From c0583f32d5d53e2a6f25f97507f9da43cf0ece06 Mon Sep 17 00:00:00 2001 From: jgarnek Date: Mon, 19 Dec 2022 14:19:50 +0000 Subject: [PATCH] de rham basis --- sage/.run.term-0.term | 504 ++++++++++++++++++++++++++++- sage/as_covers/as_cover_class.sage | 43 +++ sage/as_covers/as_form_class.sage | 5 +- sage/drafty/draft3.sage | 14 +- sage/init.sage | 3 +- 5 files changed, 553 insertions(+), 16 deletions(-) diff --git a/sage/.run.term-0.term b/sage/.run.term-0.term index 8fcc158..64f48b1 100644 --- a/sage/.run.term-0.term +++ b/sage/.run.term-0.term @@ -16485,4 +16485,506 @@ no 24 -th root; divide by 2 ^C^C^C^C^C^C^C^C^C^C^C^C ^C -]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ \ No newline at end of file +]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ git add -u +]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ git commit status\ +> ^C +]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 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: ../elementary_covers_of_superelliptic_curves.ipynb + modified: .run.term-0.term + modified: as_covers/as_auxilliary.sage + modified: as_covers/as_cover_class.sage + modified: as_covers/as_form_class.sage + modified: as_covers/as_function_class.sage + modified: as_covers/combination_components.sage + modified: as_covers/dual_element.sage + modified: as_covers/ith_magical_component.sage + modified: as_covers/tests/dual_element_test.sage + modified: drafty/draft.sage + modified: drafty/draft2.sage + modified: drafty/draft3.sage + modified: init.sage + modified: tests.sage + modified: ../superelliptic.ipynb + +Changes not staged for commit: + (use "git add ..." to update what will be committed) + (use "git restore ..." to discard changes in working directory) + modified: .run.term-0.term + +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 + as_covers/as_reduction.sage + as_covers/tests/diffn_test.sage + drafty/better_trace.sage + drafty/draft4.sage + drafty/draft5.sage + drafty/draft6.sage + drafty/draft8.sage + drafty/lift_to_de_rham.sage + drafty/pole_numbers.sage + ../superelliptic_arbitrary_field.ipynb + +]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ git assdd a*omegad as_covers/tests/diffn_test.sage +]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ git commit -m "cohomology of structure sheaf" + +*** Please tell me who you are. + +Run + + git config --global user.email "you@example.com" + git config --global user.name "Your Name" + +to set your account's default identity. +Omit --global to set the identity only in this repository. + +fatal: empty ident name (for ) not allowed +]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ git config --global user.email "you@example.com""""""""""""""""j"g"a"r"n"e"k"@"a"m"u"."e"d"u"."p"l" +]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ git config --global user.name "Your Name""""""""""j"g"a"r"n"e"k" +]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ gir t pushgit config --global user.name "jgarnek"email "jgarnek@amu.edu.pl"mmit -m "cohomology of structure sheaf" +[master c28c4a4] cohomology of structure sheaf + 17 files changed, 17238 insertions(+), 24743 deletions(-) + rewrite sage/.run.term-0.term (82%) + rewrite sage/as_covers/as_auxilliary.sage (63%) + create mode 100644 sage/as_covers/tests/diffn_test.sage + rewrite sage/drafty/draft.sage (93%) + rewrite sage/drafty/draft2.sage (83%) + rewrite sage/drafty/draft3.sage (100%) +]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ git push +Username for 'https://git.wmi.amu.edu.pl': jgarnek +Password for 'https://jgarnek@git.wmi.amu.edu.pl': +Enumerating objects: 43, done. +Counting objects: 2% (1/43) Counting objects: 4% (2/43) Counting objects: 6% (3/43) Counting objects: 9% (4/43) Counting