From a5c2ce2c64e1035417817b44ad2e29764a95cef2 Mon Sep 17 00:00:00 2001 From: jgarnek Date: Fri, 31 Mar 2023 16:03:09 +0000 Subject: [PATCH] naprawione C.cohomology_of_str_sh.coordinates. Ale drw_cech.reduce nadal zmienia argument --- sage/.run.term-0.term | 1582 ++++++++++++++++- sage/drafty/draft.sage | 8 +- .../superelliptic_function_class.sage | 2 +- 3 files changed, 1586 insertions(+), 6 deletions(-) diff --git a/sage/.run.term-0.term b/sage/.run.term-0.term index 2cbf9a1..0baea02 100644 --- a/sage/.run.term-0.term +++ b/sage/.run.term-0.term @@ -30295,4 +30295,1584 @@ File :5, in decomposition_g0_pth_power(fct) (((2*x^5 + x)/y) dx, 2/x^5*y, ((-2*x^2 + 1)/(x^5*y)) dx), (((-2*x^8 - 2*x^4)/y) dx, 2/x^6*y, ((2*x^4 + x^2 - 1)/(x^6*y)) dx), (((x^7 - x^3)/y) dx, 2/x^7*y, ((x^6 - x^4 - x^2 + 2)/(x^7*y)) dx)] -[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h \ No newline at end of file +[?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$ cd .. +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -u +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git commit -m ""n"a"p"r"a"w"i"o"n"e" "r"e"g"u"l"a"r" "f"o"r"m";" "s"u"p"e"r"e"l"l"i"p"t"y"c"z"n"e" "m"a"j"a" "C"."x"_"s"e"r"i"e"s" "i"t"d" +[master 64fe2ee] naprawione regular form; superelliptyczne maja C.x_series itd + 10 files changed, 20233 insertions(+), 46862 deletions(-) +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git push +Username for 'https://git.wmi.amu.edu.pl': 3Cardano +Password for 'https://3Cardano@git.wmi.amu.edu.pl': +remote: Unauthorized +fatal: Authentication failed for 'https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git/' +]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: 30, done. +Counting objects: 3% (1/30) Counting objects: 6% (2/30) Counting objects: 10% (3/30) Counting objects: 13% (4/30) Counting objects: 16% (5/30) Counting objects: 20% (6/30) Counting objects: 23% (7/30) Counting objects: 26% (8/30) Counting objects: 30% (9/30) Counting objects: 33% (10/30) Counting objects: 36% (11/30) Counting objects: 40% (12/30) Counting objects: 43% (13/30) Counting objects: 46% (14/30) Counting objects: 50% (15/30) Counting objects: 53% (16/30) Counting objects: 56% (17/30) Counting objects: 60% (18/30) Counting objects: 63% (19/30) Counting objects: 66% (20/30) Counting objects: 70% (21/30) Counting objects: 73% (22/30) Counting objects: 76% (23/30) Counting objects: 80% (24/30) Counting objects: 83% (25/30) Counting objects: 86% (26/30) Counting objects: 90% (27/30) Counting objects: 93% (28/30) Counting objects: 96% (29/30) Counting objects: 100% (30/30) Counting objects: 100% (30/30), done. +Delta compression using up to 4 threads +Compressing objects: 6% (1/16) Compressing objects: 12% (2/16) Compressing objects: 18% (3/16) Compressing objects: 25% (4/16) Compressing objects: 31% (5/16) Compressing objects: 37% (6/16) Compressing objects: 43% (7/16) Compressing objects: 50% (8/16) Compressing objects: 56% (9/16) Compressing objects: 62% (10/16) Compressing objects: 68% (11/16) Compressing objects: 75% (12/16) Compressing objects: 81% (13/16) Compressing objects: 87% (14/16) Compressing objects: 93% (15/16) Compressing objects: 100% (16/16) Compressing objects: 100% (16/16), done. +Writing objects: 6% (1/16) Writing objects: 12% (2/16) Writing objects: 18% (3/16) Writing objects: 25% (4/16) Writing objects: 31% (5/16) Writing objects: 37% (6/16) Writing objects: 43% (7/16) Writing objects: 50% (8/16) Writing objects: 56% (9/16) Writing objects: 62% (10/16) Writing objects: 68% (11/16) Writing objects: 75% (12/16) Writing objects: 81% (13/16) Writing objects: 87% (14/16) Writing objects: 93% (15/16) Writing objects: 100% (16/16) Writing objects: 100% (16/16), 71.97 KiB | 402.00 KiB/s, done. +Total 16 (delta 13), reused 0 (delta 0) +remote: . Processing 1 references +remote: Processed 1 references in total +To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git + eda1cca..64fe2ee master -> master +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.8, Release Date: 2023-02-11 │ +│ Create a "Sage Worksheet" file for the notebook interface. │ +│ Enhanced for CoCalc. │ +│ Using Python 3.11.1. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/superelliptic_drw_auxilliaries.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/superelliptic_drw_auxilliaries.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l;[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l'superelliptic_drw/superelliptic_drw_auxilliaries.sage')[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7l(nit.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lComputing 0. basis element +Computing 1. basis element +( [3*x*y] d[x] + [3*x^2 + 2] d[y] + V(((3*x^19 + 2*x^17 + x^15 + x^13 + 3*x^9 + 4*x^7 + x^5 + x^3 + x)*y) dx + (3*x^20 + 4*x^18 + 4*x^16 + 4*x^12 + 3*x^10 + x^8 + 2*x^6 + 4) dy) + dV(0), V((4*x^14 + x^12 + 3*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 4)*y) ) +( [3*x^2*y] d[x] + [3*x^3 + 2*x] d[y] + V(((3*x^24 + 4*x^22 + x^20 + 3*x^18 + 3*x^16 + 3*x^10 + 2*x^8 + 3*x^4 + 3*x^2)*y) dx + (3*x^25 + x^23 + 2*x^21 + 2*x^19 + 2*x^15 + 3*x^11 + 4*x^9 + 3*x^7 + 3*x^5 + 2*x) dy) + dV(0), [2/x*y] + V(((4*x^20 + x^18 + 3*x^16 + 3*x^14 + x^12 + x^10 + 3*x^8 + 4*x^6 + 4*x^4 + 3*x^2 + 4)/x)*y) ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].omega0[?7h[?12l[?25h[?25l[?7l1[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[?7lB[0].omega0[?7h[?12l[?25h[?25l[?7l1[0].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: B1[0] +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Cell In [2], line 1 +----> 1 B1[Integer(0)] + +NameError: name 'B1' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB1[0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[0][?7h[?12l[?25h[?25l[?7l[][?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[0] +[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + x))*y] d[x] + V(((-x^2 + 2)/(x^4*y + 2*x^2*y + y)) dx) + dV([((4*x^18 + 4*x^16 + 4*x^14 + x^8 + x^6 + x^4)/(x^4 + 2*x^2 + 1))*y]), V((4*x^14 + x^12 + 3*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 4)*y), [(1/(x^3 + x))*y] d[x] + V(((-x^2 + 2)/(x^4*y + 2*x^2*y + y)) dx) + dV([((4*x^2 + 1)/(x^4 + 2*x^2 + 1))*y])) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0][?7h[?12l[?25h[?25l[?7l[].omega0[?7h[?12l[?25h[?25l[?7lregular_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[?7lomega0[?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.regular_form()[?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[?7h[3*x*y] d[x] + [3*x^2 + 2] d[y] + V(((3*x^19 + 2*x^17 + x^15 + x^13 + 3*x^9 + 4*x^7 + x^5 + x^3 + x)*y) dx + (3*x^20 + 4*x^18 + 4*x^16 + 4*x^12 + 3*x^10 + x^8 + 2*x^6 + 4) dy) + dV(0) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.de_rham_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].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[?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[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B[0].omega0.r() +[?7h[?12l[?25h[?2004l[?7h(1/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].omega0.r()[?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[?7lla[?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.r().regular_form() +[?7h[?12l[?25h[?2004l[?7h(3*x*y) dx + (3*x^2 + 2) dy +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.de_rham_basis()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l = superelliptic(f1, m, prec = 500)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1 = superelliptic(f1, m, prec = 500)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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[?7lf1 = f(x = x^5 - x)[?7h[?12l[?25h[?25l[?7lsage: f1 = f(x = x^5 - x) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.de_rham_basis()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l = superelliptic(f1, m, prec = 500)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(f1, m, prec = 500)[?7h[?12l[?25h[?25l[?7lsage: C1 = superelliptic(f1, m, prec = 500) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1 = superelliptic(f1, m, prec = 500)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C1.de_rham_basis() +[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx), + ((x/y) dx, 0, (x/y) dx), + ((x^2/y) dx, 0, (x^2/y) dx), + ((x^3/y) dx, 0, (x^3/y) dx), + ((x^4/y) dx, 0, (x^4/y) dx), + ((x^5/y) dx, 0, (x^5/y) dx), + ((x^6/y) dx, 0, (x^6/y) dx), + (((-2*x^13 - 2*x^9 - 2*x^3 - x)/y) dx, 2/x*y, ((-1)/(x*y)) dx), + (((x^12 - x^8 - x^4 + x^2 + 1)/y) dx, 2/x^2*y, (2/(x^2*y)) dx), + (((-x^11 - 2*x^3 - x)/y) dx, 2/x^3*y, (2/(x*y)) dx), + (((2*x^10 + x^6 + 2*x^2 + 2)/y) dx, 2/x^4*y, ((-2)/(x^4*y)) dx), + (((2*x^5 + x)/y) dx, 2/x^5*y, ((-2*x^2 + 1)/(x^5*y)) dx), + (((-2*x^8 - 2*x^4)/y) dx, 2/x^6*y, ((2*x^4 + x^2 - 1)/(x^6*y)) dx), + (((x^7 - x^3)/y) dx, 2/x^7*y, ((x^6 - x^4 - x^2 + 2)/(x^7*y)) dx)] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(A - A1 - C1.y).diffn()[?7h[?12l[?25h[?25l[?7lx^36 +2*x^34 + 2*x^32 + 2*x^30 + 2*x^28 + 4*x^26 + x^24 + 2*x^22 + 3*x^20 + 2*x^18 + x^14 + 4*x^12 + x^8 + x^6 + 3*x^4 + 4).factor()[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7lsage: (x^5 - x)^4 +[?7h[?12l[?25h[?2004l[?7hx^20 + x^16 + x^12 + x^8 + x^4 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(A.h2.function)[?7h[?12l[?25h[?25l[?7lsage: p +[?7h[?12l[?25h[?2004l[?7h5 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.de_rham_basis()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: C1 +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^15 + 2*x^11 + 3*x^7 + x^5 + 4*x^3 + 4*x over Finite Field of size 5 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + x over Finite Field of size 5 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()[4] +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +IndexError Traceback (most recent call last) +Cell In [14], line 1 +----> 1 C.de_rham_basis()[Integer(4)] + +IndexError: list index out of range +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[4][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()[0] +[?7h[?12l[?25h[?2004l[?7h((1/y) dx, 0, (1/y) dx) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l4][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C1.de_rham_basis()[4] +[?7h[?12l[?25h[?2004l[?7h((x^4/y) dx, 0, (x^4/y) dx) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.de_rham_basis()[4][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: C1.de_rham_basis()[4].omega0.regular_form() +[?7h[?12l[?25h[?2004l[?7h((3*x^9 + 2*x^5)*y) dx + (2*x^14 + x^10 + 2*x^6 + 3*x^4) dy +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7ldic_expansion(x^7, x^3 - x)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lsage: adic_expansion + adic_expansion  + adic_expansion_polynomial + + + [?7h[?12l[?25h[?25l[?7l(x^7, x^3 - x)[?7h[?12l[?25h[?25l[?7l + adic_expansion  + + [?7h[?12l[?25h[?25l[?7l_polynomial + adic_expansion  + adic_expansion_polynomial[?7h[?12l[?25h[?25l[?7l( + + +[?7h[?12l[?25h[?25l[?7l3*x^9 + 2*x^5[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?