7h[?12l[?25h[?2004lComputing 0. basis element +Computing 1. basis element +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 100, info = 1)[?7h[?12l[?25h[?25l[?7l[0].omega0.regular_frm()[?7h[?12l[?25h[?25l[?7l0].omega0.regular_form()[?7h[?12l[?25h[?25l[?7lsage: B[0].omega0.regular_form() +[?7h[?12l[?25h[?2004l[?7h[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) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l1].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B[1].omega0.regular_form() +[?7h[?12l[?25h[?2004l[?7h[0] d[x] + [x] d[y] + V((0) dy) + dV((x^6 + 2*x^4)*y) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[1].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohmology_basis(prec = 100, info = 1)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis(prec = 100, info = 1)[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis(prec = 100, info = 1) +[?7h[?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 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 100, info = 1)[?7h[?12l[?25h[?25l[?7l[1].omega0.regular_frm()[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lregular_form()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B[0].regular_form() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [13], in () +----> 1 B[Integer(0)].regular_form() + +File :90, in regular_drw_cech(cocycle) + +TypeError: can only concatenate str (not "superelliptic_regular_drw_form") to str +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].regular_form()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lomega0.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0.regular_form()[?7h[?12l[?25h[?25l[?7lsage: B[0].omega0.regular_form() +[?7h[?12l[?25h[?2004l[?7h[0] d[x] + [1] d[y] + V((0) dy) + dV((x^9 + 2*x)*y) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l7].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B[7].omega0.regular_form() +[?7h[?12l[?25h[?2004l[?7h[0] d[x] + [x^4] d[y] + V((0) dy) + dV(0) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def regular_drw_cech(cocycle): +....:  print("( " + str(cocycle.omega0.regular_form()) + ", " + str(cocycle.f) + " )") +....:  +....: superelliptic_drw_cech.regular_form = regular_drw_cech[?7h[?12l[?25h[?25l[?7lsage: def regular_drw_cech(cocycle): +....:  print("( " + str(cocycle.omega0.regular_form()) + ", " + str(cocycle.f) + " )") +....:  +....: superelliptic_drw_cech.regular_form = regular_drw_cech +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[7].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lregular_form()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lgular_form()[?7h[?12l[?25h[?25l[?7lsage: B[0].regular_form() +[?7h[?12l[?25h[?2004l( [0] d[x] + [1] d[y] + V((0) dy) + dV((x^9 + 2*x)*y), V(x*y) ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lor i i lau.expoents():[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lrange[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: for i in range(8): +....: [?7h[?12l[?25h[?25l[?7lprint("( " + str(cocycle.omega0.regular_form()) + ", " + str(cocycle.f) + " )")[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:  print(B[i].regular_form()) +....: [?7h[?12l[?25h[?25l[?7lsage: for i in range(8): +....:  print(B[i].regular_form()) +....:  +[?7h[?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--------------------------------------------------------------------------- +KeyboardInterrupt Traceback (most recent call last) +Input In [18], in () + 1 for i in range(Integer(8)): +----> 2 print(B[i].regular_form()) + +Input In [16], in regular_drw_cech(cocycle) + 1 def regular_drw_cech(cocycle): +----> 2 print("( " + str(cocycle.omega0.regular_form()) + ", " + str(cocycle.f) + " )") + +File :80, in regular_drw_form(omega) + +File :73, in diffn(self, dy_w) + +File :177, in dy_w(C) + +File :149, in auxilliary_derivative(P) + +File :84, in __add__(self, other) + +File :65, in __mul__(self, other) + +File :28, in __sub__(self, other) + +File :7, in __init__(self, C, g) + +File :252, in reduction_form(C, g) + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:647, in PolynomialRing(base_ring, *args, **kwds) + 644 raise TypeError("variable names specified twice inconsistently: %r and %r" % (names, kwnames)) + 646 if multivariate or len(names) != 1: +--> 647 return _multi_variate(base_ring, names, **kwds) + 648 else: + 649 return _single_variate(base_ring, names, **kwds) + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:762, in _multi_variate(base_ring, names, sparse, order, implementation) + 760 from sage.rings.polynomial.term_order import TermOrder + 761 n = len(names) +--> 762 order = TermOrder(order, n) + 764 # "implementation" must be last + 765 key = [base_ring, names, n, order, implementation] + +File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() + +KeyboardInterrupt: +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for i in range(8): +....:  print(B[i].regular_form())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lprintB[i].regular_form()[?7h[?12l[?25h[?25l[?7lB[i].regular_form()[?7h[?12l[?25h[?25l[?7lB[i].regular_form()[?7h[?12l[?25h[?25l[?7lB[i].regular_form()[?7h[?12l[?25h[?25l[?7lB[i].regular_form()[?7h[?12l[?25h[?25l[?7lB[i].regular_form()[?7h[?12l[?25h[?25l[?7l....:  +....:  B[i].regular_form()[?7h[?12l[?25h[?25l[?7lB[i].regular_form()[?7h[?12l[?25h[?25l[?7lB[i].regular_form()[?7h[?12l[?25h[?25l[?7lB[i].regular_form()[?7h[?12l[?25h[?25l[?7lB[i].regular_form()[?7h[?12l[?25h[?25l[?7lB[i].regular_form() + [?7h[?12l[?25h[?25l[?7lB[i].regular_form()[?7h[?12l[?25h[?25l[?7l B[i].regular_form()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l() +....: [?7h[?12l[?25h[?25l[?7lsage: for i in range(8): +....:  B[i].regular_form() +....:  +[?7h[?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) ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^9 + 2*x over Finite Field of size 3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C1 = superelliptic(x^3 + x, 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].regular_form()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l1.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7ltalline_cohomology_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7linf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l`[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B1 = C1.crystalline_cohomology_basis(prec = 100, info = 1) +[?7h[?12l[?25h[?2004lComputing 0. basis element +Computing 1. basis element +^C--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +File :58, in __mul__(self, other) + +AttributeError: 'superelliptic_form' object has no attribute 'function' + +During handling of the above exception, another exception occurred: + +KeyboardInterrupt Traceback (most recent call last) +Input In [22], in () +----> 1 B1 = C1.crystalline_cohomology_basis(prec = Integer(100), info = Integer(1)) + +File :41, in crystalline_cohomology_basis(self, prec, info) + +File :33, in de_rham_witt_lift(cech_class, prec) + +File :6, in __init__(self, omega0, f) + +File :90, in diffn(self, dy_w) + +File :73, in diffn(self, dy_w) + +File :177, in dy_w(C) + +File :65, in __mul__(self, other) + +File :65, in __mul__(self, other) + +File :7, in __init__(self, C, g) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce) + 704 x0, y0 = x, y + 705 try: +--> 706 x, y = resolve_fractions(x0, y0) + 707 except (AttributeError, TypeError): + 708 raise TypeError("cannot convert {!r}/{!r} to an element of {}".format( + 709 x0, y0, self)) + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:688, in FractionField_generic._element_constructor_..resolve_fractions(x, y) + 686 yd = y.denominator() + 687 try: +--> 688 return (xn * yd, yn * xd) + 689 except (AttributeError, TypeError, ValueError): + 690 pass + +File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__() + 1514 return (left)._mul_(right) + 1515 if BOTH_ARE_ELEMENT(cl): +-> 1516 return coercion_model.bin_op(left, right, mul) + 1517 + 1518 cdef long value + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1200, in sage.structure.coerce.CoercionModel.bin_op() + 1198 # Now coerce to a common parent and do the operation there + 1199 try: +-> 1200 xy = self.canonical_coercion(x, y) + 1201 except TypeError: + 1202 self._record_exception() + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1311, in sage.structure.coerce.CoercionModel.canonical_coercion() + 1309 x_map, y_map = coercions + 1310 if x_map is not None: +-> 1311 x_elt = (x_map)._call_(x) + 1312 else: + 1313 x_elt = x + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_() + 285 raise TypeError("Cannot coerce {} to {}".format(x, C)) + 286 cdef Map m +--> 287 cdef Element e = method(C) + 288 if e is None: + 289 raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x))) + +File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:198, in sage.rings.polynomial.multi_polynomial.MPolynomial._polynomial_() + 196 var = R.variable_name() + 197 if var in self._parent.variable_names(): +--> 198 return R(self.polynomial(self._parent(var))) + 199 else: + 200 return R([self]) + +File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:419, in sage.rings.polynomial.multi_polynomial.MPolynomial.polynomial() + 417 w = {remove_from_tuple(e, ind): val + 418 for e, val in self.dict().iteritems() if not e[ind]} +--> 419 v = [B(w)] # coefficients that don't involve var + 420 z = var + 421 for i in range(1,d+1): + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:309, in PolynomialRing_general._element_constructor_(self, x, check, is_gen, construct, **kwds) + 306 args = (self.base_ring(), self.variable_names(), None, self.is_sparse()) + 307 return unpickle_PolynomialRing, args +--> 309 def _element_constructor_(self, x=None, check=True, is_gen=False, + 310 construct=False, **kwds): + 311 r""" + 312  Convert ``x`` into this univariate polynomial ring, + 313  possibly non-canonically. + (...) + 412  λ^2 + 413  """ + 414 C = self.element_class + +File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() + +KeyboardInterrupt: +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB1 = C1.crystalline_cohomology_basis(prec = 100, info = 1)[?7h[?12l[?25h[?25l[?7lsage: B1 = C1.crystalline_cohomology_basis(prec = 100, info = 1) +[?7h[?12l[?25h[?2004lComputing 0. basis element +Computing 1. basis element +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in range(8):[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l i in range(8):[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l):[?7h[?12l[?25h[?25l[?7l2):[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: for i in range(2): +....: [?7h[?12l[?25h[?25l[?7lprint(B[i].regular_form())[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l(B[i].regular_form())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l1[i].regular_form()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  print(B1[i].regular_form()) +....: [?7h[?12l[?25h[?25l[?7lsage: for i in range(2): +....:  print(B1[i].regular_form()) +....:  +[?7h[?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 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la^(-1)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lxpansion[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l(x^63 + 2*x^55 + 2*x^39 + x^31)[?7h[?12l[?25h[?25l[?7l(),[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: adic_expansion((x^63 + 2*x^55 + 2*x^39 + x^31), x^3 - x) +[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, x, 1, x, 2, 0, 1, x, 1, x, 0, 0, 2, 0, 0, 0, 1, 0, 1] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion((x^63 + 2*x^55 + 2*x^39 + x^31), x^3 - x)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(x^3 - x, x^3 - x) +[?7h[?12l[?25h[?2004l[?7h[0, 1] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRt. = LaurentSeriesRing(F, default_prec = 100)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l<[?7h[?12l[?25h[?25l[?7l>[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt>[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lP[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: Rxt. = PolynomialRing(Rx) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxt. = PolynomialRing(Rx)[?7h[?12l[?25h[?25l[?7ladic_expansion(x^3 - x, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcadic_expansion(x^3 - x, x^3 - x)[?7h[?12l[?25h[?25l[?7loadic_expansion(x^3 - x, x^3 - x)[?7h[?12l[?25h[?25l[?7loadic_expansion(x^3 - x, x^3 - x)[?7h[?12l[?25h[?25l[?7l adic_expansion(x^3 - x, x^3 - x)[?7h[?12l[?25h[?25l[?7l=adic_expansion(x^3 - x, x^3 - x)[?7h[?12l[?25h[?25l[?7l adic_expansion(x^3 - x, x^3 - x)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: coo = adic_expansion(x^3 - x, x^3 - x) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcoo = adic_expansion(x^3 - x, x^3 - x)[?7h[?12l[?25h[?25l[?7lRxt. = PolynomalRing(Rx)[?7h[?12l[?25h[?25l[?7ladic_expansion(x^3 - x, x^3 - x)[?7h[?12l[?25h[?25l[?7l(x^63+ 2*x^55+ 2*x^39 + x^31), x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcadic_expansion(x^63 + 2*x^5 + 2*x^39 + x^31), x^3 - x)[?7h[?12l[?25h[?25l[?7loadic_expansion(x^63 + 2*x^5 + 2*x^39 + x^31), x^3 - x)[?7h[?12l[?25h[?25l[?7loadic_expansion(x^63 + 2*x^5 + 2*x^39 + x^31), x^3 - x)[?7h[?12l[?25h[?25l[?7l adic_expansion(x^63 + 2*x^5 + 2*x^39 + x^31), x^3 - x)[?7h[?12l[?25h[?25l[?7l=adic_expansion(x^63 + 2*x^5 + 2*x^39 + x^31), x^3 - x)[?7h[?12l[?25h[?25l[?7l adic_expansion(x^63 + 2*x^5 + 2*x^39 + x^31), x^3 - x)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: coo = adic_expansion((x^63 + 2*x^55 + 2*x^39 + x^31), x^3 - x) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in range(2):[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li in range(2):[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lenumerate[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: for i, a in enumerate(coo): +....: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lenumerat[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: FF = Rxt(0) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in range(2):[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFF = Rxt(0)[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lsum[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lenumerate[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: FF = sum(a*t^i for i, a in enumerate(coo)) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFF = sum(a*t^i for i, a in enumerate(coo))[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7lsage: FF +[?7h[?12l[?25h[?2004l[?7ht^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 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1 = superelliptic(x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l.genus()[?7h[?12l[?25h[?25l[?7ld_rham_basis()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis() +[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx), + ((x/y) dx, 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)] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7ly^2[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/C.x^3)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.y/C.x^3).expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-3 + t^13 + O(t^17) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/C.x^3).