objects: 11% (5/43) Counting objects: 13% (6/43) Counting objects: 16% (7/43) Counting objects: 18% (8/43) Counting objects: 20% (9/43) Counting objects: 23% (10/43) Counting objects: 25% (11/43) Counting objects: 27% (12/43) Counting objects: 30% (13/43) Counting objects: 32% (14/43) Counting objects: 34% (15/43) Counting objects: 37% (16/43) Counting objects: 39% (17/43) Counting objects: 41% (18/43) Counting objects: 44% (19/43) Counting objects: 46% (20/43) Counting objects: 48% (21/43) Counting objects: 51% (22/43) Counting objects: 53% (23/43) Counting objects: 55% (24/43) Counting objects: 58% (25/43) Counting objects: 60% (26/43) Counting objects: 62% (27/43) Counting objects: 65% (28/43) Counting objects: 67% (29/43) Counting objects: 69% (30/43) Counting objects: 72% (31/43) Counting objects: 74% (32/43) Counting objects: 76% (33/43) Counting objects: 79% (34/43) Counting objects: 81% (35/43) Counting objects: 83% (36/43) Counting objects: 86% (37/43) Counting objects: 88% (38/43) Counting objects: 90% (39/43) Counting objects: 93% (40/43) Counting objects: 95% (41/43) Counting objects: 97% (42/43) Counting objects: 100% (43/43) Counting objects: 100% (43/43), done. +Delta compression using up to 4 threads +Compressing objects: 4% (1/23) Compressing objects: 8% (2/23) Compressing objects: 13% (3/23) Compressing objects: 17% (4/23) Compressing objects: 21% (5/23) Compressing objects: 26% (6/23) Compressing objects: 30% (7/23) Compressing objects: 34% (8/23) Compressing objects: 39% (9/23) Compressing objects: 43% (10/23) Compressing objects: 47% (11/23) Compressing objects: 52% (12/23) Compressing objects: 56% (13/23) Compressing objects: 60% (14/23) Compressing objects: 65% (15/23) Compressing objects: 69% (16/23) Compressing objects: 73% (17/23) Compressing objects: 78% (18/23) Compressing objects: 82% (19/23) Compressing objects: 86% (20/23) Compressing objects: 91% (21/23) Compressing objects: 95% (22/23) Compressing objects: 100% (23/23) Compressing objects: 100% (23/23), done. +Writing objects: 4% (1/23) Writing objects: 8% (2/23) Writing objects: 13% (3/23) Writing objects: 17% (4/23) Writing objects: 17% (4/23), 1.05 MiB | 1.34 MiB/s Writing objects: 21% (5/23), 1.05 MiB | 1.34 MiB/s Writing objects: 26% (6/23), 1.05 MiB | 1.34 MiB/s Writing objects: 30% (7/23), 1.05 MiB | 1.34 MiB/s Writing objects: 34% (8/23), 1.05 MiB | 1.34 MiB/s Writing objects: 39% (9/23), 1.05 MiB | 1.34 MiB/s Writing objects: 43% (10/23), 1.05 MiB | 1.34 MiB/s Writing objects: 47% (11/23), 1.05 MiB | 1.34 MiB/s Writing objects: 52% (12/23), 1.05 MiB | 1.34 MiB/s Writing objects: 56% (13/23), 1.05 MiB | 1.34 MiB/s Writing objects: 60% (14/23), 1.05 MiB | 1.34 MiB/s Writing objects: 65% (15/23), 1.05 MiB | 1.34 MiB/s Writing objects: 69% (16/23), 1.05 MiB | 1.34 MiB/s Writing objects: 73% (17/23), 1.05 MiB | 1.34 MiB/s Writing objects: 78% (18/23), 1.05 MiB | 1.34 MiB/s Writing objects: 82% (19/23), 1.05 MiB | 1.34 MiB/s Writing objects: 86% (20/23), 1.05 MiB | 1.34 MiB/s Writing objects: 91% (21/23), 1.05 MiB | 1.34 MiB/s Writing objects: 95% (22/23), 1.05 MiB | 1.34 MiB/s Writing objects: 100% (23/23), 1.05 MiB | 1.34 MiB/s Writing objects: 100% (23/23), 1.20 MiB | 1.07 MiB/s, done. +Total 23 (delta 15), reused 0 (delta 0) +remote: . Processing 1 references +remote: Processed 1 references in total +To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git + 6edd5f9..c28c4a4 master -> master +]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.7, Release Date: 2022-09-19 │ +│ Using Python 3.10.5. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^7 +z1^3 - z1 = x^4 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.magical_element()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lomology_of_structure_sheaf_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.cohomology_of_structure_sheaf_basis() +[?7h[?12l[?25h[?2004l[?7h[z1/x, + z1^2/x, + z0/x, + z0*z1/x, + z0*z1^2/x, + z0^2/x, + z0^2*z1/x, + z0^2*z1^2/x, + z1^2/x^2, + z0*z1/x^2, + z0*z1^2/x^2, + z0^2/x^2, + z0^2*z1/x^2, + z0^2*z1^2/x^2, + z0*z1^2/x^3, + z0^2*z1/x^3, + z0^2*z1^2/x^3, + z0*z1^2/x^4, + z0^2*z1/x^4, + z0^2*z1^2/x^4, + z0^2*z1^2/x^5] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfz*o[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmology_of_structure_sheaf_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: fct = AS.cohomology_of_structure_sheaf_basis()[0] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lr[?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'init.sage')[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lty/[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lft_to_de_rham.sage[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('drafty/lift_to_de_rham.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift_to_de_rham(AS, fct, threshold = 8)[?7h[?12l[?25h[?25l[?7lsage: lift_to_de_rham(AS, fct, threshold = 8) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Input In [6], in () +----> 1 lift_to_de_rham(AS, fct, threshold = Integer(8)) + +File :4, in lift_to_de_rham(AS, fct, threshold) + +NameError: name 'self' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift_to_de_rham(AS, fct, threshold = 8)[?7h[?12l[?25h[?25l[?7load('drafty/lift_to_de_rham.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/lift_to_de_rham.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/lift_to_de_rham.sage')[?7h[?12l[?25h[?25l[?7lift_to_de_rham(AS, fct, threshold = 8)[?7h[?12l[?25h[?25l[?7lsage: lift_to_de_rham(AS, fct, threshold = 8) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Input In [8], in () +----> 1 lift_to_de_rham(AS, fct, threshold = Integer(8)) + +File :24, in lift_to_de_rham(AS, fct, threshold) + +NameError: name 'self' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift_to_de_rham(AS, fct, threshold = 8)[?7h[?12l[?25h[?25l[?7load('drafty/lift_to_de_rham.sage')[?7h[?12l[?25h[?25l[?7lift_to_de_rham(AS, fct, threshold = 8)[?7h[?12l[?25h[?25l[?7lsage: lift_to_de_rham(AS, fct, threshold = 8) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Input In [9], in () +----> 1 lift_to_de_rham(AS, fct, threshold = Integer(8)) + +File :24, in lift_to_de_rham(AS, fct, threshold) + +NameError: name 'self' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift_to_de_rham(AS, fct, threshold = 8)[?7h[?12l[?25h[?25l[?7load('drafty/lift_to_de_rham.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/lift_to_de_rham.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/lift_to_de_rham.sage')[?7h[?12l[?25h[?25l[?7lift_to_de_rham(AS, fct, threshold = 8)[?7h[?12l[?25h[?25l[?7lsage: lift_to_de_rham(AS, fct, threshold = 8) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [11], in () +----> 1 lift_to_de_rham(AS, fct, threshold = Integer(8)) + +File :30, in lift_to_de_rham(AS, fct, threshold) + +AttributeError: 'as_form' object has no attribute 'valuation' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift_to_de_rham(AS, fct, threshold = 8)[?7h[?12l[?25h[?25l[?7load('drafty/lift_to_de_rham.sage')[?7h[?12l[?25h[?25l[?7lift_to_de_rham(AS, fct, threshold = 8)[?7h[?12l[?25h[?25l[?7load('drafty/lift_to_de_rham.sage')[?7h[?12l[?25h[?25l[?7lift_to_de_rham(AS, fct, threshold = 8)[?7h[?12l[?25h[?25l[?7load('drafty/lift_to_de_rham.sage')[?7h[?12l[?25h[?25l[?7lfct = AS.cohomology_of_structure_sheaf_basis()[0][?7h[?12l[?25h[?25l[?7lAS.cohomolgy_f_structure_sheafbasis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lift_to_de_rham(AS, fct, threshold = 8)[?7h[?12l[?25h[?25l[?7lsage: lift_to_de_rham(AS, fct, threshold = 8) +[?7h[?12l[?25h[?2004l[?7h(0) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfct = AS.cohomology_of_structure_sheaf_basis()[0][?