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_polynomial(3*x^9 + 2*x^5, x^5 - x) +[?7h[?12l[?25h[?2004l[?7h3*x^4*t +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + [?7h[?12l[?25h[?25l[?7ladic_expansion_polynomial(3*x^9 + 2*x^5, x^5 - x)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_expansion_polynomial(3*x^9 + 2*x^5, x^5 - 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^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 -x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l2*14 + x^10 + 2*x^6 + 3*x^4, x^5 - 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[?7lsage: adic_expansion_polynomial(2*x^14 + x^10 + 2*x^6 + 3*x^4, x^5 - x) +[?7h[?12l[?25h[?2004l[?7h2*x^4*t^2 + 3*x^4 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + [?7h[?12l[?25h[?25l[?7ladic_expansion_polynomial(2*x^14 + x^10 + 2*x^6 + 3*x^4, x^5 - x)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lic_expansion_polynomial(2*x^14 + x^10 + 2*x^6 + 3*x^4, x^5 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l,x^5 -x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7l, x^5 - x)[?7h[?12l[?25h[?25l[?7lx^119+4*x^115 + 4*x^111 + x^107 + 3*x^105 + 3*x^103 + x^101 + 3*x^99 + x^97 + 4*x^95 + 3*x^93 + 3*x^89 + 2*x^87 + 4*x^85 + 2*x^8 3 +....:  + 4*x^81 + x^79 + 4*x^69 + x^65 + 4*x^63 + 4*x^59 + 3*x^57 + 3*x^55 + x^53 + x^51 + 4*x^47 + 3*x^45 + 4*x^43 + 2*x^41 + 2*x^39 + 3*x^37 + 4*x^35 + 3*x^33 + +....: 2*x^31 + 3*x^29 + 4*x^25 + x^23 + 3*x^21 + 4*x^19 + 2*x^17 + x^15 + x^13 + 2*x^9 + x^7 + 2*x^5 + 4*x, x^5 - 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[?7lsage: adic_expansion_polynomial(x^119 + 4*x^115 + 4*x^111 + x^107 + 3*x^105 + 3*x^103 + x^101 + 3*x^99 + x^97 + 4*x^95 + 3*x^93 + 3*x^89 + 2*x^87 + 4*x^85 + 2*x^8 3 +....:  + 4*x^81 + x^79 + 4*x^69 + x^65 + 4*x^63 + 4*x^59 + 3*x^57 + 3*x^55 + x^53 + x^51 + 4*x^47 + 3*x^45 + 4*x^43 + 2*x^41 + 2*x^39 + 3*x^37 + 4*x^35 + 3*x^33 + +....: 2*x^31 + 3*x^29 + 4*x^25 + x^23 + 3*x^21 + 4*x^19 + 2*x^17 + x^15 + x^13 + 2*x^9 + x^7 + 2*x^5 + 4*x, x^5 - x) +[?7h[?12l[?25h[?2004l[?7h(x^4 + 2)*t^23 + 2*x*t^22 + 3*t^21 + (3*x^3 + 4*x)*t^20 + (2*x^4 + x^2 + 3)*t^19 + (2*x^3 + x)*t^18 + (3*x^4 + 4*x^2)*t^17 + (4*x^3 + x)*t^16 + (4*x^4 + 4*x^2 + 1)*t^15 + (4*x^3 + 4*x)*t^14 + (4*x^4 + 3*x^2 + 4)*t^13 + (3*x^3 + 4*x)*t^12 + (3*x^4 + 1)*t^11 + 3*x*t^10 + (2*x^4 + 4*x^2 + 2)*t^9 + (x^3 + 4*x)*t^8 + (4*x^4 + x^2 + 2)*t^7 + (3*x^3 + x)*t^6 + (4*x^4 + x^2)*t^5 + 4*x^3*t^4 + (x^4 + 4*x^2)*t^3 + t +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ( ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmulle r +....: ().diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +....: + 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x ^ +....: 47 + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +....: + 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y).teichmuller() *C1.x.teichmuller().diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^1 1 +....: 4 + 3*C1.x^112 + 2*C1.x^110 + 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + +....: C1.x^80 + 4*C1.x^78 + 4*C1.x^76 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + +....:  3*C1.x^48 + 3*C1.x^46 + 4*C1.x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2 +....: *C1.x^6 + 4*C1.x^4 + 4*C1.x^2 + C1.one).teichmuller()*C1.y.diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7l....: *C1.x^6 + 4*C1.x^4 + 4*C1.x^2 + C1.one).teichmuller()*C1.y.diffn()).verschiebung() +....: [?7h[?12l[?25h[?25l[?7l....:  +....: [?7h[?12l[?25h[?25l[?7l....:  +....: [?7h[?12l[?25h[?25l[?7l +  +  +  +  +  +  +  +  +  +  + [?7h[?12l[?25h[?25l[?7lom = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller( ) +....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 + +....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4 7 +....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 + +....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y).teichmuller() *C1.x.teichmuller().diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 +....: + 3*C1.x^112 + 2*C1.x^110 + 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C 1 +....: .x^80 + 4*C1.x^78 + 4*C1.x^76 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3 +....: *C1.x^48 + 3*C1.x^46 + 4*C1.x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2* C +....: 1.x^6 + 4*C1.x^4 + 4*C1.x^2 + C1.one).teichmuller()*C1.y.diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7lsage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller( ) +....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 + +....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4 7 +....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 + +....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y).teichmuller() *C1.x.teichmuller().diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 +....: + 3*C1.x^112 + 2*C1.x^110 + 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C 1 +....: .x^80 + 4*C1.x^78 + 4*C1.x^76 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3 +....: *C1.x^48 + 3*C1.x^46 + 4*C1.x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2* C +....: 1.x^6 + 4*C1.x^4 + 4*C1.x^2 + C1.one).teichmuller()*C1.y.diffn()).verschiebung() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [21], line 1 +----> 1 om = ((Integer(3)*C1.x**Integer(9) + Integer(2)*C1.x**Integer(5))*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (Integer(2)*C1.x**Integer(14) + C1.x**Integer(10) + Integer(2)*C1.x**Integer(6) + Integer(3)*C1.x**Integer(4)).teichmuller() * C1.y.teichmuller().diffn() + (((C1.x**Integer(119) + Integer(4)*C1.x**Integer(115) + Integer(4)*C1.x**Integer(111) + C1.x**Integer(107) + Integer(3)*C1.x**Integer(105) + Integer(3)*C1.x**Integer(103) + C1.x**Integer(101) + Integer(3)*C1.x**Integer(99) + C1.x**Integer(97) + Integer(4)*C1.x**Integer(95) + Integer(3)*C1.x**Integer(93) + Integer(3)*C1.x**Integer(89) + Integer(2)*C1.x**Integer(87) + Integer(4)*C1.x**Integer(85) + Integer(2)*C1.x**Integer(83) + Integer(4)*C1.x**Integer(81) + C1.x**Integer(79) + Integer(4)*C1.x**Integer(69) + C1.x**Integer(65) + Integer(4)*C1.x**Integer(63) + Integer(4)*C1.x**Integer(59) + Integer(3)*C1.x**Integer(57) + Integer(3)*C1.x**Integer(55) + C1.x**Integer(53) + C1.x**Integer(51) + Integer(4)*C1.x**Integer(47) + Integer(3)*C1.x**Integer(45) + Integer(4)*C1.x**Integer(43) + Integer(2)*C1.x**Integer(41) + Integer(2)*C1.x**Integer(39) + Integer(3)*C1.x**Integer(37) + Integer(4)*C1.x**Integer(35) + Integer(3)*C1.x**Integer(33) + Integer(2)*C1.x**Integer(31) + Integer(3)*C1.x**Integer(29) + Integer(4)*C1.x**Integer(25) + C1.x**Integer(23) + Integer(3)*C1.x**Integer(21) + Integer(4)*C1.x**Integer(19) + Integer(2)*C1.x**Integer(17) + C1.x**Integer(15) + C1.x**Integer(13) + Integer(2)*C1.x**Integer(9) + C1.x**Integer(7) + Integer(2)*C1.x**Integer(5) + Integer(4)*C1.x)*C1.y).teichmuller() *C1.x.teichmuller().diffn() + (Integer(4)*C1.x**Integer(124) + Integer(2)*C1.x**Integer(120) + C1.x**Integer(114) + Integer(3)*C1.x**Integer(112) + Integer(2)*C1.x**Integer(110) + Integer(3)*C1.x**Integer(108) + C1.x**Integer(106) + Integer(2)*C1.x**Integer(100) + C1.x**Integer(98) + Integer(3)*C1.x**Integer(96) + C1.x**Integer(94) + Integer(3)*C1.x**Integer(92) + Integer(4)*C1.x**Integer(90) + Integer(3)*C1.x**Integer(88) + Integer(2)*C1.x**Integer(84) + C1.x**Integer(82) + C1.x**Integer(80) + Integer(4)*C1.x**Integer(78) + Integer(4)*C1.x**Integer(76) + C1.x**Integer(74) + Integer(4)*C1.x**Integer(72) + Integer(3)*C1.x**Integer(70) + C1.x**Integer(66) + Integer(3)*C1.x**Integer(64) + Integer(2)*C1.x**Integer(62) + C1.x**Integer(58) + C1.x**Integer(56) + Integer(4)*C1.x**Integer(54) + Integer(4)*C1.x**Integer(52) + Integer(3)*C1.x**Integer(50) + Integer(3)*C1.x**Integer(48) + Integer(3)*C1.x**Integer(46) + Integer(4)*C1.x**Integer(40) + Integer(2)*C1.x**Integer(34) + Integer(3)*C1.x**Integer(32) + Integer(3)*C1.x**Integer(28) + Integer(4)*C1.x**Integer(26) + Integer(4)*C1.x**Integer(24) + Integer(4)*C1.x**Integer(22) + Integer(4)*C1.x**Integer(20) + Integer(2)*C1.x**Integer(14) + Integer(4)*C1.x**Integer(10) + Integer(3)*C1.x**Integer(8) + Integer(2)*C1.x**Integer(6) + Integer(4)*C1.x**Integer(4) + Integer(4)*C1.x**Integer(2) + C1.one).teichmuller()*C1.y.diffn()).verschiebung() + +File :81, in __add__(self, other) + +AttributeError: 'NoneType' object has no attribute 'h1' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller( ) +....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +   +....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4 7 +....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +   +....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y).teichmuller() *C1.x.teichmuller().diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114   +....: + 3*C1.x^112 + 2*C1.x^110 + 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C 1 +....: .x^80 + 4*C1.x^78 + 4*C1.x^76 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3 +....: *C1.x^48 + 3*C1.x^46 + 4*C1.x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2* C +....: 1.x^6 + 4*C1.x^4 + 4*C1.x^2 + C1.one).teichmuller()*C1.y.diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7lsage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller( ) +....: .diffn() +[?7h[?12l[?25h[?2004l +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + [?7h[?12l[?25h[?25l[?7lom = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller( ) +....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 + +....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4 7 +....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 + +....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 + +....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^ 7 +....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1 . +....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2 +....: + C1.one)*C1.y.diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7lsage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller( ) +....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 + +....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4 7 +....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 + +....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 + +....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^ 7 +....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1 . +....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2 +....: + C1.one)*C1.y.diffn()).verschiebung() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 3 +....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34 +....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1. o +....: ne)/C1.x^2)*C1.y).verschiebung()[?7h[?12l[?25h[?25l[?7lsage: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 3 +....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34 +....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1. o +....: ne)/C1.x^2)*C1.y).verschiebung() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_drw_cech(xi, f); xi = xi.reduce(); print(xi.regular_form())[?7h[?12l[?25h[?25l[?7lsage: xi = superelliptic_drw_cech(xi, f); xi = xi.reduce(); print(xi.regular_form()) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Cell In [25], line 1 +----> 1 xi = superelliptic_drw_cech(xi, f); xi = xi.reduce(); print(xi.regular_form()) + +NameError: name 'xi' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_drw_cech(xi, f); xi = xi.reduce(); print(xi.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, f); xi = xi.reduce(); print(xi.regular_form()[?7h[?12l[?25h[?25l[?7l, f); xi = xi.reduce(); print(xi.regular_form()[?7h[?12l[?25h[?25l[?7lo, f); xi = xi.reduce(); print(xi.regular_form()[?7h[?12l[?25h[?25l[?7lm, f); xi = xi.reduce(); print(xi.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[?7lsage: xi = superelliptic_drw_cech(om, f); xi = xi.reduce(); print(xi.regular_form()) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [26], line 1 +----> 1 xi = superelliptic_drw_cech(om, f); xi = xi.reduce(); print(xi.regular_form()) + +File :6, in __init__(self, omega0, f) + +File /ext/sage/9.8/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() + 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' + 493 """ +--> 494 return self.getattr_from_category(name) + 495 + 496 cdef getattr_from_category(self, name): + +File /ext/sage/9.8/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() + 505 else: + 506 cls = P._abstract_element_class +--> 507 return getattr_from_other_class(self, cls, name) + 508 + 509 def __dir__(self): + +File /ext/sage/9.8/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() + 359 dummy_error_message.cls = type(self) + 360 dummy_error_message.name = name +--> 361 raise AttributeError(dummy_error_message) + 362 attribute = attr + 363 # Check for a descriptor (__get__ in Python) + +AttributeError: 'sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint' object has no attribute 'diffn' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_drw_cech(om, f); xi = xi.reduce(); print(xi.regular_form())[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l = superelliptic_drw_cech(om, f); xi = xi.reduce(); print(xi.