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lx).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.y/C.x).expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-7 + O(t^13) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/C.x).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l^).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l4).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: (C.y/C.x^4).expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-1 + O(t^19) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/C.x^4).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l5).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: (C.y/C.x^5).expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht + 2*t^17 + O(t^21) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/C.x^5).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.y/C.x^5).diffn() +[?7h[?12l[?25h[?2004l[?7h(x^3/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/C.x^5).diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l).difn()[?7h[?12l[?25h[?25l[?7l7).difn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.y/C.x^7).diffn() +[?7h[?12l[?25h[?2004l[?7h((-x^8 - 1)/(x^7*y)) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/C.x^7).diffn()[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx - a(-2)).expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.x^5*C.y.diffn()).int() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ZeroDivisionError Traceback (most recent call last) +Input In [40], in () +----> 1 (C.x**Integer(5)*C.y.diffn()).int() + +File :198, in int(self) + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:3994, in sage.rings.polynomial.polynomial_element.Polynomial.integral() + 3992 cdef Py_ssize_t n + 3993 zero = Q.zero() +-> 3994 p = [zero] + [cm.bin_op(Q(self.get_unsafe(n)), n + 1, operator.truediv) + 3995 if self.get_unsafe(n) else zero for n in range(self.degree() + 1)] + 3996 return S(p) + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op() + 1202 self._record_exception() + 1203 else: +-> 1204 return PyObject_CallObject(op, xy) + 1205 + 1206 if op is mul: + +File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__() + 1735 cdef int cl = classify_elements(left, right) + 1736 if HAVE_SAME_PARENT(cl): +-> 1737 return (left)._div_(right) + 1738 if BOTH_ARE_ELEMENT(cl): + 1739 return coercion_model.bin_op(left, right, truediv) + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_() + 2621 right_inverse = self.__modulus.inverses[(right).ivalue] + 2622 if right_inverse is None: +-> 2623 raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist") + 2624 else: + 2625 return self._new_c((self.ivalue * (right_inverse).ivalue) % self.__modulus.int32) + +ZeroDivisionError: inverse of Mod(0, 3) does not exist +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x^5*C.y.diffn()).int()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.x^5*C.y.diffn()).cartier() +[?7h[?12l[?25h[?2004l[?7h(x^4/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x^5*C.y.diffn()).cartier()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7linv[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.x^5*C.y.diffn()).cartier().inv_cartier() +[?7h[?12l[?25h[?2004l[?7h((x^21 - x^13)/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x^5*C.y.diffn()).cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l *C.y.difn().cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7l-*C.y.difn().cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7l *C.y.difn().cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7lC*C.y.difn().cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7l.