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lsage: fct +[?7h[?12l[?25h[?2004l[?7hz1/x +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lzmag = AS.magical_element(threshold = 18)[0][?7h[?12l[?25h[?25l[?7l1[?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[?7lfct[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fct.valuation() +[?7h[?12l[?25h[?2004l[?7h-3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldef Frob(x,y):[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfct.valuation()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?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: fct.diffn() +[?7h[?12l[?25h[?2004l[?7h((-x^4 - z1)/x^2) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfct.diffn()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fct.diffn().valuation() +[?7h[?12l[?25h[?2004l[?7h22 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l\[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfct.diffn().valuation()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lvaluation()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift_to_de_rham(AS, fct, threshold = 8)[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lift_to_de_rham(AS, fct, threshold = 8)[?7h[?12l[?25h[?25l[?7load('drafty/lift_to_de_rham.sage')[?7h[?12l[?25h[?25l[?7lift_to_de_rham(AS, fct, threshold = 8)[?7h[?12l[?25h[?25l[?7load('drafty/lift_to_de_rham.sage')[?7h[?12l[?25h[?25l[?7lift_to_de_rham(AS, fct, threshold = 8)[?7h[?12l[?25h[?25l[?7load('drafty/lift_to_de_rham.sage')[?7h[?12l[?25h[?25l[?7lfct = AS.cohomology_of_structure_sheaf_basis()[0][?7h[?12l[?25h[?25l[?7lAS.cohomolgy_f_structure_sheafbasis()[?7h[?12l[?25h[?25l[?7lfct = AS.chomlogy_of_structuresheaf_basis()[0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l1][?7h[?12l[?25h[?25l[?7lsage: fct = AS.cohomology_of_structure_sheaf_basis()[1] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfct = AS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l.diffn().valuation()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lvaluation()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift_to_de_rham(AS, fct, threshold = 8)[?7h[?12l[?25h[?25l[?7lsage: lift_to_de_rham(AS, fct, threshold = 8) +[?7h[?12l[?25h[?2004l[?7h(0) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift_to_de_rham(AS, fct, threshold = 8)[?7h[?12l[?25h[?25l[?7lfct = AS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l5][?7h[?12l[?25h[?25l[?7lsage: fct = AS.cohomology_of_structure_sheaf_basis()[5] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfct = AS.cohomology_of_structure_sheaf_basis()[5][?7h[?12l[?25h[?25l[?7llift_to_de_rham(AS, fct, threshold = 8)[?7h[?12l[?25h[?25l[?7lsage: lift_to_de_rham(AS, fct, threshold = 8) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift_to_de_rham(AS, fct, threshold = 8)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: lift_to_de_rham(AS, fct, threshold = 20) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift_to_de_rham(AS, fct, threshold = 20)[?7h[?12l[?25h[?25l[?7l8)[?7h[?12l[?25h[?25l[?7lfct = AS.cohomology_of_structure_sheaf_basis()[5][?7h[?12l[?25h[?25l[?7llift_to_de_rham(AS, fct, threshold = 8)[?7h[?12l[?25h[?25l[?7lfct = AS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l.diffn().valuation()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lvaluation()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift_to_de_rham(AS, fct, threshold = 8)[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lift_to_de_rham(AS, fct, threshold = 8)[?7h[?12l[?25h[?25l[?7load('drafty/lift_to_de_rham.sage')[?7h[?12l[?25h[?25l[?7lift_to_de_rham(AS, fct, threshold = 8)[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lift_to_de_rham(AS, fct, threshold = 20)[?7h[?12l[?25h[?25l[?7l8)[?7h[?12l[?25h[?25l[?7lfct = AS.cohomology_of_structure_sheaf_basis()[5][?7h[?12l[?25h[?25l[?7lsage: fct = AS.cohomology_of_structure_sheaf_basis()[5] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfct = AS.cohomology_of_structure_sheaf_basis()[5][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lift_to_de_rham(AS, fct, threshold = 20)[?7h[?12l[?25h[?25l[?7lsage: lift_to_de_rham(AS, fct, threshold = 20) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift_to_de_rham(AS, fct, threshold = 20)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l30)[?7h[?12l[?25h[?25l[?7lsage: lift_to_de_rham(AS, fct, threshold = 30) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift_to_de_rham(AS, fct, threshold = 30)[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l40)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: lift_to_de_rham(AS, fct, threshold = 40) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift_to_de_rham(AS, fct, threshold = 40)[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lfct = AS.cohomology_of_structure_sheaf_basis()[5][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lift_to_de_rham(AS, fct, threshold = 40)[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lfct = AS.cohomology_of_structure_sheaf_basis()[5][?7h[?12l[?25h[?25l[?7lsage: fct = AS.cohomology_of_structure_sheaf_basis()[5] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfct = AS.cohomology_of_structure_sheaf_basis()[5][?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lsage: fct +[?7h[?12l[?25h[?2004l[?7hz0^2/x +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfct[?7h[?12l[?25h[?25l[?7l = AS.cohomology_of_structure_sheaf_basis()[5][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lift_to_de_rham(AS, fct, threshold = 40)[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: lift_to_de_rham(AS, fct, threshold = 30) +[?7h[?12l[?25h[?2004l22 21 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift_to_de_rham(AS, fct, threshold = 30)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfct[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l.diffn().valuation()[?7h[?12l[?25h[?25l[?7lvaluation()[?7h[?12l[?25h[?25l[?7laluation()[?7h[?12l[?25h[?25l[?7lsage: fct.valuation() +[?7h[?12l[?25h[?2004l[?7h-33 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfct.valuation()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldiffn().valuation()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln().valuation()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: fct.diffn().valuation() +[?7h[?12l[?25h[?2004l[?7h-26 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo = AS.holomorphic_differentials_basis()[0][?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: om = AS.holomorphic_differentials_basis()[1] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2+2[?7h[?12l[?25h[?25l[?7l*AS.genus()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: 2*om +[?7h[?12l[?25h[?2004l[?7h(-z1) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentials_basis()[1][?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om +[?7h[?12l[?25h[?2004l[?7h(z1) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7l2*om[?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentials_basis()[1][?7h[?12l[?25h[?25l[?7lfct.diffn().valuation()[?7h[?12l[?25h[?25l[?7lvaluation()[?7h[?12l[?25h[?25l[?7llift_to_de_rham(AS, fct, threshold = 30)[?7h[?12l[?25h[?25l[?7lfct[?7h[?12l[?25h[?25l[?7l = AS.cohomology_of_structure_sheaf_basis()[5][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7l2*om[?