From 995d5f02d87e7a044ed436b690cbfb471fce3cca Mon Sep 17 00:00:00 2001 From: jgarnek Date: Fri, 24 Mar 2023 11:27:05 +0000 Subject: [PATCH] naprawiony problem z uniformizatorem w superelliptic; decomposition_omega8_hpdh dziala --- sage/.run.term-0.term | 3524 +++++++++++++++++ sage/init.sage | 2 + sage/superelliptic/superelliptic_class.sage | 18 +- .../superelliptic_function_class.sage | 3 +- .../decomposition_into_g0_g8.sage | 9 +- .../superelliptic_drw_auxilliaries.sage | 49 + .../superelliptic_drw_cech.sage | 48 +- 7 files changed, 3618 insertions(+), 35 deletions(-) create mode 100644 sage/superelliptic_drw/superelliptic_drw_auxilliaries.sage diff --git a/sage/.run.term-0.term b/sage/.run.term-0.term index 142281a..b46964a 100644 --- a/sage/.run.term-0.term +++ b/sage/.run.term-0.term @@ -50685,3 +50685,3527 @@ Untracked files: no changes added to commit (use "git add" and/or "git commit -a") ]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add sage/as_covers/tests/cartier_test.sage sage/superelliptic_drw/tests/ sage/as_cosuperelliptic/tests/ +]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-m ""w"s"p"o"l"r"z"e"d"n"i"e" "p"r"a"w"i"e" "d"z"[1@b[1@a[1@z[1@a[1@ [1@c[1@r[1@y[1@s[1@ [1@d[1@z[1@i[1@a[1@l[1@a[1@;[1@ [1@p[1@o[1@p[1@r[1@a[1@w[1@k[1@i[1@ [1@w[1@ [1@c[1@o[1@o[1@r[1@d[1@i[1@n[1@a[1@t[1@e[1@s[1@ [1@d[1@r[1@l[1@;[1@ [1@ [1@c[1@r[1@i[1@s[1@ i"a"l"a"j"a" +[master 42ccc4d] baza crys dziala; poprawki w coordinates dr; wspolrzednie cris prawie dzialaja + 20 files changed, 16269 insertions(+), 87 deletions(-) + create mode 100644 sage/as_covers/tests/cartier_test.sage + create mode 100644 sage/superelliptic/tests/a_number_test.sage + create mode 100644 sage/superelliptic/tests/form_coordinates_test.sage + create mode 100644 sage/superelliptic/tests/p_rank_test.sage + create mode 100644 sage/superelliptic/tests/pth_root_test.sage + create mode 100644 sage/superelliptic_drw/tests/decomposition_into_g0_g8_tests.sage + create mode 100644 sage/superelliptic_drw/tests/superelliptic_drw_tests.sage +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git push +Username for 'https://git.wmi.amu.edu.pl': jgarnek +Password for 'https://jgarnek@git.wmi.amu.edu.pl': +Enumerating objects: 50, done. +Counting objects: 2% (1/50) Counting objects: 4% (2/50) Counting objects: 6% (3/50) Counting objects: 8% (4/50) Counting objects: 10% (5/50) Counting objects: 12% (6/50) Counting objects: 14% (7/50) Counting objects: 16% (8/50) Counting objects: 18% (9/50) Counting objects: 20% (10/50) Counting objects: 22% (11/50) Counting objects: 24% (12/50) Counting objects: 26% (13/50) Counting objects: 28% (14/50) Counting objects: 30% (15/50) Counting objects: 32% (16/50) Counting objects: 34% (17/50) Counting objects: 36% (18/50) Counting objects: 38% (19/50) Counting objects: 40% (20/50) Counting objects: 42% (21/50) Counting objects: 44% (22/50) Counting objects: 46% (23/50) Counting objects: 48% (24/50) Counting objects: 50% (25/50) Counting objects: 52% (26/50) Counting objects: 54% (27/50) Counting objects: 56% (28/50) Counting objects: 58% (29/50) Counting objects: 60% (30/50) Counting objects: 62% (31/50) Counting objects: 64% (32/50) Counting objects: 66% (33/50) Counting objects: 68% (34/50) Counting objects: 70% (35/50) Counting objects: 72% (36/50) Counting objects: 74% (37/50) Counting objects: 76% (38/50) Counting objects: 78% (39/50) Counting objects: 80% (40/50) Counting objects: 82% (41/50) Counting objects: 84% (42/50) Counting objects: 86% (43/50) Counting objects: 88% (44/50) Counting objects: 90% (45/50) Counting objects: 92% (46/50) Counting objects: 94% (47/50) Counting objects: 96% (48/50) Counting objects: 98% (49/50) Counting objects: 100% (50/50) Counting objects: 100% (50/50), done. +Delta compression using up to 4 threads +Compressing objects: 3% (1/30) Compressing objects: 6% (2/30) Compressing objects: 10% (3/30) Compressing objects: 13% (4/30) Compressing objects: 16% (5/30) Compressing objects: 20% (6/30) Compressing objects: 23% (7/30) Compressing objects: 26% (8/30) Compressing objects: 30% (9/30) Compressing objects: 33% (10/30) Compressing objects: 36% (11/30) Compressing objects: 40% (12/30) Compressing objects: 43% (13/30) Compressing objects: 46% (14/30) Compressing objects: 50% (15/30) Compressing objects: 53% (16/30) Compressing objects: 56% (17/30) Compressing objects: 60% (18/30) Compressing objects: 63% (19/30) Compressing objects: 66% (20/30) Compressing objects: 70% (21/30) Compressing objects: 73% (22/30) Compressing objects: 76% (23/30) Compressing objects: 80% (24/30) Compressing objects: 83% (25/30) Compressing objects: 86% (26/30) Compressing objects: 