*C.y.difn().cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7lx*C.y.difn().cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7l^*C.y.difn().cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7l3*C.y.difn().cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7l()*C.y.difn().cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(C.x^5 - C.x^3)*C.y.difn().cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((C.x^5 - C.x^3)*C.y.diffn()).cartier() +[?7h[?12l[?25h[?2004l[?7h(x^4/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion(x^3 - x, x^3 - x)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lic_expansion(x^3 - x, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l7, x^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(x^7, x^3 - x) +[?7h[?12l[?25h[?2004l[?7h[x, 2*x^2 + 1, x] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxt. = PolynomialRing(Rx)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l<[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion(x^7, x^3 - x)[?7h[?12l[?25h[?25l[?7l((C.x^5 - C.x^3)*C.y.diffn()).cartier()[?7h[?12l[?25h[?25l[?7lC.x^5*C.y.diffn()).cartier(inv_catier()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lint()[?7h[?12l[?25h[?25l[?7ly/C.x^7).difn()[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7lexpasion_at_infty()[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l^3).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7lFF[?7h[?12l[?25h[?25l[?7l = sum(a*t^i for i, a in enumerate(coo))[?7h[?12l[?25h[?25l[?7lRxt0)[?7h[?12l[?25h[?25l[?7lcoo = adic_expansion((x^63 + 2*x^55 + 2*x^39 + x^31), x^3 - x)[?7h[?12l[?25h[?25l[?7lFF = Rxt(0)[?7h[?12l[?25h[?25l[?7lsuma*t^i for i, a in enumerate(coo))[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lenumerat[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsu[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx[?7h[?12l[?25h[?25l[?7lsage: x +[?7h[?12l[?25h[?2004l[?7hx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(parent(lau))[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: parent(x) +[?7h[?12l[?25h[?2004l[?7hUnivariate Polynomial Ring in x over Finite Field of size 3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxt. = PolynomialRing(Rx)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l<[?7h[?12l[?25h[?25l[?7l>[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx>[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lP[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lComputing 0. basis element +Computing 1. basis element +Computing 0. basis element +--------------------------------------------------------------------------- +IndexError Traceback (most recent call last) +Input In [47], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :12, in  + +File :41, in crystalline_cohomology_basis(self, prec, info) + +File :29, in de_rham_witt_lift(cech_class, prec) + +File :7, in decomposition_g0_g8(fct, prec) + +File :107, in coordinates(self, basis, basis_holo, prec) + +File :79, in serre_duality_pairing(self, fct, prec) + +File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__() + 542 return type(self)(self._parent, f, self.__n) + 543 +--> 544 return self.__u[i - self.__n] + 545 + 546 def __iter__(self): + +File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__() + 451 return self.base_ring().zero() + 452 else: +--> 453 raise IndexError("coefficient not known") + 454 return self.__f[n] + 455 + +IndexError: coefficient not known +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lComputing 0. basis element +Computing 1. basis element +Computing 0. basis element +Computing 1. basis element +Computing 2. basis element +Computing 3. basis element +--------------------------------------------------------------------------- +IndexError Traceback (most recent call last) +Input In [48], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :12, in  + +File :41, in crystalline_cohomology_basis(self, prec, info) + +File :32, in de_rham_witt_lift(cech_class, prec) + +File :36, in decomposition_omega0_omega8(omega, prec) + +File /ext/sage/9.7/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds) + 583 return expression.sum(*args, **kwds) + 584 elif max(len(args),len(kwds)) <= 1: +--> 585 return sum(expression, *args, **kwds) + 586 else: + 587 from sage.symbolic.ring import SR + +File :36, in (.0) + +File :156, in residue(self, place, prec) + +File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__() + 542 return type(self)(self._parent, f, self.__n) + 543 +--> 544 return self.__u[i - self.__n] + 545 + 546 def __iter__(self): + +File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__() + 451 return self.base_ring().zero() + 452 else: +--> 453 raise IndexError("coefficient not known") + 454 return self.