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[?7lprin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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[?7lxi = superelliptic_drw_cech(om, ff); xi = xi.reduce(); print(xi.regular_form())[?7h[?12l[?25h[?25l[?7lsage: xi = superelliptic_drw_cech(om, ff); xi = xi.reduce(); print(xi.regular_form()) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [27], line 1 +----> 1 xi = superelliptic_drw_cech(om, ff); xi = xi.reduce(); print(xi.regular_form()) + +File :92, in regular_drw_cech(cocycle) + +File :84, in regular_drw_form(omega) + +File :9, in decomposition_g0_pth_power(fct) + +AttributeError: 'NoneType' object has no attribute 'int' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_drw_cech(om, ff); xi = xi.reduce(); print(xi.regular_form())[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: xi +[?7h[?12l[?25h[?2004l[?7h([(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((x^38 + 2*x^34 + 3*x^32 + x^30 + 4*x^28 + 4*x^26 + 4*x^24 + 3*x^20 + x^18 + 2*x^16 + 4*x^12 + 2*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 2)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y]), V(1/x^2*y), [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^32 + 3*x^30 + x^28 + 2*x^24 + 3*x^20 + 4*x^18 + 2*x^16 + 4*x^14 + 4*x^12 + 2*x^10 + 2*x^6 + 1)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y])) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7limport itertools[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: xi.r() +[?7h[?12l[?25h[?2004l[?7h((x^4/y) dx, 0, (x^4/y) dx) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.r()[?7h[?12l[?25h[?25l[?7li[?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: xi.regular_form() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [30], line 1 +----> 1 xi.regular_form() + +File :92, in regular_drw_cech(cocycle) + +File :84, in regular_drw_form(omega) + +File :9, in decomposition_g0_pth_power(fct) + +AttributeError: 'NoneType' object has no attribute 'int' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def decomposition_g0_pth_power(fct): +....:  print(fct) +....:  C = fct.curve +....:  Fxy, Rxy, xy, y = C.fct_field +....:  if fct.function in Rxy: +....:  return (fct, 0*C.x) +....:  '''Decompose fct as g0 + A^p, if possible. Output: (g0, A).''' +....:  omega = fct.diffn().regular_form() +....:  print(omega) +....:  g0 = omega.int() +....:  A = (fct - g0).pth_root() +....:  return (g0, A)[?7h[?12l[?25h[?25l[?7l....:  return (g0, A) +....: [?7h[?12l[?25h[?25l[?7lsage: def decomposition_g0_pth_power(fct): +....:  print(fct) +....:  C = fct.curve +....:  Fxy, Rxy, xy, y = C.fct_field +....:  if fct.function in Rxy: +....:  return (fct, 0*C.x) +....:  '''Decompose fct as g0 + A^p, if possible. Output: (g0, A).''' +....:  omega = fct.diffn().regular_form() +....:  print(omega) +....:  g0 = omega.int() +....:  A = (fct - g0).pth_root() +....:  return (g0, A) +....:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def decomposition_g0_pth_power(fct): +....:  print(fct) +....:  C = fct.curve +....:  Fxy, Rxy, xy, y = C.fct_field +....:  if fct.function in Rxy: +....:  return (fct, 0*C.x) +....:  '''Decompose fct as g0 + A^p, if possible. Output: (g0, A).''' +....:  omega = fct.diffn().regular_form() +....:  print(omega) +....:  g0 = omega.int() +....:  A = (fct - g0).pth_root() +....:  return (g0, A)[?7h[?12l[?25h[?25l[?7l() +()[?7h[?12l[?25h[?25l[?7l() +()[?7h[?12l[?25h[?25l[?7l() +()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lxi.regular_form() +  +  +  +  +  +  +  +  +  +  + [?7h[?12l[?25h[?25l[?7lsage: xi.regular_form() +[?7h[?12l[?25h[?2004l((3*x^98 + x^94 + 4*x^92 + 2*x^90 + x^86 + 3*x^84 + x^82 + 3*x^78 + 4*x^76 + 2*x^74 + 4*x^72 + 2*x^70 + 4*x^68 + 2*x^66 + 3*x^64 + 2*x^62 + 4*x^60 + x^56 + 2*x^54 + 4*x^52 + 3*x^50 + 4*x^48 + 2*x^46 + 3*x^44 + x^38 + 4*x^36 + 3*x^34 + x^32 + 4*x^30 + 4*x^28 + x^26 + 3*x^24 + x^22 + 2*x^18 + 2*x^14 + x^12 + 2*x^10 + 2*x^6 + 3*x^4 + 2*x^2 + 2)/x^2)*y +None +--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [32], line 1 +----> 1 xi.regular_form() + +File :92, in regular_drw_cech(cocycle) + +File :84, in regular_drw_form(omega) + +Cell In [31], line 10, in decomposition_g0_pth_power(fct) + 8 omega = fct.diffn().regular_form() + 9 print(omega) +---> 10 g0 = omega.int() + 11 A = (fct - g0).pth_root() + 12 return (g0, A) + +AttributeError: 'NoneType' object has no attribute 'int' +[?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 +^C--------------------------------------------------------------------------- +KeyError Traceback (most recent call last) +File /ext/sage/9.8/src/sage/structure/category_object.pyx:839, in sage.structure.category_object.CategoryObject.getattr_from_category() + 838 try: +--> 839 return self.__cached_methods[name] + 840 except KeyError: + +KeyError: '_mpoly_base_ring' + +During handling of the above exception, another exception occurred: + +AttributeError Traceback (most recent call last) +File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_ring.py:1117, in PolynomialRing_general._mpoly_base_ring(self, variables) + 1116 try: +-> 1117 return self.base_ring()._mpoly_base_ring(variables[:variables.index(var)]) + 1118 except AttributeError: + +File /ext/sage/9.8/src/sage/structure/category_object.pyx:833, in sage.structure.category_object.CategoryObject.__getattr__() + 832 """ +--> 833 return self.getattr_from_category(name) + 834 + +File /ext/sage/9.8/src/sage/structure/category_object.pyx:848, in sage.structure.category_object.CategoryObject.getattr_from_category() + 847 +--> 848 attr = getattr_from_other_class(self, cls, name) + 849 self.__cached_methods[name] = attr + +File /ext/sage/9.8/src/sage/cpython/getattr.pyx:356, in sage.cpython.getattr.getattr_from_other_class() + 355 dummy_error_message.name = name +--> 356 raise AttributeError(dummy_error_message) + 357 cdef PyObject* attr = instance_getattr(cls, name) + +AttributeError: 'FpT_with_category' object has no attribute '_mpoly_base_ring' + +During handling of the above exception, another exception occurred: + +KeyboardInterrupt Traceback (most recent call last) +Cell In [33], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 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 + +File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 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 + +File :44, in crystalline_cohomology_basis(self, prec, info) + +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/9.8/src/sage/rings/rational.pyx:2406, in sage.rings.rational.Rational.__mul__() + 2404 return x + 2405 +-> 2406 return coercion_model.bin_op(left, right, operator.mul) + 2407 + 2408 cpdef _mul_(self, right): + +File /ext/sage/9.8/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/9.8/src/sage/structure/element.pyx:1527, in sage.structure.element.Element.__mul__() + 1525 if not err: + 1526 return (right)._mul_long(value) +-> 1527 return coercion_model.bin_op(left, right, mul) + 1528 except TypeError: + 1529 return NotImplemented + +File /ext/sage/9.8/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/9.8/src/sage/structure/element.pyx:1527, in sage.structure.element.Element.__mul__() + 1525 if not err: + 1526 return (right)._mul_long(value) +-> 1527 return coercion_model.bin_op(left, right, mul) + 1528 except TypeError: + 1529 return NotImplemented + +File /ext/sage/9.8/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 :263, in reduction(C, g) + +File /ext/sage/9.8/src/sage/structure/parent.pyx:896, in sage.structure.parent.Parent.__call__() + 894 if mor is not None: + 895 if no_extra_args: +--> 896 return mor._call_(x) + 897 else: + 898 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.8/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/9.8/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:920, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() + 918 + 919 elif isinstance(element, polynomial_element.Polynomial): +--> 920 if base_ring.has_coerce_map_from(element.parent()._mpoly_base_ring(self.variable_names())): + 921 return self(element._mpoly_dict_recursive(self.variable_names(), base_ring)) + 922 + +File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_ring.py:1119, in PolynomialRing_general._mpoly_base_ring(self, variables) + 1117 return self.base_ring()._mpoly_base_ring(variables[:variables.index(var)]) + 1118 except AttributeError: +-> 1119 return self.base_ring() + +File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() + +KeyboardInterrupt: +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lxi.regular_form([?7h[?12l[?25h[?25l[?7lsage: def decomposition_g0_pth_power(fct): +....:  print(fct) +....:  C = fct.curve +....:  Fxy, Rxy, xy, y = C.fct_field +....:  if fct.function in Rxy: +....:  return (fct, 0*C.x) +....:  '''Decompose fct as g0 + A^p, if possible. Output: (g0, A).''' +....:  omega = fct.diffn().regular_form() +....:  print(omega) +....:  g0 = omega.int() +....:  A = (fct - g0).pth_root() +....:  return (g0, A)[?7h[?12l[?25h[?25l[?7lxi.regular_form() +  +  +  +  +  +  +  +  +  +  + [?7h[?12l[?25h[?25l[?7lload('init.sage'[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller( ) +....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 + +....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4 7 +....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 + +....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 + +....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^ 7 +....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1 . +....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2 +....: + C1.one)*C1.y.diffn()).verschiebung() +....:  +....: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 3 +....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34 +....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1. o +....: ne)/C1.x^2)*C1.y).verschiebung() +....:  +....: xi = superelliptic_drw_cech(om, ff); xi = xi.reduce(); print(xi.regular_form())[?7h[?12l[?25h[?25l[?7lsage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller( ) +....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 + +....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4 7 +....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 + +....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 + +....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^ 7 +....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1 . +....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2 +....: + C1.one)*C1.y.diffn()).verschiebung() +....:  +....: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 3 +....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34 +....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1. o +....: ne)/C1.x^2)*C1.y).verschiebung() +....:  +....: xi = superelliptic_drw_cech(om, ff); xi = xi.reduce(); print(xi.regular_form()) +[?7h[?12l[?25h[?2004l +^C--------------------------------------------------------------------------- +KeyboardInterrupt Traceback (most recent call last) +File :59, in __mul__(self, other) + +File :261, in reduction(C, g) + +File /ext/sage/9.8/src/sage/structure/element.pyx:1515, in sage.structure.element.Element.__mul__() + 1514 if BOTH_ARE_ELEMENT(cl): +-> 1515 return coercion_model.bin_op(left, right, mul) + 1516 + +File /ext/sage/9.8/src/sage/structure/coerce.pyx:1200, in sage.structure.coerce.CoercionModel.bin_op() + 1199 try: +-> 1200 xy = self.canonical_coercion(x, y) + 1201 except TypeError: + +File /ext/sage/9.8/src/sage/structure/coerce.pyx:1311, in sage.structure.coerce.CoercionModel.canonical_coercion() + 1310 if x_map is not None: +-> 1311 x_elt = (x_map)._call_(x) + 1312 else: + +File /ext/sage/9.8/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_() + 286 cdef Map m +--> 287 cdef Element e = method(C) + 288 if e is None: + +File /ext/sage/9.8/src/sage/rings/polynomial/multi_polynomial.pyx:198, in sage.rings.polynomial.multi_polynomial.MPolynomial._polynomial_() + 197 if var in self._parent.variable_names(): +--> 198 return R(self.polynomial(self._parent(var))) + 199 return R([self]) + +File /ext/sage/9.8/src/sage/rings/polynomial/multi_polynomial.pyx:410, in sage.rings.polynomial.multi_polynomial.MPolynomial.polynomial() + 409 # Make polynomial ring over all variables except var. +--> 410 S = R.base_ring()[tuple(Z)] + 411 ring = S[var] + +File /ext/sage/9.8/src/sage/structure/parent.pyx:1274, in sage.structure.parent.Parent.