90% (27/30) Compressing objects: 93% (28/30) Compressing objects: 96% (29/30) Compressing objects: 100% (30/30) Compressing objects: 100% (30/30), done. +Writing objects: 3% (1/30) Writing objects: 6% (2/30) Writing objects: 10% (3/30) Writing objects: 13% (4/30) Writing objects: 16% (5/30) Writing objects: 20% (6/30) Writing objects: 23% (7/30) Writing objects: 26% (8/30) Writing objects: 30% (9/30) Writing objects: 33% (10/30) Writing objects: 36% (11/30) Writing objects: 40% (12/30) Writing objects: 43% (13/30) Writing objects: 46% (14/30) Writing objects: 50% (15/30) Writing objects: 53% (16/30) Writing objects: 56% (17/30) Writing objects: 60% (18/30) Writing objects: 63% (19/30) Writing objects: 66% (20/30) Writing objects: 70% (21/30) Writing objects: 73% (22/30) Writing objects: 76% (23/30) Writing objects: 80% (24/30) Writing objects: 83% (25/30) Writing objects: 86% (26/30) Writing objects: 90% (27/30) Writing objects: 93% (28/30) Writing objects: 96% (29/30) Writing objects: 100% (30/30) Writing objects: 100% (30/30), 143.28 KiB | 1.06 MiB/s, done. +Total 30 (delta 18), reused 0 (delta 0) +remote: . Processing 1 references +remote: Processed 1 references in total +To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git + ce0ac0d..42ccc4d master -> master +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ sacd sa +bash: cd: sa: No such file or directory +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ cd sage/ +]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.7, Release Date: 2022-09-19 │ +│ Using Python 3.10.5. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg.diffn()[?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[?7lg.diffn()[?7h[?12l[?25h[?25l[?7l = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.diffn() +[?7h[?12l[?25h[?2004l[?7h((x^18*y + x^16*y - x^12*y - x^10*y - x^6 - x^4 - x^2 - y - 1)/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7l().int()[?7h[?12l[?25h[?25l[?7lregular_form()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7llar_form()[?7h[?12l[?25h[?25l[?7lsage: g.diffn().regular_form() +[?7h[?12l[?25h[?2004l[?7h(x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.diffn().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[?7log.difn().regular_form()[?7h[?12l[?25h[?25l[?7lmg.difn().regular_form()[?7h[?12l[?25h[?25l[?7l g.difn().regular_form()[?7h[?12l[?25h[?25l[?7l=g.difn().regular_form()[?7h[?12l[?25h[?25l[?7l g.difn().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[?7lsage: om = g.diffn().regular_form() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn().regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.is_regular_on_U0()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7ly[?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[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: om.dy = 0*C.x +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.dy = 0*C.x[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lis_regular_on_U0()[?7h[?12l[?25h[?25l[?7lint()[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int() +[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx +m dx x^18 +int(self) (x^16 + 2*x^12 + 2*x^10 + 2) dx +m dx x^16 +int(self) (2*x^12 + 2*x^10 + 2) dx +m dx x^12 +int(self) (2*x^10 + 2) dx +m dx x^10 +int(self) (2) dx +m dx 1 +int(self) (0) dy +[?7hx^19 + 2*x^17 + 2*x^13 + x^11 + 2*x +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.diffn().regular_form()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y=C.fct_field[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7ly, Rxy, x, y=C.fct_field[?7h[?12l[?25h[?25l[?7lsage: Fxy, Rxy, x, y=C.fct_field +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.diffn().regular_form()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(g.function)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (g.function).quo_rem(y) +[?7h[?12l[?25h[?2004l[?7h(2*x^4 + x^2 + 2, x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.diffn().regular_form()[?7h[?12l[?25h[?25l[?7lsage: g +[?7h[?12l[?25h[?2004l[?7h(2*x^4 + x^2 + 2)*y + x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.diffn().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[?7lg[?7h[?12l[?25h[?25l[?7l(g.function).quo_rem(y)[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA(g.function).quo_rem(y)[0][?7h[?12l[?25h[?25l[?7l (g.function).quo_rem(y)[0][?7h[?12l[?25h[?25l[?7l=(g.function).quo_rem(y)[0][?7h[?12l[?25h[?25l[?7l (g.function).quo_rem(y)[0][?7h[?12l[?25h[?25l[?7lsage: A = (g.function).quo_rem(y)[0] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = (g.function).quo_rem(y)[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = (g.function).quo_rem(y)[0][?