__f[n] + 455 + +IndexError: coefficient not known +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lComputing 0. basis element +^C--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +File :58, in __mul__(self, other) + +AttributeError: 'superelliptic_form' object has no attribute 'function' + +During handling of the above exception, another exception occurred: + +KeyboardInterrupt Traceback (most recent call last) +Input In [49], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :11, in  + +File :41, in crystalline_cohomology_basis(self, prec, info) + +File :25, in de_rham_witt_lift(cech_class, prec) + +File :15, in de_rham_witt_lift_form8(omega) + +File :90, in diffn(self, dy_w) + +File :73, in diffn(self, dy_w) + +File :177, in dy_w(C) + +File :65, in __mul__(self, other) + +File :65, in __mul__(self, other) + +File :7, in __init__(self, C, g) + +File :271, in reduction_form(C, g) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce) + 636 ring_one = self.ring().one() + 637 try: +--> 638 return self._element_class(self, x, ring_one, coerce=coerce) + 639 except (TypeError, ValueError): + 640 pass + +File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__() + 112 FieldElement.__init__(self, parent) + 113 if coerce: +--> 114 self.__numerator = parent.ring()(numerator) + 115 self.__denominator = parent.ring()(denominator) + 116 else: + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1009, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() + 1007 try: + 1008 # now try calling the base ring's __call__ methods +-> 1009 element = self.base_ring()(element) + 1010 _p = p_NSet(sa2si(element,_ring), _ring) + 1011 return new_MP(self,_p) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x) + 1143 """ + 1144 TESTS:: + 1145 + (...) + 1182  True + 1183 """ + 1184 try: +-> 1185 return integer_mod.IntegerMod(self, x) + 1186 except (NotImplementedError, PariError): + 1187 raise TypeError("error coercing to finite field") + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod() + 199 return a + 200 t = modulus.element_class() +--> 201 return t(parent, value) + 202 + 203 + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:380, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__() + 378 else: + 379 try: +--> 380 z = integer_ring.Z(value) + 381 except (TypeError, ValueError): + 382 from sage.structure.element import Expression + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_() + 285 raise TypeError("Cannot coerce {} to {}".format(x, C)) + 286 cdef Map m +--> 287 cdef Element e = method(C) + 288 if e is None: + 289 raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x))) + +File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:831, in sage.rings.fraction_field_element.FractionFieldElement._conversion() + 829 return R(self.__numerator) + 830 else: +--> 831 self.reduce() + 832 num = R(self.__numerator) + 833 inv_den = R(self.__denominator).inverse_of_unit() + +File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:1239, in sage.rings.fraction_field_element.FractionFieldElement_1poly_field.reduce() + 1237 if self._is_reduced: + 1238 return +-> 1239 super(self.__class__, self).reduce() + 1240 self.normalize_leading_coefficients() + 1241 + +File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:164, in sage.rings.fraction_field_element.FractionFieldElement.reduce() + 162 return codomain.coerce(nnum/nden) + 163 +--> 164 cpdef reduce(self): + 165 """ + 166 Reduce this fraction. + +File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:197, in sage.rings.fraction_field_element.FractionFieldElement.reduce() + 195 return + 196 try: +--> 197 g = self.__numerator.gcd(self.__denominator) + 198 if not g.is_unit(): + 199 self.__numerator //= g + +File /ext/sage/9.7/src/sage/structure/element.pyx:4494, in sage.structure.element.coerce_binop.new_method() + 4492 def new_method(self, other, *args, **kwargs): + 4493 if have_same_parent(self, other): +-> 4494 return method(self, other, *args, **kwargs) + 4495 else: + 4496 a, b = coercion_model.canonical_coercion(self, other) + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:4913, in sage.rings.polynomial.polynomial_element.Polynomial.gcd() + 4911 raise NotImplementedError("%s does not provide a gcd implementation for univariate polynomials"%self._parent._base) + 4912 else: +-> 4913 return doit(self, other) + 4914 + 4915 @coerce_binop + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:944, in FractionField_generic._gcd_univariate_polynomial(self, f, g) + 942 Pol = f.parent() + 943 Num = Pol.change_ring(self.base()) +--> 944 f1 = Num(f.numerator()) + 945 g1 = Num(g.numerator()) + 946 return Pol(f1.gcd(g1)).monic() + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:452, in PolynomialRing_general._element_constructor_(self, x, check, is_gen, construct, **kwds) + 450 except NameError: + 451 raise TypeError("Unable to coerce string") +--> 452 elif isinstance(x, FractionFieldElement): + 453 if x.denominator().is_unit(): + 454 x = x.numerator() * x.denominator().inverse_of_unit() + +File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() + +KeyboardInterrupt: +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt^(-8).integral()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ltry[?7h[?12l[?25h[?25l[?7ltryL[?7h[?12l[?25h[?25l[?7ltry[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7lsage: try: +....: [?7h[?12l[?25h[?25l[?7lprint(B1[i].regular_form())[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l....:  print(0/0) +....: [?