__getitem__() + 1273 return self.list()[n] +-> 1274 return meth(n) + 1275 + +File /ext/sage/9.8/src/sage/categories/rings.py:1220, in Rings.ParentMethods.__getitem__(self, arg) + 1219 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing +-> 1220 return PolynomialRing(self, elts) + +File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_ring_constructor.py:678, in PolynomialRing(base_ring, *args, **kwds) + 676 raise TypeError("you must specify the names of the variables") +--> 678 names = normalize_names(n, names) + 680 # At this point, we have only handled the "names" keyword if it was + 681 # needed. Since we know the variable names, it would logically be + 682 # an error to specify an additional "names" keyword. However, + (...) + 685 # and we allow this for historical reasons. However, the names + 686 # must be consistent! + +File /ext/sage/9.8/src/sage/structure/category_object.pyx:900, in sage.structure.category_object.normalize_names() + 899 +--> 900 cpdef normalize_names(Py_ssize_t ngens, names): + 901 r""" + +File /ext/sage/9.8/src/sage/structure/category_object.pyx:993, in sage.structure.category_object.normalize_names() + 992 # Convert names to strings and strip whitespace +--> 993 names = [str(x).strip() for x in names] + 994 else: + +File /ext/sage/9.8/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__() + 193 return super().__repr__() +--> 194 result = reprfunc() + 195 if isinstance(result, str): + +File /ext/sage/9.8/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2464, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular._repr_() + 2463 cdef ring *_ring = self._parent_ring +-> 2464 s = singular_polynomial_str(self._poly, _ring) + 2465 return s + +File /ext/sage/9.8/src/sage/libs/singular/polynomial.pyx:440, in sage.libs.singular.polynomial.singular_polynomial_str() + 439 s = bytes_to_str(p_String(p, r, r)) +--> 440 s = plusminus_pattern.sub("\\1 \\2 ", s) + 441 s = parenthvar_pattern.sub("\\1", s) + +File /ext/sage/9.8/local/var/lib/sage/venv-python3.11.1/lib/python3.11/re/__init__.py:315, in _subx(pattern, template) + 313 return _parser.expand_template(template, match) +--> 315 def _subx(pattern, template): + 316 # internal: Pattern.sub/subn implementation helper + 317 template = _compile_repl(template, pattern) + +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) +Cell In [34], line 1 +----> 1 om = ((Integer(3)*C1.x**Integer(9) + Integer(2)*C1.x**Integer(5))*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (Integer(2)*C1.x**Integer(14) + C1.x**Integer(10) + Integer(2)*C1.x**Integer(6) + Integer(3)*C1.x**Integer(4)).teichmuller() * C1.y.teichmuller().diffn() + (((C1.x**Integer(119) + Integer(4)*C1.x**Integer(115) + Integer(4)*C1.x**Integer(111) + C1.x**Integer(107) + Integer(3)*C1.x**Integer(105) + Integer(3)*C1.x**Integer(103) + C1.x**Integer(101) + Integer(3)*C1.x**Integer(99) + C1.x**Integer(97) + Integer(4)*C1.x**Integer(95) + Integer(3)*C1.x**Integer(93) + Integer(3)*C1.x**Integer(89) + Integer(2)*C1.x**Integer(87) + Integer(4)*C1.x**Integer(85) + Integer(2)*C1.x**Integer(83) + Integer(4)*C1.x**Integer(81) + C1.x**Integer(79) + Integer(4)*C1.x**Integer(69) + C1.x**Integer(65) + Integer(4)*C1.x**Integer(63) + Integer(4)*C1.x**Integer(59) + Integer(3)*C1.x**Integer(57) + Integer(3)*C1.x**Integer(55) + C1.x**Integer(53) + C1.x**Integer(51) + Integer(4)*C1.x**Integer(47) + Integer(3)*C1.x**Integer(45) + Integer(4)*C1.x**Integer(43) + Integer(2)*C1.x**Integer(41) + Integer(2)*C1.x**Integer(39) + Integer(3)*C1.x**Integer(37) + Integer(4)*C1.x**Integer(35) + Integer(3)*C1.x**Integer(33) + Integer(2)*C1.x**Integer(31) + Integer(3)*C1.x**Integer(29) + Integer(4)*C1.x**Integer(25) + C1.x**Integer(23) + Integer(3)*C1.x**Integer(21) + Integer(4)*C1.x**Integer(19) + Integer(2)*C1.x**Integer(17) + C1.x**Integer(15) + C1.x**Integer(13) + Integer(2)*C1.x**Integer(9) + C1.x**Integer(7) + Integer(2)*C1.x**Integer(5) + Integer(4)*C1.x)*C1.y) *C1.x.diffn() + (Integer(4)*C1.x**Integer(124) + Integer(2)*C1.x**Integer(120) + C1.x**Integer(114) + Integer(3)*C1.x**Integer(112) + Integer(2)*C1.x**Integer(110) + Integer(3)*C1.x**Integer(108) + C1.x**Integer(106) + Integer(2)*C1.x**Integer(100) + C1.x**Integer(98) + Integer(3)*C1.x**Integer(96) + C1.x**Integer(94) + Integer(3)*C1.x**Integer(92) + Integer(4)*C1.x**Integer(90) + Integer(3)*C1.x**Integer(88) + Integer(2)*C1.x**Integer(84) + C1.x**Integer(82) + C1.x**Integer(80) + Integer(4)*C1.x**Integer(78) + Integer(4)*C1.x**Integer(76) + C1.x**Integer(74) + Integer(4)*C1.x**Integer(72) + Integer(3)*C1.x**Integer(70) + C1.x**Integer(66) + Integer(3)*C1.x**Integer(64) + Integer(2)*C1.x**Integer(62) + C1.x**Integer(58) + C1.x**Integer(56) + Integer(4)*C1.x**Integer(54) + Integer(4)*C1.x**Integer(52) + Integer(3)*C1.x**Integer(50) + Integer(3)*C1.x**Integer(48) + Integer(3)*C1.x**Integer(46) + Integer(4)*C1.x**Integer(40) + Integer(2)*C1.x**Integer(34) + Integer(3)*C1.x**Integer(32) + Integer(3)*C1.x**Integer(28) + Integer(4)*C1.x**Integer(26) + Integer(4)*C1.x**Integer(24) + Integer(4)*C1.x**Integer(22) + Integer(4)*C1.x**Integer(20) + Integer(2)*C1.x**Integer(14) + Integer(4)*C1.x**Integer(10) + Integer(3)*C1.x**Integer(8) + Integer(2)*C1.x**Integer(6) + Integer(4)*C1.x**Integer(4) + Integer(4)*C1.x**Integer(2) + C1.one)*C1.y.diffn()).verschiebung() + 3 ff = (((Integer(2)*C1.x**Integer(98) + Integer(4)*C1.x**Integer(94) + C1.x**Integer(92) + Integer(3)*C1.x**Integer(90) + Integer(4)*C1.x**Integer(86) + Integer(2)*C1.x**Integer(84) + Integer(4)*C1.x**Integer(82) + Integer(2)*C1.x**Integer(78) + C1.x**Integer(76) + Integer(3)*C1.x**Integer(74) + C1.x**Integer(72) + Integer(3)*C1.x**Integer(70) + C1.x**Integer(68) + Integer(3)*C1.x**Integer(66) + Integer(2)*C1.x**Integer(64) + Integer(3)*C1.x**Integer(62) + C1.x**Integer(60) + Integer(4)*C1.x**Integer(56) + Integer(3)*C1.x**Integer(54) + C1.x**Integer(52) + Integer(2)*C1.x**Integer(50) + C1.x**Integer(48) + Integer(3)*C1.x**Integer(46) + Integer(2)*C1.x**Integer(44) + Integer(4)*C1.x**Integer(38) + C1.x**Integer(36) + Integer(2)*C1.x**Integer(34) + Integer(4)*C1.x**Integer(32) + C1.x**Integer(30) + C1.x**Integer(28) + Integer(4)*C1.x**Integer(26) + Integer(2)*C1.x**Integer(24) + Integer(4)*C1.x**Integer(22) + Integer(3)*C1.x**Integer(18) + Integer(3)*C1.x**Integer(14) + Integer(4)*C1.x**Integer(12) + Integer(3)*C1.x**Integer(10) + Integer(3)*C1.x**Integer(6) + Integer(2)*C1.x**Integer(4) + Integer(3)*C1.x**Integer(2) + Integer(4)*C1.one)/C1.x**Integer(2))*C1.y).verschiebung() + 5 xi = superelliptic_drw_cech(om, ff); xi = xi.reduce(); print(xi.regular_form()) + +File :73, in diffn(self, dy_w) + +File :177, in dy_w(C) + +File :149, in auxilliary_derivative(P) + +File :55, in __rmul__(self, other) + +File /ext/sage/9.8/src/sage/rings/integer.pyx:1961, in sage.rings.integer.Integer.__mul__() + 1959 return y + 1960 +-> 1961 return coercion_model.bin_op(left, right, operator.mul) + 1962 + 1963 cpdef _mul_(self, right): + +File /ext/sage/9.8/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 :55, in __rmul__(self, other) + +File /ext/sage/9.8/src/sage/rings/integer.pyx:1961, in sage.rings.integer.Integer.__mul__() + 1959 return y + 1960 +-> 1961 return coercion_model.bin_op(left, right, operator.mul) + 1962 + 1963 cpdef _mul_(self, right): + +File /ext/sage/9.8/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 + + [... skipping similar frames: __rmul__ at line 55 (9 times), sage.rings.integer.Integer.__mul__ at line 1961 (8 times), sage.structure.coerce.CoercionModel.bin_op at line 1242 (8 times)] + +File /ext/sage/9.8/src/sage/rings/integer.pyx:1961, in sage.rings.integer.Integer.__mul__() + 1959 return y + 1960 +-> 1961 return coercion_model.bin_op(left, right, operator.mul) + 1962 + 1963 cpdef _mul_(self, right): + +File /ext/sage/9.8/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 :55, in __rmul__(self, other) + +File :84, in __add__(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[?7lsage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller( ) +....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 + +....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4 7 +....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 + +....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 + +....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^ 7 +....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1 . +....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2 +....: + C1.one)*C1.y.diffn()).verschiebung() +....:  +....: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 3 +....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34 +....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1. o +....: ne)/C1.x^2)*C1.y).verschiebung() +....:  +....: xi = superelliptic_drw_cech(om, ff); xi = xi.reduce(); print(xi.regular_form())[?7h[?12l[?25h[?25l[?7lsage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller( ) +....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 + +....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4 7 +....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 + +....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 + +....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^ 7 +....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1 . +....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2 +....: + C1.one)*C1.y.diffn()).verschiebung() +....:  +....: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 3 +....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34 +....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1. o +....: ne)/C1.x^2)*C1.y).verschiebung() +....:  +....: xi = superelliptic_drw_cech(om, ff) +[?7h[?12l[?25h[?2004l^C--------------------------------------------------------------------------- +KeyboardInterrupt Traceback (most recent call last) +Cell In [35], line 1 +----> 1 om = ((Integer(3)*C1.x**Integer(9) + Integer(2)*C1.x**Integer(5))*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (Integer(2)*C1.x**Integer(14) + C1.x**Integer(10) + Integer(2)*C1.x**Integer(6) + Integer(3)*C1.x**Integer(4)).teichmuller() * C1.y.teichmuller().diffn() + (((C1.x**Integer(119) + Integer(4)*C1.x**Integer(115) + Integer(4)*C1.x**Integer(111) + C1.x**Integer(107) + Integer(3)*C1.x**Integer(105) + Integer(3)*C1.x**Integer(103) + C1.x**Integer(101) + Integer(3)*C1.x**Integer(99) + C1.x**Integer(97) + Integer(4)*C1.x**Integer(95) + Integer(3)*C1.x**Integer(93) + Integer(3)*C1.x**Integer(89) + Integer(2)*C1.x**Integer(87) + Integer(4)*C1.x**Integer(85) + Integer(2)*C1.x**Integer(83) + Integer(4)*C1.x**Integer(81) + C1.x**Integer(79) + Integer(4)*C1.x**Integer(69) + C1.x**Integer(65) + Integer(4)*C1.x**Integer(63) + Integer(4)*C1.x**Integer(59) + Integer(3)*C1.x**Integer(57) + Integer(3)*C1.x**Integer(55) + C1.x**Integer(53) + C1.x**Integer(51) + Integer(4)*C1.x**Integer(47) + Integer(3)*C1.x**Integer(45) + Integer(4)*C1.x**Integer(43) + Integer(2)*C1.x**Integer(41) + Integer(2)*C1.x**Integer(39) + Integer(3)*C1.x**Integer(37) + Integer(4)*C1.x**Integer(35) + Integer(3)*C1.x**Integer(33) + Integer(2)*C1.x**Integer(31) + Integer(3)*C1.x**Integer(29) + Integer(4)*C1.x**Integer(25) + C1.x**Integer(23) + Integer(3)*C1.x**Integer(21) + Integer(4)*C1.x**Integer(19) + Integer(2)*C1.x**Integer(17) + C1.x**Integer(15) + C1.x**Integer(13) + Integer(2)*C1.x**Integer(9) + C1.x**Integer(7) + Integer(2)*C1.x**Integer(5) + Integer(4)*C1.x)*C1.y) *C1.x.diffn() + (Integer(4)*C1.x**Integer(124) + Integer(2)*C1.x**Integer(120) + C1.x**Integer(114) + Integer(3)*C1.x**Integer(112) + Integer(2)*C1.x**Integer(110) + Integer(3)*C1.x**Integer(108) + C1.x**Integer(106) + Integer(2)*C1.x**Integer(100) + C1.x**Integer(98) + Integer(3)*C1.x**Integer(96) + C1.x**Integer(94) + Integer(3)*C1.x**Integer(92) + Integer(4)*C1.x**Integer(90) + Integer(3)*C1.x**Integer(88) + Integer(2)*C1.x**Integer(84) + C1.x**Integer(82) + C1.x**Integer(80) + Integer(4)*C1.x**Integer(78) + Integer(4)*C1.x**Integer(76) + C1.x**Integer(74) + Integer(4)*C1.x**Integer(72) + Integer(3)*C1.x**Integer(70) + C1.x**Integer(66) + Integer(3)*C1.x**Integer(64) + Integer(2)*C1.x**Integer(62) + C1.x**Integer(58) + C1.x**Integer(56) + Integer(4)*C1.x**Integer(54) + Integer(4)*C1.x**Integer(52) + Integer(3)*C1.x**Integer(50) + Integer(3)*C1.x**Integer(48) + Integer(3)*C1.x**Integer(46) + Integer(4)*C1.x**Integer(40) + Integer(2)*C1.x**Integer(34) + Integer(3)*C1.x**Integer(32) + Integer(3)*C1.x**Integer(28) + Integer(4)*C1.x**Integer(26) + Integer(4)*C1.x**Integer(24) + Integer(4)*C1.x**Integer(22) + Integer(4)*C1.x**Integer(20) + Integer(2)*C1.x**Integer(14) + Integer(4)*C1.x**Integer(10) + Integer(3)*C1.x**Integer(8) + Integer(2)*C1.x**Integer(6) + Integer(4)*C1.x**Integer(4) + Integer(4)*C1.x**Integer(2) + C1.one)*C1.y.diffn()).verschiebung() + 