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A = Rx(A) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = Rx(A)[?7h[?12l[?25h[?25l[?7l.omega.cartier().cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.monomial_coefficient(x^3) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [13], in () +----> 1 A.monomial_coefficient(x**Integer(3)) + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:6094, in sage.rings.polynomial.polynomial_element.Polynomial.monomial_coefficient() + 6092 """ + 6093 if not m.parent() is self._parent: +-> 6094 raise TypeError("monomial must have same parent as self.") + 6095 + 6096 d = m.degree() + +TypeError: monomial must have same parent as self. +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.monomial_coefficient(x^3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx^3)[?7h[?12l[?25h[?25l[?7lx^3)[?7h[?12l[?25h[?25l[?7l(x^3)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: A.monomial_coefficient(Rx(x^3)) +[?7h[?12l[?25h[?2004l[?7h0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.monomial_coefficient(Rx(x^3))[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lsage: A.monomial_coefficient(Rx(x^3)) + A.abs A.all_roots_in_interval A.base_ring A.change_variable_name A.compose_trunc  + A.adams_operator A.any_root A.cartesian_product A.coefficients A.composed_op  + A.add_bigoh A.args A.category A.complex_roots A.constant_coefficient > + A.additive_order A.base_extend A.change_ring A.compose_power A.content_ideal  + [?7h[?12l[?25h[?25l[?7labs + A.abs  + + + + [?7h[?12l[?25h[?25l[?7lll_roots_in_interval + A.abs  A.all_roots_in_interval [?7h[?12l[?25h[?25l[?7lbase_ring + A.all_roots_in_interval  A.base_ring [?7h[?12l[?25h[?25l[?7lchange_variable_name + A.base_ring  A.change_variable_name [?7h[?12l[?25h[?25l[?7lompose_tunc + A.change_variable_name  A.compose_trunc [?7h[?12l[?25h[?25l[?7lycltomic_part + ll_roots_in_intervalbase_ring change_variable_nameompose_tunc ycltomic_part + ny_rot cartesian_productoefficients mposed_op degree  +<rgs categoryomplex_rootsnstant_cefficientdeomiator  + base_extend chang_rigompose_powerntentidealderivaive [?7h[?12l[?25h[?25l[?7ldit +base_ring change_variable_nameompose_tunc ycltomic_partdit  +cartesian_productoefficients mposed_op degree iff  +categoryomplex_rootsnstant_cefficientdeomiator iffereniate +chang_rigompose_powerntentidealderivaive iscrimnant[?7h[?12l[?25h[?25l[?7lspersion +change_variable_nameompose_tunc ycltomic_partdit spersion +oefficients mposed_op degree iff spersion_set +omplex_rootsnstant_cefficientdeomiator iffereniatevides  +ompose_powerntentidealderivaive iscrimnantump [?7h[?12l[?25h[?25l[?7lums +ompose_tunc ycltomic_partdit spersionums  +mposed_op degree iff spersion_seteuclidean_degree +nstant_cefficientdeomiator iffereniatevides exponnts +ntentidealderivaive iscrimnantump factor[?7h[?12l[?25h[?25l[?7lgcd +ycltomic_partdit spersionums gcd  +degree iff spersion_seteuclidean_degreeget_cparent  +deomiator iffereniatevides exponntsglobal_height +derivaive iscrimnantump factorgradient[?7h[?12l[?25h[?25l[?7lhamming_weight +dit spersionums gcd hamming_weight +iff spersion_seteuclidean_degreeget_cparent hasyclotomic_factor +iffereniatevides exponntsglobal_heighthomogenize  +iscrimnantump factorgradientintegral[?7h[?12l[?25h[?25l[?7linversemod +spersionums gcd hamming_weightinversemod  +spersion_seteuclidean_degreeget_cparent hasyclotomic_factorinverse_f_unit  +vides exponntsglobal_heighthomogenize inverse_sries_trunc +ump factorgradientintegrals_constant[?7h[?12l[?25h[?25l[?7ls_cyclotmic +ums gcd hamming_weightinversemod s_cyclotmic +euclidean_degreeget_cparent hasyclotomic_factorinverse_f_unit s_cyclotomic_product +exponntsglobal_heighthomogenize inverse_sries_truncs_gen  +factorgradientintegrals_constanthmogeeous[?7h[?12l[?25h[?25l[?7lidempotent +gcd hamming_weightinversemod s_cyclotmicidempotent +get_cparent hasyclotomic_factorinverse_f_unit s_cyclotomic_productirreducible  +global_heighthomogenize inverse_sries_truncs_gen moic +gradientintegrals_constanthmogeeousmnmial [?7h[?12l[?25h[?25l[?7lnilpotent +hamming_weightinversemod s_cyclotmicidempotentnilpotent  +hasyclotomic_factorinverse_f_unit s_cyclotomic_productirreducible one  +homogenize inverse_sries_truncs_gen moicprime +integrals_constanthmogeeousmnmial primitive[?7h[?12l[?25h[?25l[?7lreal_rooed +inversemod s_cyclotmicidempotentnilpotent real_rooed +inverse_f_unit s_cyclotomic_productirreducible one square +inverse_sries_truncs_gen moicprimesquarefree +s_constanthmogeeousmnmial primitiveter [?7h[?12l[?25h[?25l[?7lunit +s_cyclotmicidempotentnilpotent real_rooedunit  +s_cyclotomic_productirreducible one squareweil_polynomial +s_gen moicprimesquarefreezero  +hmogeeousmnmial primitiveter lc [?7h[?12l[?25h[?25l[?7llcm +idempotentnilpotent real_rooedunit lcm  +irreducible one squareweil_polynomialleadingcefficent +moicprimesquarefreezero list  +mnmial primitiveter lc m[?7h[?12l[?25h[?25l[?7local_height +nilpotent real_rooedunit lcm ocal_height +one squareweil_polynomialleadingcefficentocal_height_arch  +primesquarefreezero list t  +primitiveter lc mmap_coefficients[?7h[?12l[?25h[?25l[?7lmd +real_rooedunit lcm ocal_heightmd  +squareweil_polynomialleadingcefficentocal_height_arch mnic  +squarefreezero list t monomial_coefficient +ter lc mmap_coefficientsonomials [?7h[?12l[?25h[?25l[?7lultiplication_trunc +unit lcm ocal_heightmd ultiplication_trunc +weil_polynomialleadingcefficentocal_height_arch mnic ultiplicative_order +zero list t monomial_coefficientn  +lc mmap_coefficientsonomials newton_raphson[?7h[?12l[?25h[?25l[?7lod + A.mod  A.multiplication_trunc [?7h[?12l[?25h[?25l[?7llcal_height + A.local_height  A.mod [?7h[?12l[?25h[?25l[?7lcm + A.lcm  A.local_height [?7h[?12l[?25h[?25l[?7leading_coefficient + A.lcm  + A.leading_coefficient [?7h[?12l[?25h[?25l[?7l( + + + + +[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.leading_coefficient() +[?7h[?12l[?25h[?2004l[?7h2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  + + + [?7h[?12l[?25h[?25l[?7lA.leading_coefficient()[?7h[?12l[?25h[?25l[?7lsage: A +[?7h[?12l[?25h[?2004l[?7h2*x^4 + x^2 + 2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  + [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lega8_lift0.omega8 - compare[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = g.diffn().regular_form()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn().regular_form()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn().regular_form() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn().regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om +[?7h[?12l[?25h[?2004l[?7h(x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int() +[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy +[?7h((x^20 + x^18 + 2*x^14 + 2*x^12 + 2*x^6 + 2*x^4 + x^2 + 2)/x^2)*y +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l().diffn()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int().diffn() +[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy +[?7h((-x^18 + x^12 - x^6 + x^4 + x^2)/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int().diffn()[?7h[?12l[?25h[?25l[?7l() == om[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int().diffn() == om.form() +[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy +[?7hFalse +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?7h[?12l[?25h[?25l[?7l;[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn().regular_form()[?7h[?12l[?25h[?25l[?7l();[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l();[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om) +[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy +result przed (x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y +((x^20 + x^18 + 2*x^14 + 2*x^12 + 2*x^6 + 2*x^4 + x^2 + 2)/x^2)*y +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om) +[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy +result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [27], in () +----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om) + +File :48, in int(self) + +File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__() + 1514 return (left)._mul_(right) + 1515 if BOTH_ARE_ELEMENT(cl): +-> 1516 return coercion_model.bin_op(left, right, mul) + 1517 + 1518 cdef long value + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op() + 1246 # We should really include the underlying error. + 1247 # This causes so much headache. +-> 1248 raise bin_op_exception(op, x, y) + 1249 + 1250 cpdef canonical_coercion(self, x, y): + +TypeError: unsupported operand parent(s) for *: 'Finite Field of size 3' and 'Rational Field' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om) +[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy +result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x +W 0 +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [29], in () +----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om) + +File :49, in int(self) + +File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__() + 1514 return (left)._mul_(right) + 1515 if BOTH_ARE_ELEMENT(cl): +-> 1516 return coercion_model.bin_op(left, right, mul) + 1517 + 1518 cdef long value + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op() + 1246 # We should really include the underlying error. + 1247 # This causes so much headache. +-> 1248 raise bin_op_exception(op, x, y) + 1249 + 1250 cpdef