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l() + [?7h[?12l[?25h[?25l[?7l()e[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l() +....: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2 - B[1][?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lexcept[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lIndexError[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l....: except IndexError: +....: [?7h[?12l[?25h[?25l[?7lprint(B1[i].regular_form())[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l"( " + str(cocycle.omega0.regular_form()) + ", " + str(cocycle.f) + " )")[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l"[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l....:  print("a") +....: [?7h[?12l[?25h[?25l[?7lsage: try: +....:  print(0/0) +....: except IndexError: +....:  print("a") +....:  +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ZeroDivisionError Traceback (most recent call last) +Input In [50], in () + 1 try: +----> 2 print(Integer(0)/Integer(0)) + 3 except IndexError: + 4 print("a") + +File /ext/sage/9.7/src/sage/rings/integer.pyx:2022, in sage.rings.integer.Integer.__truediv__() + 2020 if type(left) is type(right): + 2021 if mpz_sgn((right).value) == 0: +-> 2022 raise ZeroDivisionError("rational division by zero") + 2023 x = Rational.__new__(Rational) + 2024 mpq_div_zz(x.value, (left).value, (right).value) + +ZeroDivisionError: rational division by zero +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: try: +....:  print(0/0) +....: except IndexError: +....:  print("a")[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lIndeError:[?7h[?12l[?25h[?25l[?7lEror:[?7h[?12l[?25h[?25l[?7lEror:[?7h[?12l[?25h[?25l[?7lEror:[?7h[?12l[?25h[?25l[?7lEror:[?7h[?12l[?25h[?25l[?7lZEror:[?7h[?12l[?25h[?25l[?7leEror:[?7h[?12l[?25h[?25l[?7lrEror:[?7h[?12l[?25h[?25l[?7loEror:[?7h[?12l[?25h[?25l[?7lDEror:[?7h[?12l[?25h[?25l[?7liEror:[?7h[?12l[?25h[?25l[?7lvEror:[?7h[?12l[?25h[?25l[?7liEror:[?7h[?12l[?25h[?25l[?7lsEror:[?7h[?12l[?25h[?25l[?7liEror:[?7h[?12l[?25h[?25l[?7loEror:[?7h[?12l[?25h[?25l[?7lZeroDivisionError:[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l +()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  print("a") +....: [?7h[?12l[?25h[?25l[?7lsage: try: +....:  print(0/0) +....: except ZeroDivisionError: +....:  print("a") +....:  +[?7h[?12l[?25h[?2004la +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?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--------------------------------------------------------------------------- +KeyboardInterrupt Traceback (most recent call last) +File :60, in __mul__(self, other) + +File :14, in __init__(self, C, g) + +File :228, in reduction(C, g) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce) + 637 try: +--> 638 return self._element_class(self, x, ring_one, coerce=coerce) + 639 except (TypeError, ValueError): + +File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__() + 113 if coerce: +--> 114 self.__numerator = parent.ring()(numerator) + 115 self.__denominator = parent.ring()(denominator) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + +File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() + 1002 try: +-> 1003 return self(str(element)) + 1004 except TypeError: + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + +File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:991, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() + 990 element = element.replace("^","**") +--> 991 element = eval(element, d, {}) + 992 except (SyntaxError, NameError): + +File :1, in  + +File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() + +KeyboardInterrupt: + +During handling of the above exception, another exception occurred: + +AttributeError Traceback (most recent call last) +Input In [52], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :12, in  + +File :44, in crystalline_cohomology_basis(self, prec, info) + +File :26, in de_rham_witt_lift(cech_class, prec) + +File :90, in diffn(self, dy_w) + +File :73, in diffn(self, dy_w) + +File :177, in dy_w(C) + +File :149, in auxilliary_derivative(P) + +File :149, in auxilliary_derivative(P) + +File :147, in auxilliary_derivative(P) + +File :35, in __sub__(self, other) + +File :31, in __add__(self, other) + +File :63, in __mul__(self, other) + +AttributeError: 'superelliptic_function' object has no attribute 'form' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit() +[?7h[?12l[?25h[?2004l +]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ gcd .. +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ 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. = 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. = 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