3 ff = (((Integer(2)*C1.x**Integer(98) + Integer(4)*C1.x**Integer(94) + C1.x**Integer(92) + Integer(3)*C1.x**Integer(90) + Integer(4)*C1.x**Integer(86) + Integer(2)*C1.x**Integer(84) + Integer(4)*C1.x**Integer(82) + Integer(2)*C1.x**Integer(78) + C1.x**Integer(76) + Integer(3)*C1.x**Integer(74) + C1.x**Integer(72) + Integer(3)*C1.x**Integer(70) + C1.x**Integer(68) + Integer(3)*C1.x**Integer(66) + Integer(2)*C1.x**Integer(64) + Integer(3)*C1.x**Integer(62) + C1.x**Integer(60) + Integer(4)*C1.x**Integer(56) + Integer(3)*C1.x**Integer(54) + C1.x**Integer(52) + Integer(2)*C1.x**Integer(50) + C1.x**Integer(48) + Integer(3)*C1.x**Integer(46) + Integer(2)*C1.x**Integer(44) + Integer(4)*C1.x**Integer(38) + C1.x**Integer(36) + Integer(2)*C1.x**Integer(34) + Integer(4)*C1.x**Integer(32) + C1.x**Integer(30) + C1.x**Integer(28) + Integer(4)*C1.x**Integer(26) + Integer(2)*C1.x**Integer(24) + Integer(4)*C1.x**Integer(22) + Integer(3)*C1.x**Integer(18) + Integer(3)*C1.x**Integer(14) + Integer(4)*C1.x**Integer(12) + Integer(3)*C1.x**Integer(10) + Integer(3)*C1.x**Integer(6) + Integer(2)*C1.x**Integer(4) + Integer(3)*C1.x**Integer(2) + Integer(4)*C1.one)/C1.x**Integer(2))*C1.y).verschiebung() + 5 xi = superelliptic_drw_cech(om, ff) + +File :73, in diffn(self, dy_w) + +File :177, in dy_w(C) + +File /ext/sage/9.8/src/sage/rings/rational.pyx:2406, in sage.rings.rational.Rational.__mul__() + 2404 return x + 2405 +-> 2406 return coercion_model.bin_op(left, right, operator.mul) + 2407 + 2408 cpdef _mul_(self, right): + +File /ext/sage/9.8/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/9.8/src/sage/structure/element.pyx:1527, in sage.structure.element.Element.__mul__() + 1525 if not err: + 1526 return (right)._mul_long(value) +-> 1527 return coercion_model.bin_op(left, right, mul) + 1528 except TypeError: + 1529 return NotImplemented + +File /ext/sage/9.8/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/9.8/src/sage/structure/element.pyx:1527, in sage.structure.element.Element.__mul__() + 1525 if not err: + 1526 return (right)._mul_long(value) +-> 1527 return coercion_model.bin_op(left, right, mul) + 1528 except TypeError: + 1529 return NotImplemented + +File /ext/sage/9.8/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) + + [... skipping similar frames: __rmul__ at line 43 (10 times), sage.structure.coerce.CoercionModel.bin_op at line 1242 (10 times), sage.structure.element.Element.__mul__ at line 1527 (10 times)] + +File /ext/sage/9.8/src/sage/structure/element.pyx:1527, in sage.structure.element.Element.__mul__() + 1525 if not err: + 1526 return (right)._mul_long(value) +-> 1527 return coercion_model.bin_op(left, right, mul) + 1528 except TypeError: + 1529 return NotImplemented + +File /ext/sage/9.8/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 :253, in reduction(C, g) + +File /ext/sage/9.8/src/sage/structure/parent.pyx:896, in sage.structure.parent.Parent.__call__() + 894 if mor is not None: + 895 if no_extra_args: +--> 896 return mor._call_(x) + 897 else: + 898 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.8/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/9.8/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/9.8/src/sage/rings/fraction_field.py:683, in FractionField_generic._element_constructor_..resolve_fractions(x, y) + 682 def resolve_fractions(x, y): +--> 683 xn = x.numerator() + 684 xd = x.denominator() + 685 yn = y.numerator() + +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[?7lC1.de_rham_basis()[4].omega0.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[?7l[?7h[?12l[?25h[?25l[?7lsage: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 3 +....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34   +....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1. o +....: ne)/C1.x^2)*C1.y).verschiebung()[?7h[?12l[?25h[?25l[?7l1fx = x^5 - x) +  +  + [?7h[?12l[?25h[?25l[?7l = f(x = x^5 - x)[?7h[?12l[?25h[?25l[?7lsage: f1 = f(x = x^5 - x) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  + + [?7h[?12l[?25h[?25l[?7lC1.de_rham_basis()[4].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[4].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 = superelliptic(f1, m, prec = 500)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(f1, m, prec = 500)[?7h[?12l[?25h[?25l[?7lsage: C1 = superelliptic(f1, m, prec = 500) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + [?7h[?12l[?25h[?25l[?7lC1 = superelliptic(f1, m, prec = 500)[?7h[?12l[?25h[?25l[?7lff(x = x^5 - x)[?7h[?12l[?25h[?25l[?7lom((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller( ) +....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 + +....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4 7 +....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 + +....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 + +....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^ 7 +....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1 . +....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2 +....: + C1.one)*C1.y.diffn()).verschiebung() +....:  +....: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 3 +....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34 +....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1. o +....: ne)/C1.x^2)*C1.y).verschiebung() +....:  +....: xi = superelliptic_drw_cech(om, ff)[?7h[?12l[?25h[?25l[?7lsage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller( ) +....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 + +....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4 7 +....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 + +....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 + +....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^ 7 +....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1 . +....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2 +....: + C1.one)*C1.y.diffn()).verschiebung() +....:  +....: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 3 +....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34 +....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1. o +....: ne)/C1.x^2)*C1.y).verschiebung() +....:  +....: xi = superelliptic_drw_cech(om, ff) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_drw_cech(om, ff)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.regla_form()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7le()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: xi.reduce() +[?7h[?12l[?25h[?2004l^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) +Cell In [39], line 1 +----> 1 xi.reduce() + +File :18, in reduce(self) + +File :73, in diffn(self, dy_w) + +File :177, in dy_w(C) + +File :149, in auxilliary_derivative(P) + +File :55, in __rmul__(self, other) + +File /ext/sage/9.8/src/sage/rings/integer.pyx:1961, in sage.rings.integer.Integer.__mul__() + 1959 return y + 1960 +-> 1961 return coercion_model.bin_op(left, right, operator.mul) + 1962 + 1963 cpdef _mul_(self, right): + +File /ext/sage/9.8/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 :55, in __rmul__(self, other) + +File /ext/sage/9.8/src/sage/rings/integer.pyx:1961, in sage.rings.integer.Integer.__mul__() + 1959 return y + 1960 +-> 1961 return coercion_model.bin_op(left, right, operator.mul) + 1962 + 1963 cpdef _mul_(self, right): + +File /ext/sage/9.8/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 + + [... skipping similar frames: __rmul__ at line 55 (4 times), sage.rings.integer.Integer.__mul__ at line 1961 (3 times), sage.structure.coerce.CoercionModel.bin_op at line 1242 (3 times)] + +File /ext/sage/9.8/src/sage/rings/integer.pyx:1961, in sage.rings.integer.Integer.__mul__() + 1959 return y + 1960 +-> 1961 return coercion_model.bin_op(left, right, operator.mul) + 1962 + 1963 cpdef _mul_(self, right): + +File /ext/sage/9.8/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 :55, in __rmul__(self, other) + +File :84, in __add__(self, other) + +File :65, in __mul__(self, other) + +File :65, in __mul__(self, other) + +File :7, in __init__(self, C, g) + +File :282, in reduction_form(C, g) + +File :260, in reduction(C, g) + +File /ext/sage/9.8/src/sage/arith/misc.py:2021, in xgcd(a, b) + 1933 r""" + 1934 Return a triple ``(g,s,t)`` such that `g = s\cdot a+t\cdot b = \gcd(a,b)`. + 1935 + (...) + 2018  (1, 7*a^2/b^2, (((-h)*a)/b^2)*y + 1/b) + 2019 """ + 2020 try: +-> 2021 return a.xgcd(b) + 2022 except AttributeError: + 2023 a = py_scalar_to_element(a) + +File /ext/sage/9.8/src/sage/structure/element.pyx:4497, in sage.structure.element.coerce_binop.new_method() + 4495 def new_method(self, other, *args, **kwargs): + 4496 if have_same_parent(self, other): +-> 4497 return method(self, other, *args, **kwargs) + 4498 else: + 4499 a, b = coercion_model.canonical_coercion(self, other) + +File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_element.pyx:8931, in sage.rings.polynomial.polynomial_element.Polynomial.xgcd() + 8929 """ + 8930 if hasattr(self.base_ring(), '_xgcd_univariate_polynomial'): +-> 8931 return self.base_ring()._xgcd_univariate_polynomial(self, other) + 8932 else: + 8933 raise NotImplementedError("%s does not provide an xgcd implementation for univariate polynomials"%self.base_ring()) + +File /ext/sage/9.8/src/sage/categories/fields.py:285, in Fields.ParentMethods._xgcd_univariate_polynomial(self, a, b) + 282 a = a.monic() + 283 return a +--> 285 def _xgcd_univariate_polynomial(self, a, b): + 286  r""" + 287  Return an extended gcd of ``a`` and ``b``. + 288 + (...) + 359  (0, 0, 0) + 360  """ + 361 R = a.parent() + +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: def reducee(self): +....: ^IC = self.curve +....: ^Ifct = self.f +....: ^If_first_comp = fct.t +....: ^If_second_comp = fct.f +....: ^Idecomp_first_comp = decomposition_g0_g8(f_first_comp) +....: ^Idecomp_second_comp = decomposition_g0_g8(f_second_comp) +....: ^Inew = self +....: ^Iprint(decomp_first_comp, decomp_second_comp) +....: ^Inew.omega0 -= decomposition_g0_g8(f_first_comp)[0].teichmuller().diffn() +....: ^Inew.omega0 -= decomposition_g0_g8(f_second_comp)[0].verschiebung().diffn() +....: ^Iprint(new.omega0) +....: ^Inew.f = decomposition_g0_g8(f_first_comp)[2].teichmuller() + decomposition_g0_g8(f_second_comp)[2].verschiebung() +....: ^Inew.omega8 = new.omega0 - new.f.diffn() +....: ^Ireturn new[?7h[?12l[?25h[?25l[?7l....: ^Ireturn new +....: [?7h[?12l[?25h[?25l[?7lsage: def reducee(self): +....: ^IC = self.curve +....: ^Ifct = self.f +....: ^If_first_comp = fct.t +....: ^If_second_comp = fct.f +....: ^Idecomp_first_comp = decomposition_g0_g8(f_first_comp) +....: ^Idecomp_second_comp = decomposition_g0_g8(f_second_comp) +....: ^Inew = self +....: ^Iprint(decomp_first_comp, decomp_second_comp) +....: ^Inew.omega0 -= decomposition_g0_g8(f_first_comp)[0].teichmuller().diffn() +....: ^Inew.omega0 -= decomposition_g0_g8(f_second_comp)[0].verschiebung().diffn() +....: ^Iprint(new.omega0) +....: ^Inew.f = decomposition_g0_g8(f_first_comp)[2].teichmuller() + decomposition_g0_g8(f_second_comp)[2].verschiebung() +....: ^Inew.omega8 = new.omega0 - new.f.diffn() +....: ^Ireturn new +....:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lregular_drw_form(B[0].omega0)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: reducee(xi) +[?7h[?12l[?25h[?2004l(0, 0, 0) (((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/x^2)*y, 0, 1/x^2*y) +[(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((x^38 + 2*x^34 + 3*x^32 + x^30 + 4*x^28 + 4*x^26 + 4*x^24 + 3*x^20 + x^18 + 2*x^16 + 4*x^12 + 2*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 