canonical_coercion(self, x, y): + +TypeError: unsupported operand parent(s) for *: 'Finite Field of size 3' and 'Rational Field' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om) +[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy +result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x +W 0 +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [31], in () +----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om) + +File :49, in int(self) + +File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__() + 1514 return (left)._mul_(right) + 1515 if BOTH_ARE_ELEMENT(cl): +-> 1516 return coercion_model.bin_op(left, right, mul) + 1517 + 1518 cdef long value + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op() + 1246 # We should really include the underlying error. + 1247 # This causes so much headache. +-> 1248 raise bin_op_exception(op, x, y) + 1249 + 1250 cpdef canonical_coercion(self, x, y): + +TypeError: unsupported operand parent(s) for *: 'Finite Field of size 3' and 'Rational Field' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om) +[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy +result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x +W 0 +n_lead, f_lead, (2*a + r) 1 1 11 +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [33], in () +----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om) + +File :50, in int(self) + +File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__() + 1514 return (left)._mul_(right) + 1515 if BOTH_ARE_ELEMENT(cl): +-> 1516 return coercion_model.bin_op(left, right, mul) + 1517 + 1518 cdef long value + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op() + 1246 # We should really include the underlying error. + 1247 # This causes so much headache. +-> 1248 raise bin_op_exception(op, x, y) + 1249 + 1250 cpdef canonical_coercion(self, x, y): + +TypeError: unsupported operand parent(s) for *: 'Finite Field of size 3' and 'Rational Field' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om) +[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy +result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x +W 0 +n_lead, f_lead, (2*a + r) 1 1 11 +W_coeff 2 +W 2*x^4 +--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [35], in () +----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om) + +File :46, in int(self) + +File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() + 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' + 493 """ +--> 494 return self.getattr_from_category(name) + 495 + 496 cdef getattr_from_category(self, name): + +File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() + 505 else: + 506 cls = P._abstract_element_class +--> 507 return getattr_from_other_class(self, cls, name) + 508 + 509 def __dir__(self): + +File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() + 359 dummy_error_message.cls = type(self) + 360 dummy_error_message.name = name +--> 361 raise AttributeError(dummy_error_message) + 362 attribute = attr + 363 # Check for a descriptor (__get__ in Python) + +AttributeError: 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular' object has no attribute 'leading_coefficient' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om) +[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy +result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x +W 0 +n_lead, f_lead, (2*a + r) 1 1 11 +W_coeff 2 +W 2*x^4 +n_lead, f_lead, (2*a + r) 1 1 7 +W_coeff 1 +W 2*x^4 + x^2 +n_lead, f_lead, (2*a + r) 1 1 3 +--------------------------------------------------------------------------- +ZeroDivisionError Traceback (most recent call last) +Input In [37], in () +----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om) + +File :50, in int(self) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 159 print(type(C), C) + 160 print(type(C._element_constructor), C._element_constructor) +--> 161 raise + 162 + 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x) + 1143 """ + 1144 TESTS:: + 1145 + (...) + 1182  True + 1183 """ + 1184 try: +-> 1185 return integer_mod.IntegerMod(self, x) + 1186 except (NotImplementedError, PariError): + 1187 raise TypeError("error coercing to finite field") + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod() + 199 return a + 200 t = modulus.element_class() +--> 201 return t(parent, value) + 202 + 203 + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:374, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__() + 372 z = value + 373 elif isinstance(value, rational.Rational): +--> 374 z = value % self.__modulus.sageInteger + 375 elif integer_check_long_py(value, &longval, &err) and not err: + 376 self.set_from_long(longval) + +File /ext/sage/9.7/src/sage/rings/rational.pyx:2825, in sage.rings.rational.Rational.