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentials_basis()[1][?7h[?12l[?25h[?25l[?7lfct.diffn().valuation()[?7h[?12l[?25h[?25l[?7lvaluation()[?7h[?12l[?25h[?25l[?7llift_to_de_rham(AS, fct, threshold = 30)[?7h[?12l[?25h[?25l[?7lfct[?7h[?12l[?25h[?25l[?7l = AS.cohomology_of_structure_sheaf_basis()[5][?7h[?12l[?25h[?25l[?7lsage: fct = AS.cohomology_of_structure_sheaf_basis()[5] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfct = AS.cohomology_of_structure_sheaf_basis()[5][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7l2*om[?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentials_basis()[1][?7h[?12l[?25h[?25l[?7lfct.diffn().valuation()[?7h[?12l[?25h[?25l[?7lvaluation()[?7h[?12l[?25h[?25l[?7llift_to_de_rham(AS, fct, threshold = 30)[?7h[?12l[?25h[?25l[?7lsage: lift_to_de_rham(AS, fct, threshold = 30) +[?7h[?12l[?25h[?2004l22 21 +((-z0^2)/x^2) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift_to_de_rham(AS, fct, threshold = 30)[?7h[?12l[?25h[?25l[?7lfct = AS.cohomology_of_structure_sheaf_basis()[5][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lift_to_de_rham(AS, fct, threshold = 30)[?7h[?12l[?25h[?25l[?7lfct = AS.cohomology_of_structure_sheaf_basis()[5][?7h[?12l[?25h[?25l[?7lsage: fct = AS.cohomology_of_structure_sheaf_basis()[5] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfct = AS.cohomology_of_structure_sheaf_basis()[5][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lfct = AS.cohomology_of_structure_sheaf_basis()[5][?7h[?12l[?25h[?25l[?7lsage: fct = AS.cohomology_of_structure_sheaf_basis()[5] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfct = AS.cohomology_of_structure_sheaf_basis()[5][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lfct = AS.cohomology_of_structure_sheaf_basis()[5][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lift_to_de_rham(AS, fct, threshold = 30)[?7h[?12l[?25h[?25l[?7lsage: lift_to_de_rham(AS, fct, threshold = 30) +[?7h[?12l[?25h[?2004l22 21 +((-z0^2)/x^2) * dx +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +-26 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift_to_de_rham(AS, fct, threshold = 30)[?7h[?12l[?25h[?25l[?7lfct = AS.cohomology_of_structure_sheaf_basis()[5][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lift_to_de_rham(AS, fct, threshold = 30)[?7h[?12l[?25h[?25l[?7lfct = AS.cohomology_of_structure_sheaf_basis()[5][?7h[?12l[?25h[?25l[?7lsage: fct = AS.cohomology_of_structure_sheaf_basis()[5] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfct = AS.cohomology_of_structure_sheaf_basis()[5][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lift_to_de_rham(AS, fct, threshold = 30)[?7h[?12l[?25h[?25l[?7lsage: lift_to_de_rham(AS, fct, threshold = 30) +[?7h[?12l[?25h[?2004l22 21 +((-z0^2)/x^2) * dx +a: 0 +-26 +a: 1 +-26 +a: 2 +-26 +a: 0 +-26 +a: 1 +-26 +a: 2 +-26 +a: 0 +-26 +a: 1 +-26 +a: 2 +-26 +a: 0 +-26 +a: 1 +-26 +a: 2 +-26 +a: 0 +-26 +a: 1 +-26 +a: 2 +-26 +a: 0 +-26 +a: 1 +-26 +a: 2 +-26 +a: 0 +-26 +a: 1 +-26 +a: 2 +-26 +a: 0 +-26 +a: 1 +-26 +a: 2 +-26 +a: 0 +-26 +a: 1 +-26 +a: 2 +-26 +a: 0 +-26 +a: 1 +-26 +a: 2 +-26 +a: 0 +-26 +a: 1 +-26 +a: 2 +-26 +a: 0 +-26 +a: 1 +-26 +a: 2 +-26 +a: 0 +-26 +a: 1 +-26 +a: 2 +-26 +a: 0 +-26 +a: 1 +-26 +a: 2 +-26 +a: 0 +-26 +a: 1 +-26 +a: 2 +-26 +a: 0 +-26 +a: 1 +-26 +a: 2 +-26 +a: 0 +-26 +a: 1 +-26 +a: 2 +-26 +a: 0 +-26 +a: 1 +-26 +a: 2 +-26 +a: 0 +-26 +a: 1 +-26 +a: 2 +-26 +a: 0 +-26 +a: 1 +-26 +a: 2 +-26 +a: 0 +-26 +a: 1 +-26 +a: 2 +-26 +a: 0 +-26 +a: 1 +-26 +a: 2 +-26 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift_to_de_rham(AS, fct, threshold = 30)[?7h[?12l[?25h[?25l[?7lfct = AS.cohomology_of_structure_sheaf_basis()[5][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lift_to_de_rham(AS, fct, threshold = 30)[?7h[?12l[?25h[?25l[?7lfct = AS.cohomology_of_structure_sheaf_basis()[5][?7h[?12l[?25h[?25l[?7lsage: fct = AS.cohomology_of_structure_sheaf_basis()[5] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfct = AS.cohomology_of_structure_sheaf_basis()[5][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lift_to_de_rham(AS, fct, threshold = 30)[?7h[?12l[?25h[?25l[?7lsage: lift_to_de_rham(AS, fct, threshold = 30) +[?7h[?12l[?25h[?2004l22 21 +((-z0^2)/x^2) * dx 16 -26 +a: 0 +-26 +a: 1 +-26 +[?7h((-z0^2)/x^2) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift_to_de_rham(AS, fct, threshold = 30)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAlift_to_de_rham(AS, fct, threshold = 30)[?7h[?12l[?25h[?25l[?7l lift_to_de_rham(AS, fct, threshold = 30)[?7h[?12l[?25h[?25l[?7l=lift_to_de_rham(AS, fct, threshold = 30)[?7h[?12l[?25h[?25l[?7l lift_to_de_rham(AS, fct, threshold = 30)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A = lift_to_de_rham(AS, fct, threshold = 30) +[?7h[?12l[?25h[?2004l22 21 +((-z0^2)/x^2) * dx 16 -26 +a: 0 +-26 +a: 1 +-26 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = lift_to_de_rham(AS, fct, threshold = 30)[?7h[?12l[?25h[?25l[?7lsage: A +[?7h[?12l[?25h[?2004l[?7h((-z0^2)/x^2) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift_to_de_rham(AS, fct, threshold = 30)[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l'init.sage')[?7h[?12l[?25h[?25l[?7ldrafty/lift_to_de_rham.sage')[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l(afty/lift_to_de_rham.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/lift_to_de_rham.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldef Frob(x,y):[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lbasis[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: de_rham_basis(AS) +[?7h[?12l[?25h[?2004l22 21 +22 21 +22 21 +22 21 +22 21 +22 21 +22 21 +22 21 +22 21 +22 21 +22 21 +22 21 +22 21 +22 21 +22 21 +22 21 +22 21 +22 21 +22 21 +22 21 +22 21 +[?7h[((1) * dx, 0), + ((z1) * dx, 0), + ((z1^2) * dx, 0), + ((z0) * dx, 0), + ((z0*z1) * dx, 0), + ((-x^5 + z0*z1^2) * dx, 0), + ((-x^2*z1^2 + z0^2) * dx, 0), + ((x^6 + x*z0*z1^2 + z0^2*z1) * dx, 0), + ((x) * dx, 0), + ((x*z1) * dx, 0), + ((x*z1^2) * dx, 0), + ((x*z0) * dx, 0), + ((-x^2*z1^2 + x*z0*z1) * dx, 0), + ((x^3*z1^2 + x^2*z0*z1 + x*z0^2) * dx, 0), + ((x^2) * dx, 0), + ((x^2*z1) * dx, 0), + ((x^2*z0) * dx, 0), + ((x^3) * dx, 0), + ((x^3*z1) * dx, 0), + ((-x^4*z1 + x^3*z0) * dx, 0), + ((x^4) * dx, 0), + (((-z0^2)/x^2) * dx, z1/x), + (((-z0^2)/x^2) * dx, z1^2/x), + (((-z0^2)/x^2) * dx, z0/x), + (((-z0^2)/x^2) * dx, z0*z1/x), + (((-z0^2)/x^2) * dx, z0*z1^2/x), + (((-z0^2)/x^2) * dx, z0^2/x), + (((-z0^2)/x^2) * dx, z0^2*z1/x), + (((-z0^2)/x^2) * dx, z0^2*z1^2/x), + (((-z0^2)/x^2) * dx, z1^2/x^2), + (((-z0^2)/x^2) * dx, z0*z1/x^2), + (((-z0^2)/x^2) * dx, z0*z1^2/x^2), + (((-z0^2)/x^2) * dx, z0^2/x^2), + (((-z0^2)/x^2) * dx, z0^2*z1/x^2), + (((-z0^2)/x^2) * dx, z0^2*z1^2/x^2), + (((-z0^2)/x^2) * dx, z0*z1^2/x^3), + (((-z0^2)/x^2) * dx, z0^2*z1/x^3), + (((-z0^2)/x^2) * dx, z0^2*z1^2/x^3), + (((-z0^2)/x^2) * dx, z0*z1^2/x^4), + (((-z0^2)/x^2) * dx, z0^2*z1/x^4), + (((-z0^2)/x^2) * dx, z0^2*z1^2/x^4), + (((-z0^2)/x^2) * dx, z0^2*z1^2/x^5)] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus() +[?7h[?12l[?25h[?2004l[?7h21 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit() +[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ git addg \ No newline at end of file diff --git a/sage/as_covers/as_cover_class.sage b/sage/as_covers/as_cover_class.sage index 89953e0..ed489b1 100644 --- a/sage/as_covers/as_cover_class.sage +++ b/sage/as_covers/as_cover_class.sage @@ -329,6 +329,49 @@ class as_cover: result_fcts += [f] i += 1 return result_fcts + + def lift_to_de_rham(AS, fct, threshold = 8): + '''Given function fct, find form eta regular on affine part such that eta - d(fct) is regular in infty. (Works for one place at infty now)''' + from itertools import product + x_series = AS.x + y_series = AS.y + z_series = AS.z + dx_series = AS.dx + delta = AS.nb_of_pts_at_infty + p = AS.characteristic + n = AS.height + prec = AS.prec + C = AS.quotient + F = AS.base_ring + m = C.exponent + r = C.polynomial.degree() + RxyzQ, Rxyz, x, y, z = AS.fct_field + Rt. = LaurentSeriesRing(F, default_prec=prec) + #Tworzymy zbiór S form z^i x^j y^k dx/y o waluacji >= waluacja z^(p-1)*dx/y + S = [(fct.diffn(), fct.diffn().expansion_at_infty())] + pr = [list(GF(p)) for _ in range(n)] + for i in range(0, threshold*r): + for j in range(0, m): + for k in product(*pr): + eta = as_form(AS, x^i * prod(z[i1]^(k[i1]) for i1 in range(n))*y^j) + eta_exp = eta.expansion_at_infty() + S += [(eta, eta_exp)] + forms = holomorphic_combinations(S) + for omega in forms: + if not are_forms_linearly_dependent(holo + [omega]): + for a in F: + if (a*omega - fct.diffn()).form in Rxyz: + return a*omega + + + def de_rham_basis(AS, threshold = 8): + result = [] + for omega in AS.holomorphic_differentials_basis(): + result += [(omega, 0)] + for f in AS.cohomology_of_structure_sheaf_basis(): + omega = lift_to_de_rham(AS, fct, threshold = 8) + result += [(omega, f)] + return result def holomorphic_combinations(S): """Given a list S of pairs (form, corresponding Laurent series at some pt), find their combinations holomorphic at that pt.""" diff --git a/sage/as_covers/as_form_class.sage b/sage/as_covers/as_form_class.sage index 146268f..b7eec1d 100644 --- a/sage/as_covers/as_form_class.sage +++ b/sage/as_covers/as_form_class.sage @@ -105,10 +105,13 @@ class as_form: Qxy = FractionField(Rxy) result = as_reduction(AS, result) return superelliptic_form(C_super, Qxy(result)) - + def residue(self, place=0): return self.expansion_at_infty(i = place).residue() + def valuation(self, place=0): + return self.expansion_at_infty(i = place).valuation() + def artin_schreier_transform(power_series, prec = 10): """Given a power_series, find correction such that power_series - (correction)^p +correction has valuation -jump non divisible by p. Also, express t (the variable) in terms of the uniformizer at infty on the curve diff --git a/sage/drafty/draft3.sage b/sage/drafty/draft3.sage index b58e59d..201ab8e 100644 --- a/sage/drafty/draft3.sage +++ b/sage/drafty/draft3.sage @@ -8,16 +8,4 @@ C_super = superelliptic(f, m) Rxy. = PolynomialRing(F, 2) f1 = superelliptic_function(C_super, x^7) f2 = superelliptic_function(C_super, x^4) -AS = as_cover(C_super, [f1, f2], prec=1000) -AS1 = as_cover(C_super, [f1], prec=1000) -#print(AS.ramification_jumps()) -#print(pole_numbers(AS)) -RxyzQ, Rxyz, x, y, z = AS.fct_field -zmag = (AS.magical_element())[0] -zvee = dual_elt(AS, zmag) -t = AS.uniformizer() -omega1 = AS1.holomorphic_differentials_basis()[4] -omega2 = as_form(AS, t.function*RxyzQ(omega1.form)) - -for g in AS.group: - print(ith_magical_component(omega2, zvee, g).expansion_at_infty().valuation(), AS.jumps[0][1]) \ No newline at end of file +AS = as_cover(C_super, [f1, f2], prec=1000) \ No newline at end of file diff --git a/sage/init.sage b/sage/init.sage index 2f55433..f2b5faa 100644 --- a/sage/init.sage +++ b/sage/init.sage @@ -15,6 +15,7 @@ load('auxilliaries/reverse.sage') load('auxilliaries/hensel.sage') ############## ############## -load('drafty/draft.sage') +load('drafty/lift_to_de_rham.sage') +load('drafty/draft3.sage') load('drafty/pole_numbers.sage') #load('drafty/draft4.sage') \ No newline at end of file