2)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y]) +[?7h([(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((x^38 + 2*x^34 + 3*x^32 + x^30 + 4*x^28 + 4*x^26 + 4*x^24 + 3*x^20 + x^18 + 2*x^16 + 4*x^12 + 2*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 2)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y]), V(1/x^2*y), [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^32 + 3*x^30 + x^28 + 2*x^24 + 3*x^20 + 4*x^18 + 2*x^16 + 4*x^14 + 4*x^12 + 2*x^10 + 2*x^6 + 1)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y])) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def reducee(self): +....: ^IC = self.curve +....: ^Ifct = self.f +....: ^If_first_comp = fct.t +....: ^If_second_comp = fct.f +....: ^Idecomp_first_comp = decomposition_g0_g8(f_first_comp) +....: ^Idecomp_second_comp = decomposition_g0_g8(f_second_comp) +....: ^Inew = self +....: ^Iprint('decomp_first_comp[0], decomp_second_comp[0]', decomp_first_comp[0], decomp_second_comp[0]) +....: ^Inew.omega0 -= decomposition_g0_g8(f_first_comp)[0].teichmuller().diffn() +....: ^Inew.omega0 -= decomposition_g0_g8(f_second_comp)[0].verschiebung().diffn() +....: ^Iprint('new.omega0', new.omega0) +....: ^Inew.f = decomposition_g0_g8(f_first_comp)[2].teichmuller() + decomposition_g0_g8(f_second_comp)[2].verschiebung() +....: ^Inew.omega8 = new.omega0 - new.f.diffn() +....: ^Ireturn new[?7h[?12l[?25h[?25l[?7l....: ^Ireturn new +....: [?7h[?12l[?25h[?25l[?7lsage: def reducee(self): +....: ^IC = self.curve +....: ^Ifct = self.f +....: ^If_first_comp = fct.t +....: ^If_second_comp = fct.f +....: ^Idecomp_first_comp = decomposition_g0_g8(f_first_comp) +....: ^Idecomp_second_comp = decomposition_g0_g8(f_second_comp) +....: ^Inew = self +....: ^Iprint('decomp_first_comp[0], decomp_second_comp[0]', decomp_first_comp[0], decomp_second_comp[0]) +....: ^Inew.omega0 -= decomposition_g0_g8(f_first_comp)[0].teichmuller().diffn() +....: ^Inew.omega0 -= decomposition_g0_g8(f_second_comp)[0].verschiebung().diffn() +....: ^Iprint('new.omega0', new.omega0) +....: ^Inew.f = decomposition_g0_g8(f_first_comp)[2].teichmuller() + decomposition_g0_g8(f_second_comp)[2].verschiebung() +....: ^Inew.omega8 = new.omega0 - new.f.diffn() +....: ^Ireturn new +....:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lreducee(xi)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lucee(xi)[?7h[?12l[?25h[?25l[?7lsage: reducee(xi) +[?7h[?12l[?25h[?2004ldecomp_first_comp[0], decomp_second_comp[0] 0 2/x^2*y +new.omega0 [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^36 + 3*x^32 + 3*x^30 + 3*x^26 + x^24 + 3*x^18 + 2*x^16 + 2*x^14 + 3*x^12 + 4*x^10 + 2*x^8 + 2*x^6 + 3*x^4 + 4*x^2 + 2)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]) +[?7h([(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^36 + 3*x^32 + 3*x^30 + 3*x^26 + x^24 + 3*x^18 + 2*x^16 + 2*x^14 + 3*x^12 + 4*x^10 + 2*x^8 + 2*x^6 + 3*x^4 + 4*x^2 + 2)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(4/x^2*y), [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^32 + 3*x^30 + x^28 + 2*x^24 + 3*x^20 + 4*x^18 + 2*x^16 + 4*x^14 + 4*x^12 + 2*x^10 + 2*x^6 + 1)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y])) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.reduce()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf.coordinates(prec = 500)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: xi.f[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: xi.f[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: xi.f[?7h[?12l[?25h[?25l[?7lsage: xi.f + + [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.coordinates(prec = 500)[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: xi.f.coordinates(prec = 500)[?7h[?12l[?25h[?25l[?7lsage: xi.f.coordinates(prec = 500) + + [?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lsage: xi.f.t +[?7h[?12l[?25h[?2004l[?7h0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldef reducee(self):[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcomposition_g0_pth_power(A)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: decomposition + decomposition decomposition_g0_pth_power decomposition_omega0_hpdh  + decomposition_g0_g8 decomposition_g8_p2th_power decomposition_omega0_omega8 + decomposition_g0_p2th_power decomposition_g8_pth_power decomposition_omega8_hpdh  + + [?7h[?12l[?25h[?25l[?7l_g0_pth_power(A)[?7h[?12l[?25h[?25l[?7l + decomposition  + + + [?7h[?12l[?25h[?25l[?7l_g0_pth_power + decomposition  decomposition_g0_pth_power [?7h[?12l[?25h[?25l[?7l82th_power + decomposition_g0_pth_power  + decomposition_g8_p2th_power[?7h[?12l[?25h[?25l[?7l0g8 + + decomposition_g0_g8  decomposition_g8_p2th_power[?7h[?12l[?25h[?25l[?7l(xi.f) + + + +[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(xi.f.t) +[?7h[?12l[?25h[?2004l[?7h(0, 0, 0) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + [?7h[?12l[?25h[?25l[?7lxi.f.t[?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[?7ldecomposition_g0_g8(xi.f.t)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(xi.f.t) +[?7h[?12l[?25h[?2004l[?7h(0, 0, 0) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + [?7h[?12l[?25h[?25l[?7lxi.f.t[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: xi.f +[?7h[?12l[?25h[?2004l[?7hV(4/x^2*y) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def aa(self): +....:  new = self +....: ^Inew += 1 +....: ^Ireturn new[?7h[?12l[?25h[?25l[?7lsage: def aa(self): +....:  new = self +....: ^Inew += 1 +....: ^Ireturn new +[?7h[?12l[?25h[?2004l Cell In [48], line 3 + new += Integer(1) + ^ +TabError: inconsistent use of tabs and spaces in indentation + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: def aa(self): +....: ^Inew = self +....: ^Inew += 1 +....: ^Ireturn new[?7h[?12l[?25h[?25l[?7l....: ^Ireturn new +....: [?7h[?12l[?25h[?25l[?7lsage: def aa(self): +....: ^Inew = self +....: ^Inew += 1 +....: ^Ireturn new +....:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldef aa(self):[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: d = 1 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: adic_expansion_polynomial(x^119 + 4*x^115 + 4*x^111 + x^107 + 3*x^105 + 3*x^103 + x^101 + 3*x^99 + x^97 + 4*x^95 + 3*x^93 + 3*x^89 + 2*x^87 + 4*x^85 + 2*x^8 3 +....:  + 4*x^81 + x^79 + 4*x^69 + x^65 + 4*x^63 + 4*x^59 + 3*x^57 + 3*x^55 + x^53 + x^51 + 4*x^47 + 3*x^45 + 4*x^43 + 2*x^41 + 2*x^39 + 3*x^37 + 4*x^35 + 3*x^33 +   +....: 2*x^31 + 3*x^29 + 4*x^25 + x^23 + 3*x^21 + 4*x^19 + 2*x^17 + x^15 + x^13 + 2*x^9 + x^7 + 2*x^5 + 4*x, x^5 - x)[?7h[?12l[?25h[?25l[?7la +  + [?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aa(d) +[?7h[?12l[?25h[?2004l[?7h2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld = 1[?7h[?12l[?25h[?25l[?7lsage: d +[?7h[?12l[?25h[?2004l[?7h1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller( ) +....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 + +....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4 7 +....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 + +....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 + +....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^ 7 +....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1 . +....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2 +....: + C1.one)*C1.y.diffn()).verschiebung() +....:  +....: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 3 +....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34 +....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1. o +....: ne)/C1.x^2)*C1.y).verschiebung() +....:  +....: xi = superelliptic_drw_cech(om, ff)[?7h[?12l[?25h[?25l[?7lsage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller( ) +....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 + +....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4 7 +....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 + +....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 + +....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^ 7 +....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1 . +....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2 +....: + C1.one)*C1.y.diffn()).verschiebung() +....:  +....: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 3 +....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34 +....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1. o +....: ne)/C1.x^2)*C1.y).verschiebung() +....:  +....: xi = superelliptic_drw_cech(om, ff) +[?7h[?12l[?25h[?2004l +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lreducee(xi)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lucee(xi)[?7h[?12l[?25h[?25l[?7lsage: reducee(xi) +[?7h[?12l[?25h[?2004ldecomp_first_comp[0], decomp_second_comp[0] 0 ((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/x^2)*y +new.omega0 [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((x^38 + 2*x^34 + 3*x^32 + x^30 + 4*x^28 + 4*x^26 + 4*x^24 + 3*x^20 + x^18 + 2*x^16 + 4*x^12 + 2*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 2)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y]) +[?7h([(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((x^38 + 2*x^34 + 3*x^32 + x^30 + 4*x^28 + 4*x^26 + 4*x^24 + 3*x^20 + x^18 + 2*x^16 + 4*x^12 + 2*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 2)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y]), V(1/x^2*y), [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^32 + 3*x^30 + x^28 + 2*x^24 + 3*x^20 + 4*x^18 + 2*x^16 + 4*x^14 + 4*x^12 + 2*x^10 + 2*x^6 + 1)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y])) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lreducee(xi)[?7h[?12l[?25h[?25l[?7lsage: reducee(xi) +[?7h[?12l[?25h[?2004ldecomp_first_comp[0], decomp_second_comp[0] 0 2/x^2*y +new.omega0 [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^36 + 3*x^32 + 3*x^30 + 3*x^26 + x^24 + 3*x^18 + 2*x^16 + 2*x^14 + 3*x^12 + 4*x^10 + 2*x^8 + 2*x^6 + 3*x^4 + 4*x^2 + 2)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]) +[?7h([(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^36 + 3*x^32 + 3*x^30 + 3*x^26 + x^24 + 3*x^18 + 2*x^16 + 2*x^14 + 3*x^12 + 4*x^10 + 2*x^8 + 2*x^6 + 3*x^4 + 4*x^2 + 2)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(4/x^2*y), [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^32 + 3*x^30 + x^28 + 2*x^24 + 3*x^20 + 4*x^18 + 2*x^16 + 4*x^14 + 4*x^12 + 2*x^10 + 2*x^6 + 1)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y])) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lreducee(xi)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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[?7lef aa(self):[?7h[?12l[?25h[?25l[?7lcompoition_g0_g8(xi.f.t)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lposition_g0_g8(xi.f.t)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?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[?7lsage: decomposition_g0_g8(ff) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [56], line 1 +----> 1 decomposition_g0_g8(ff) + +File :7, in decomposition_g0_g8(fct, prec) + +AttributeError: 'superelliptic_witt' object has no attribute 'coordinates' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(ff)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(ff.f) +[?7h[?12l[?25h[?2004l[?7h(((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/x^2)*y, + 0, + 1/x^2*y) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(ff.f)[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(ff.f)[0] +[?7h[?12l[?25h[?2004l[?7h((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/x^2)*y +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(ff.f)[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lF = GF(p)[?7h[?12l[?25h[?25l[?7lxy, Rxy, x, y=C1.fct_field[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l Rxy, x, y=C1.fct_field[?7h[?12l[?25h[?25l[?7lsage: Fxy, Rxy, x, y=C1.fct_field +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y=C1.fct_field[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(ff.f)[0][?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[?7lx[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(ff.f)[0] in Rxy +[?7h[?12l[?25h[?2004l[?7hFalse +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1 = superelliptic(f1, m, prec = 500)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[4].oega0.regular_form()[?7h[?12l[?25h[?25l[?7ly.diffn()[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C1.y/C1.