__mod__() + 2823 n = rat.numer() % other + 2824 d = rat.denom() % other +-> 2825 d = d.inverse_mod(other) + 2826 return (n * d) % other + 2827 + +File /ext/sage/9.7/src/sage/rings/integer.pyx:6774, in sage.rings.integer.Integer.inverse_mod() + 6772 sig_off() + 6773 if r == 0: +-> 6774 raise ZeroDivisionError(f"inverse of Mod({self}, {m}) does not exist") + 6775 return ans + 6776 + +ZeroDivisionError: inverse of Mod(0, 3) does not exist +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om) +[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy +result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x +W 0 +numerator x^6 + x^4 + x^2 + 1 +W 2*x^4 +numerator x^4 + x^2 + 1 +W 2*x^4 + x^2 +numerator x^2 + 1 +--------------------------------------------------------------------------- +ZeroDivisionError Traceback (most recent call last) +Input In [39], in () +----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om) + +File :50, in int(self) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 159 print(type(C), C) + 160 print(type(C._element_constructor), C._element_constructor) +--> 161 raise + 162 + 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x) + 1143 """ + 1144 TESTS:: + 1145 + (...) + 1182  True + 1183 """ + 1184 try: +-> 1185 return integer_mod.IntegerMod(self, x) + 1186 except (NotImplementedError, PariError): + 1187 raise TypeError("error coercing to finite field") + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod() + 199 return a + 200 t = modulus.element_class() +--> 201 return t(parent, value) + 202 + 203 + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:374, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__() + 372 z = value + 373 elif isinstance(value, rational.Rational): +--> 374 z = value % self.__modulus.sageInteger + 375 elif integer_check_long_py(value, &longval, &err) and not err: + 376 self.set_from_long(longval) + +File /ext/sage/9.7/src/sage/rings/rational.pyx:2825, in sage.rings.rational.Rational.__mod__() + 2823 n = rat.numer() % other + 2824 d = rat.denom() % other +-> 2825 d = d.inverse_mod(other) + 2826 return (n * d) % other + 2827 + +File /ext/sage/9.7/src/sage/rings/integer.pyx:6774, in sage.rings.integer.Integer.inverse_mod() + 6772 sig_off() + 6773 if r == 0: +-> 6774 raise ZeroDivisionError(f"inverse of Mod({self}, {m}) does not exist") + 6775 return ans + 6776 + +ZeroDivisionError: inverse of Mod(0, 3) does not exist +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int().diffn() == om.form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = g.diffn().regular_[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsage: om = ((2*C.x^74 + C.x^73 + C.x^71 + 2*C.x^70 + 2*C.x^65 + C.x^64 + C.x^62 + 2*C.x^61 + 2*C.x^56 + C.x^55 + C.x^53 + 2*C.x^52 + C.x^50 + 2*C.x^49 + 2*C.x^47 + +....:  C.x^46 + C.x^44 + 2*C.x^43 + 2*C.x^38 + C.x^37 + C.x^32 + 2*C.x^31 + 2*C.x^29 + C.x^28 + C.x^26 + 2*C.x^25 + C.x^23 + 2*C.x^22 + 2*C.x^17 + C.x^16 + C.x^14   +....: + 2*C.x^13 + 2*C.x^8 + C.x^7 + C.x^5 + 2*C.x^4 + 2*C.x^2 + C.x)/(C.x^35 + 2*C.x^34 + 2*C.x^32 + C.x^31 + C.x^27 + 2*C.x^25 + 2*C.x^24 + C.x^22 + C.x^19 + C. x +....: ^16 + C.x^13 + 2*C.x^11 + 2*C.x^10 + C.x^8 + C.x^4 + 2*C.x^3 + 2*C.x + C.one))*C.y[?7h[?12l[?25h[?25l[?7lC.y/C.x).diffn() +  +  + [?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[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: om = (C.x^2 + C.one)/C.y * C.dx +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + [?7h[?12l[?25h[?25l[?7lom = (C.x^2 + C.one)/C.y * C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int().diffn() == omform()[?7h[?12l[?25h[?25l[?7lcartier()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.cartier() +[?7h[?12l[?25h[?2004l[?7h(x/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.cartier()[?7h[?12l[?25h[?25l[?7l = (C.x^2 + C.one)/C.y * C.dx[?7h[?12l[?25h[?25l[?7lg = C.x^7 *C.y^8 + 2*C.xC.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om) +[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy +result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x +(superelliptic_function(C, numerator)*C.dx).cartier() 1 dx +W 0 +numerator x^6 + x^4 + x^2 + 1 +(superelliptic_function(C, numerator)*C.dx).cartier() 1 dx +W 2*x^4 +numerator x^4 + x^2 + 1 +(superelliptic_function(C, numerator)*C.dx).cartier() 1 dx +W 2*x^4 + x^2 +numerator x^2 + 1 +--------------------------------------------------------------------------- +ZeroDivisionError Traceback (most recent call last) +Input In [43], in () +----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om) + +File :51, in int(self) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 159 print(type(C), C) + 160 print(type(C._element_constructor), C._element_constructor) +--> 161 raise + 162 + 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x) + 1143 """ + 1144 TESTS:: + 1145 + (...) + 1182  True + 1183 """ + 1184 try: +-> 1185 return integer_mod.IntegerMod(self, x) + 1186 except (NotImplementedError, PariError): + 1187 raise TypeError("error coercing to finite field") + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod() + 199 return a + 200 t = modulus.element_class() +--> 201 return t(parent, value) + 202 + 203 + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:374, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__() + 372 z = value + 373 elif isinstance(value, rational.Rational): +--> 374 z = value % self.__modulus.sageInteger + 375 elif integer_check_long_py(value, &longval, &err) and not err: + 376 self.set_from_long(longval) + +File /ext/sage/9.7/src/sage/rings/rational.pyx:2825, in sage.rings.rational.Rational.__mod__() + 2823 n = rat.numer() % other + 2824 d = rat.denom() % other +-> 2825 d = d.inverse_mod(other) + 2826 return (n * d) % other + 2827 + +File /ext/sage/9.7/src/sage/rings/integer.pyx:6774, in sage.rings.integer.Integer.inverse_mod() + 6772 sig_off() + 6773 if r == 0: +-> 6774 raise ZeroDivisionError(f"inverse of Mod({self}, {m}) does not exist") + 6775 return ans + 6776 + +ZeroDivisionError: inverse of Mod(0, 3) does not exist +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om) +[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy +result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x +(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx +W 0 +numerator x^6 + x^4 + x^2 + 1 +(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx +W 2*x^4 +numerator x^4 + x^2 + 1 +(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() (x/y) dx +W 2*x^4 + x^2 +numerator x^2 + 1 +--------------------------------------------------------------------------- +ZeroDivisionError Traceback (most recent call last) +Input In [45], in () +----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om) + +File :51, in int(self) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 159 print(type(C), C) + 160 print(type(C._element_constructor), C._element_constructor) +--> 161 raise + 162 + 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x) + 1143 """ + 1144 TESTS:: + 1145 + (...) + 1182  True + 1183 """ + 1184 try: +-> 1185 return integer_mod.IntegerMod(self, x) + 1186 except (NotImplementedError, PariError): + 1187 raise TypeError("error coercing to finite field") + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod() + 199 return a + 200 t = modulus.element_class() +--> 201 return t(parent, value) + 202 + 203 + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:374, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__() + 372 z = value + 373 elif isinstance(value, rational.Rational): +--> 374 z = value % self.__modulus.sageInteger + 375 elif integer_check_long_py(value, &longval, &err) and not err: + 376 self.set_from_long(longval) + +File /ext/sage/9.7/src/sage/rings/rational.pyx:2825, in sage.rings.rational.Rational.__mod__() + 2823 n = rat.numer() % other + 2824 d = rat.denom() % other +-> 2825 d = d.inverse_mod(other) + 2826 return (n * d) % other + 2827 + +File /ext/sage/9.7/src/sage/rings/integer.pyx:6774, in sage.rings.integer.Integer.inverse_mod() + 6772 sig_off() + 6773 if r == 0: +-> 6774 raise ZeroDivisionError(f"inverse of Mod({self}, {m}) does not exist") + 6775 return ans + 6776 + +ZeroDivisionError: inverse of Mod(0, 3) does not exist +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om) +[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy +result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x +(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx +W 0 +numerator x^6 + x^4 + x^2 + 1 +2*f*W.derivative() + W*f.derivative(), numerator x^6 x^6 + x^4 + x^2 + 1 +(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx +W 2*x^4 +numerator x^4 + x^2 + 1 +2*f*W.derivative() + W*f.derivative(), numerator x^6 + x^4 + x^2 x^4 + x^2 + 1 +(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() (x/y) dx +W 2*x^4 + x^2 +numerator x^2 + 1 +--------------------------------------------------------------------------- +ZeroDivisionError Traceback (most recent call last) +Input In [47], in () +----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om) + +File :51, in int(self) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 159 print(type(C), C) + 160 print(type(C._element_constructor), C._element_constructor) +--> 161 raise + 162 + 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x) + 1143 """ + 1144 TESTS:: + 1145 + (...) + 1182  True + 1183 """ + 1184 try: +-> 1185 return integer_mod.IntegerMod(self, x) + 1186 except (NotImplementedError, PariError): + 1187 raise TypeError("error coercing to finite field") + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod() + 199 return a + 200 t = modulus.element_class() +--> 201 return t(parent, value) + 202 + 203 + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:374, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__() + 372 z = value + 373 elif isinstance(value, rational.Rational): +--> 374 z = value % self.