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[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lrt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?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: (C1.y/C1.x^2).expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-11 + 3*t^29 + 4*t^89 + t^109 + 2*t^129 + 2*t^149 + 4*t^169 + t^229 + 2*t^269 + t^289 + 2*t^309 + 3*t^329 + t^369 + 2*t^389 + 3*t^449 + t^469 + O(t^489) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 3 +....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34   +....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1. o +....: ne)/C1.x^2)*C1.y).verschiebung()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.expansion_at_infty() +  +  + [?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ff.f.coordinates() +[?7h[?12l[?25h[?2004l[?7h[0, 3, 0, 0, 0, 0, 0] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + [?7h[?12l[?25h[?25l[?7lff.f.coordinates()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 3 +....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34   +....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1. o +....: ne)/C1.x^2)*C1.y).verschiebung()[?7h[?12l[?25h[?25l[?7l- +  +  + [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l + C1.a_number C1.cartier_matrix C1.de_rham_basis  + C1.base_ring C1.characteristic C1.degrees_de_rham0  +  C1.basis_de_rham_degrees C1.cohomology_of_structure_sheaf_basis C1.degrees_de_rham1 > + C1.basis_holomorphic_differentials_degree C1.crystalline_cohomology_basis C1.degrees_holomorphic_differentials  + [?7h[?12l[?25h[?25l[?7la_number + C1.a_number  + + + + [?7h[?12l[?25h[?25l[?7lcartier_matrix + C1.a_number  C1.cartier_matrix [?7h[?12l[?25h[?25l[?7lde_rhambsis + C1.cartier_matrix  C1.de_rham_basis [?7h[?12l[?25h[?25l[?7lcartiermtrix + C1.cartier_matrix  C1.de_rham_basis [?7h[?12l[?25h[?25l[?7lharacteristc + C1.cartier_matrix  + C1.characteristic [?7h[?12l[?25h[?25l[?7lohomology_of_structure_sheaf_basis + + C1.characteristic  + C1.cohomology_of_structure_sheaf_basis [?7h[?12l[?25h[?25l[?7l( + + + + +[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: ff - 3*C1.cohomology_of_structure_sheaf_basis()[1] +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [63], line 1 +----> 1 ff - Integer(3)*C1.cohomology_of_structure_sheaf_basis()[Integer(1)] + +File :35, in __sub__(self, other) + +File :29, in __add__(self, other) + +AttributeError: 'superelliptic_function' object has no attribute 't' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff - 3*C1.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laf - 3*C1.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7laf - 3*C1.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l f - 3*C1.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l=f - 3*C1.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l f - 3*C1.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l. - 3*C1.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7lf - 3*C1.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: aa = ff.f - 3*C1.cohomology_of_structure_sheaf_basis()[1] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laa = ff.f - 3*C1.cohomology_of_structure_sheaf_basis()[1][?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[?7ldecomposition_g0_g8(ff.f)[0] in Rxy[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lposition_g0_g8(ff.f)[0] in Rxy[?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[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(aa) +[?7h[?12l[?25h[?2004l[?7h(((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 1)/x^2)*y, + 0, + 2/x^2*y) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aa)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lomposition_g0_g8(aa)[?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[?7lf)[?7h[?12l[?25h[?25l[?7l)[0] in Rxy[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(ff.f) +[?7h[?12l[?25h[?2004l[?7h(((2*x^98 + 4*x^94 + x^92 + 3*x^90 + 4*x^86 + 2*x^84 + 4*x^82 + 2*x^78 + x^76 + 3*x^74 + x^72 + 3*x^70 + x^68 + 3*x^66 + 2*x^64 + 3*x^62 + x^60 + 4*x^56 + 3*x^54 + x^52 + 2*x^50 + x^48 + 3*x^46 + 2*x^44 + 4*x^38 + x^36 + 2*x^34 + 4*x^32 + x^30 + x^28 + 4*x^26 + 2*x^24 + 4*x^22 + 3*x^18 + 3*x^14 + 4*x^12 + 3*x^10 + 3*x^6 + 2*x^4 + 3*x^2 + 3)/x^2)*y, + 0, + 1/x^2*y) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff - 3*C1.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.f.coordinates()[?7h[?12l[?25h[?25l[?7lf.coordinates()[?7h[?12l[?25h[?25l[?7lsage: ff.f.coordinates() +[?7h[?12l[?25h[?2004l[?7h[0, 3, 0, 0, 0, 0, 0] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7llogy_of_structure_sheaf_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: 3*C1.cohomology_of_structure_sheaf_basis()[1] +[?7h[?12l[?25h[?2004l[?7h1/x^2*y +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.f.coordinates()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lsage: ff.f.coordinates() +[?7h[?12l[?25h[?2004l[?7h[0, 3, 0, 0, 0, 0, 0] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laa = ff.f - 3*C1.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aa.coordinates() +[?7h[?12l[?25h[?2004l[?7h[0, 1, 0, 0, 0, 0, 0] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laa.coordinates()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = ff.f - 3*C1.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lff.f - 3*C1.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l 3*C1.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l+ 3*C1.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: aa = ff.f + 3*C1.cohomology_of_structure_sheaf_basis()[1] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laa = ff.f + 3*C1.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: aa.coordinates() +[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0, 0] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laa.coordinates()[?7h[?12l[?25h[?25l[?7l = ff.f + 3*C1.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7l3*C1homology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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.f.coordinates()[?7h[?12l[?25h[?25l[?7lor b in B1:[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lhomology_of_structure_sheaf_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: for b in C1.cohomology_of_structure_sheaf_basis(): +....: [?7h[?12l[?25h[?25l[?7lprint(omega)[?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.regular_form())[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l....:  print(b.coordinates()) +....: [?7h[?12l[?25h[?25l[?7lsage: for b in C1.cohomology_of_structure_sheaf_basis(): +....:  print(b.coordinates()) +....:  +[?7h[?12l[?25h[?2004l[4, 0, 0, 0, 0, 0, 0] +[0, 4, 0, 0, 0, 0, 0] +[0, 0, 4, 0, 0, 0, 0] +[0, 0, 0, 4, 0, 0, 0] +[0, 0, 0, 0, 4, 0, 0] +[0, 0, 0, 0, 0, 4, 0] +[0, 0, 0, 0, 0, 0, 4] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?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 +( [3*x*y] d[x] + [3*x^2 + 2] d[y] + V(((3*x^19 + 2*x^17 + x^15 + x^13 + 3*x^9 + 4*x^7 + x^5 + x^3 + x)*y) dx + (3*x^20 + 4*x^18 + 4*x^16 + 4*x^12 + 3*x^10 + x^8 + 2*x^6 + 4) dy) + dV(0), V((4*x^14 + x^12 + 3*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 4)*y) ) +( [3*x^2*y] d[x] + [3*x^3 + 2*x] d[y] + V(((3*x^24 + 4*x^22 + x^20 + 3*x^18 + 3*x^16 + 3*x^10 + 2*x^8 + 3*x^4 + 3*x^2)*y) dx + (3*x^25 + x^23 + 2*x^21 + 2*x^19 + 2*x^15 + 3*x^11 + 4*x^9 + 3*x^7 + 3*x^5 + 2*x) dy) + dV(0), [2/x*y] + V(((4*x^20 + x^18 + 3*x^16 + 3*x^14 + x^12 + x^10 + 3*x^8 + 4*x^6 + 4*x^4 + 3*x^2 + 4)/x)*y) ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor b in C1.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7l1 = f(x= x^5 - x)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= f(x = x^5 - x)[?7h[?12l[?25h[?25l[?7lsage: f1 = f(x = x^5 - x) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1 = superelliptic(f1, m, prec = 500)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= superelliptic(f1, m, prec = 500)[?7h[?12l[?25h[?25l[?7lsage: C1 = superelliptic(f1, m, prec = 500) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = f(x = x^5 - x)[?7h[?12l[?25h[?25l[?7lf.f.coordinates()[?7h[?12l[?25h[?25l[?7l - 3*C1.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7lsage: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 3 +....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34   +....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1. o +....: ne)/C1.x^2)*C1.y).verschiebung()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l(((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 3 +*C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34  ++ 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1. o +ne)/C1.x^2)*C1.y).verschiebung()[?7h[?12l[?25h[?25l[?7lsage: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 3 +....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34 +....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1. o +....: ne)/C1.x^2)*C1.y).verschiebung() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(ff.f)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lomposition_g0_g8(ff.f)[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(ff.f) +[?7h[?12l[?25h[?2004l[?7h((2*x^96 + 4*x^92 + x^90 + 3*x^88 + 4*x^84 + 2*x^82 + 4*x^80 + 2*x^76 + x^74 + 3*x^72 + x^70 + 3*x^68 + x^66 + 3*x^64 + 2*x^62 + 3*x^60 + x^58 + 4*x^54 + 3*x^52 + x^50 + 2*x^48 + x^46 + 3*x^44 + 2*x^42 + 4*x^36 + x^34 + 2*x^32 + 4*x^30 + x^28 + x^26 + 4*x^24 + 2*x^22 + 4*x^20 + 3*x^16 + 3*x^12 + 4*x^10 + 3*x^8 + 3*x^4 + 2*x^2 + 3)*y, + 0, + 4/x^2*y) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller( ) +....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +   +....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4 7 +....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +   +....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 +   +....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^ 7 +....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1 . +....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2   +....: + C1.one)*C1.y.diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller( ) +.diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +  +2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4 7 + + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +  +2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 +  +3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^ 7 +6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1 . +x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2  ++ C1.one)*C1.y.diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7lsage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller( ) +....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 + +....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4 7 +....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 + +....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 + +....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^ 7 +....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1 . +....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2 +....: + C1.one)*C1.y.diffn()).verschiebung() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_drw_cech(om, ff)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li = superelliptic_drw_cech(om, ff)[?7h[?12l[?25h[?25l[?7l = superelliptic_drw_cech(om, ff)[?7h[?12l[?25h[?25l[?7lsage: xi = superelliptic_drw_cech(om, ff) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_drw_cech(om, ff)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_drw_cech(om, ff)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.f[?7h[?12l[?25h[?25l[?7lreduce()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lreducee(xi)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_drw_cech(om, ff)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.f[?7h[?12l[?25h[?25l[?7lreduce()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lduce()[?7h[?12l[?25h[?25l[?7lsage: xi.reduce() +[?7h[?12l[?25h[?2004l(0, 0, 0) ((2*x^96 + 4*x^92 + x^90 + 3*x^88 + 4*x^84 + 2*x^82 + 4*x^80 + 2*x^76 + x^74 + 3*x^72 + x^70 + 3*x^68 + x^66 + 3*x^64 + 2*x^62 + 3*x^60 + x^58 + 4*x^54 + 3*x^52 + x^50 + 2*x^48 + x^46 + 3*x^44 + 2*x^42 + 4*x^36 + x^34 + 2*x^32 + 4*x^30 + x^28 + x^26 + 4*x^24 + 2*x^22 + 4*x^20 + 3*x^16 + 3*x^12 + 4*x^10 + 3*x^8 + 3*x^4 + 2*x^2 + 3)*y, 0, 4/x^2*y) +[(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^36 + 3*x^32 + 3*x^30 + 3*x^26 + x^24 + 3*x^18 + 2*x^16 + 2*x^14 + 3*x^12 + 4*x^10 + 2*x^8 + 2*x^6 + 3*x^4 + 4*x^2 + 2)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]) +[?7h([(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^36 + 3*x^32 + 3*x^30 + 3*x^26 + x^24 + 3*x^18 + 2*x^16 + 2*x^14 + 3*x^12 + 4*x^10 + 2*x^8 + 2*x^6 + 3*x^4 + 4*x^2 + 2)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(4/x^2*y), [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^32 + 3*x^30 + x^28 + 2*x^24 + 3*x^20 + 4*x^18 + 2*x^16 + 4*x^14 + 4*x^12 + 2*x^10 + 2*x^6 + 1)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y])) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.reduce()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lduce()[?7h[?12l[?25h[?25l[?7lsage: xi.reduce() +[?7h[?12l[?25h[?2004l(0, 0, 0) (0, 0, 4/x^2*y) +[(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^36 + 3*x^32 + 3*x^30 + 3*x^26 + x^24 + 3*x^18 + 2*x^16 + 2*x^14 + 3*x^12 + 4*x^10 + 2*x^8 + 2*x^6 + 3*x^4 + 4*x^2 + 2)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]) +[?7h([(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^36 + 3*x^32 + 3*x^30 + 3*x^26 + x^24 + 3*x^18 + 2*x^16 + 2*x^14 + 3*x^12 + 4*x^10 + 2*x^8 + 2*x^6 + 3*x^4 + 4*x^2 + 2)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(4/x^2*y), [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^32 + 3*x^30 + x^28 + 2*x^24 + 3*x^20 + 4*x^18 + 2*x^16 + 4*x^14 + 4*x^12 + 2*x^10 + 2*x^6 + 1)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y])) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.reduce()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: xi.reduce() +[?7h[?12l[?25h[?2004l(0, 0, 0) (0, 0, 4/x^2*y) +^C--------------------------------------------------------------------------- +KeyboardInterrupt Traceback (most recent call last) +Cell In [83], line 1 +----> 1 xi.reduce() + +File :20, in reduce(self) + +File :73, in diffn(self, dy_w) + +File :177, in dy_w(C) + +File /ext/sage/9.8/src/sage/rings/rational.pyx:2406, in sage.rings.rational.Rational.__mul__() + 2404 return x + 2405 +-> 2406 return coercion_model.bin_op(left, right, operator.mul) + 2407 + 2408 cpdef _mul_(self, right): + +File /ext/sage/9.8/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/9.8/src/sage/structure/element.pyx:1527, in sage.structure.element.Element.__mul__() + 1525 if not err: + 1526 return (right)._mul_long(value) +-> 1527 return coercion_model.bin_op(left, right, mul) + 1528 except TypeError: + 1529 return NotImplemented + +File /ext/sage/9.8/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/9.8/src/sage/structure/element.pyx:1527, in sage.structure.element.Element.__mul__() + 1525 if not err: + 1526 return (right)._mul_long(value) +-> 1527 return coercion_model.bin_op(left, right, mul) + 1528 except TypeError: + 1529 return NotImplemented + +File /ext/sage/9.8/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) + + [... skipping similar frames: __rmul__ at line 43 (6 times), sage.structure.coerce.CoercionModel.bin_op at line 1242 (6 times), sage.structure.element.Element.__mul__ at line 1527 (6 times)] + +File /ext/sage/9.8/src/sage/structure/element.pyx:1527, in sage.structure.element.Element.__mul__() + 1525 if not err: + 1526 return (right)._mul_long(value) +-> 1527 return coercion_model.bin_op(left, right, mul) + 1528 except TypeError: + 1529 return NotImplemented + +File /ext/sage/9.8/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 :253, in reduction(C, g) + +File /ext/sage/9.8/src/sage/structure/parent.pyx:896, in sage.structure.parent.Parent.__call__() + 894 if mor is not None: + 895 if no_extra_args: +--> 896 return mor._call_(x) + 897 else: + 898 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.8/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/9.8/src/sage/rings/fraction_field.py:711, in FractionField_generic._element_constructor_(self, x, y, coerce) + 708 raise TypeError("cannot convert {!r}/{!r} to an element of {}".format( + 709 x0, y0, self)) + 710 try: +--> 711 return self._element_class(self, x, y, coerce=coerce) + 712 except TypeError: + 713 if parent(x) is parent(x0): + +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: class test: +....: ^Idef __init__(self, gg): +....: ^I^Iself.gg = gg +....: ^I +....: ^Idef aa(self): +....: ^I^Inew = self.gg +....: ^I^Inew += 1 +....: ^I^Ireturn new[?7h[?12l[?25h[?25l[?7l....: ^I^Ireturn new +....: [?7h[?12l[?25h[?25l[?7lsage: class test: +....: ^Idef __init__(self, gg): +....: ^I^Iself.gg = gg +....: ^I +....: ^Idef aa(self): +....: ^I^Inew = self.gg +....: ^I^Inew += 1 +....: ^I^Ireturn new +....:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: D = test(1) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD = test(1)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: D.aa() +[?7h[?12l[?25h[?2004l[?7h2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD.aa()[?7h[?12l[?25h[?25l[?7lsage: D +[?7h[?12l[?25h[?2004l[?7h<__main__.test object at 0x7f22ef213390> +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD[?7h[?12l[?25h[?25l[?7l.aa()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lsage: D.gg +[?7h[?12l[?25h[?2004l[?7h1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lComputing 0. basis element +Computing 1. basis element +( [3*x*y] d[x] + [3*x^2 + 2] d[y] + V(((3*x^19 + 2*x^17 + x^15 + x^13 + 3*x^9 + 4*x^7 + x^5 + x^3 + x)*y) dx + (3*x^20 + 4*x^18 + 4*x^16 + 4*x^12 + 3*x^10 + x^8 + 2*x^6 + 4) dy) + dV(0), V((4*x^14 + x^12 + 3*x^10 + 3*x^8 + x^6 + x^4 + 3*x^2 + 4)*y) ) +( [3*x^2*y] d[x] + [3*x^3 + 2*x] d[y] + V(((3*x^24 + 4*x^22 + x^20 + 3*x^18 + 3*x^16 + 3*x^10 + 2*x^8 + 3*x^4 + 3*x^2)*y) dx + (3*x^25 + x^23 + 2*x^21 + 2*x^19 + 2*x^15 + 3*x^11 + 4*x^9 + 3*x^7 + 3*x^5 + 2*x) dy) + dV(0), [2/x*y] + V(((4*x^20 + x^18 + 3*x^16 + 3*x^14 + x^12 + x^10 + 3*x^8 + 4*x^6 + 4*x^4 + 3*x^2 + 4)/x)*y) ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller( ) +....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +   +....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4 7 +....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +   +....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 +   +....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^ 7 +....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1 . +....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2   +....: + C1.one)*C1.y.diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller( ) +.diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +  +2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4 7 + + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +  +2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 +  +3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^ 7 +6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1 . +x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2  ++ C1.one)*C1.y.diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7lsage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller( ) +....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 + +....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4 7 +....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 + +....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 + +....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^ 7 +....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1 . +....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2 +....: + C1.one)*C1.y.diffn()).verschiebung() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1 = superelliptic(f1, m, prec = 500)[?7h[?12l[?25h[?25l[?7l2[?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[?7l7[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l +1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l 1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C2 = superelliptic(x^7 + x + 1, 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 3 +....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34   +....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1. o +....: ne)/C1.x^2)*C1.y).verschiebung()[?7h[?12l[?25h[?25l[?7lor b in C1.cohomology_of_structure_sheaf_basis(): +  +  + [?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC1.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7l2.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l +....: [?7h[?12l[?25h[?25l[?7lprint(b.coordinates())[?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(b.coordinates())[?7h[?12l[?25h[?25l[?7l() +....: [?7h[?12l[?25h[?25l[?7lsage: for b in C2.cohomology_of_structure_sheaf_basis(): +....:  print(b.coordinates()) +....:  +[?7h[?12l[?25h[?2004l[1, 0, 0] +[0, 1, 0] +[0, 0, 1] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for b in C2.cohomology_of_structure_sheaf_basis(): +....:  print(b.coordinates())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7lbasis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7lbasis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7lbasis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7ld_basis():[?7h[?12l[?25h[?25l[?7le_basis():[?7h[?12l[?25h[?25l[?7l_basis():[?7h[?12l[?25h[?25l[?7lr_basis():[?7h[?12l[?25h[?25l[?7lh_basis():[?7h[?12l[?25h[?25l[?7la_basis():[?7h[?12l[?25h[?25l[?7lm_basis():[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l() +()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:  print(b.coordinates()) +....: [?7h[?12l[?25h[?25l[?7lsage: for b in C2.de_rham_basis(): +....:  print(b.coordinates()) +....:  +[?7h[?12l[?25h[?2004l(1, 0, 0, 0, 0, 0) +(0, 1, 0, 0, 0, 0) +(0, 0, 1, 0, 0, 0) +(0, 0, 0, 1, 0, 0) +(0, 0, 0, 0, 1, 0) +(0, 0, 0, 0, 0, 1) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for b in C2.de_rham_basis(): +....:  print(b.coordinates())[?7h[?12l[?25h[?25l[?7l() +()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(:[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l.:[?7h[?12l[?25h[?25l[?7lh:[?7h[?12l[?25h[?25l[?7lo:[?7h[?12l[?25h[?25l[?7lm:[?7h[?12l[?25h[?25l[?7lo:[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7l +....:  +....:  print(b.coordinates())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l print(b.coordinates()) + [?7h[?12l[?25h[?25l[?7l +()[?7h[?12l[?25h[?25l[?7l() +....: [?7h[?12l[?25h[?25l[?7lsage: for b in C2.holomorphic_differentials_basis(): +....:  print(b.coordinates()) +....:  +[?7h[?12l[?25h[?2004l[1, 0, 0] +[0, 1, 0] +[0, 0, 1] +[?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$ cd .. +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -u \ No newline at end of file diff --git a/sage/drafty/draft.sage b/sage/drafty/draft.sage index f4033be..ca94803 100644 --- a/sage/drafty/draft.sage +++ b/sage/drafty/draft.sage @@ -6,9 +6,9 @@ Rxx. = PolynomialRing(F) f = x^3 + x f1 = f(x = x^5 - x) C = superelliptic(f, m) -C1 = superelliptic(f1, m, prec = 500) +#C1 = superelliptic(f1, m, prec = 500) B = C.crystalline_cohomology_basis(prec = 100, info = 1) -B1 = C1.crystalline_cohomology_basis(prec = 100, info = 1) +#B1 = C1.crystalline_cohomology_basis(prec = 100, info = 1) def crystalline_matrix(C, prec = 50): B = C.crystalline_cohomology_basis(prec = prec) @@ -23,8 +23,8 @@ def crystalline_matrix(C, prec = 50): for b in B: print(b.regular_form()) -for b in B1: - print(b.regular_form()) +#for b in B1: +# print(b.regular_form()) #M = crystalline_matrix(C, prec = 150) #print(M) diff --git a/sage/superelliptic/superelliptic_function_class.sage b/sage/superelliptic/superelliptic_function_class.sage index 9ffc1c3..7aed0fe 100644 --- a/sage/superelliptic/superelliptic_function_class.sage +++ b/sage/superelliptic/superelliptic_function_class.sage @@ -103,7 +103,7 @@ class superelliptic_function: g = C.genus() coordinates = g*[0] for i, omega in enumerate(basis_holo): - coordinates[i] = omega.serre_duality_pairing(self, prec=prec) + coordinates[i] = -omega.serre_duality_pairing(self, prec=prec) return coordinates def expansion_at_infty(self, place = 0, prec=20):