__modulus.sageInteger + 375 elif integer_check_long_py(value, &longval, &err) and not err: + 376 self.set_from_long(longval) + +File /ext/sage/9.7/src/sage/rings/rational.pyx:2825, in sage.rings.rational.Rational.__mod__() + 2823 n = rat.numer() % other + 2824 d = rat.denom() % other +-> 2825 d = d.inverse_mod(other) + 2826 return (n * d) % other + 2827 + +File /ext/sage/9.7/src/sage/rings/integer.pyx:6774, in sage.rings.integer.Integer.inverse_mod() + 6772 sig_off() + 6773 if r == 0: +-> 6774 raise ZeroDivisionError(f"inverse of Mod({self}, {m}) does not exist") + 6775 return ans + 6776 + +ZeroDivisionError: inverse of Mod(0, 3) does not exist +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om) +[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy +result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x +(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx +W 0 +numerator x^6 + x^4 + x^2 + 1 +2*f*W.derivative() + W*f.derivative(), numerator x^6 x^6 + x^4 + x^2 + 1 +(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx +W 2*x^4 +numerator x^4 + x^2 + 1 +2*f*W.derivative() + W*f.derivative(), numerator x^6 + x^4 + x^2 x^4 + x^2 + 1 +(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx +W 2*x^4 + x^2 +numerator 1 +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [49], in () +----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om) + +File :52, in int(self) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 159 print(type(C), C) + 160 print(type(C._element_constructor), C._element_constructor) +--> 161 raise + 162 + 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:456, in PolynomialRing_general._element_constructor_(self, x, check, is_gen, construct, **kwds) + 454 x = x.numerator() * x.denominator().inverse_of_unit() + 455 else: +--> 456 raise TypeError("denominator must be a unit") + 457 elif isinstance(x, pari_gen): + 458 if x.type() == 't_RFRAC': + +TypeError: denominator must be a unit +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om) +[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy +result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x +(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx +W 0 +numerator x^6 + x^4 + x^2 + 1 +W_coeff 2 +2*f*W.derivative() + W*f.derivative(), numerator x^6 x^6 + x^4 + x^2 + 1 +(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx +W 2*x^4 +numerator x^4 + x^2 + 1 +W_coeff 1 +2*f*W.derivative() + W*f.derivative(), numerator x^6 + x^4 + x^2 x^4 + x^2 + 1 +(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx +W 2*x^4 + x^2 +numerator 1 +W_coeff 2 +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [51], in () +----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om) + +File :53, in int(self) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 159 print(type(C), C) + 160 print(type(C._element_constructor), C._element_constructor) +--> 161 raise + 162 + 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:456, in PolynomialRing_general._element_constructor_(self, x, check, is_gen, construct, **kwds) + 454 x = x.numerator() * x.denominator().inverse_of_unit() + 455 else: +--> 456 raise TypeError("denominator must be a unit") + 457 elif isinstance(x, pari_gen): + 458 if x.type() == 't_RFRAC': + +TypeError: denominator must be a unit +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om) +[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy +result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x +(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx +W 0 +numerator x^6 + x^4 + x^2 + 1 +a 4 +2*f*W.derivative() + W*f.derivative(), numerator x^6 x^6 + x^4 + x^2 + 1 +(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx +W 2*x^4 +numerator x^4 + x^2 + 1 +a 2 +2*f*W.derivative() + W*f.derivative(), numerator x^6 + x^4 + x^2 x^4 + x^2 + 1 +(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx +W 2*x^4 + x^2 +numerator 1 +a -2 +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [53], in () +----> 1 g = C.x**Integer(7) * C.y**Integer(8) + Integer(2)*C.x*C.y**Integer(3) - C.x - C.y; om = g.diffn().regular_form().int(); print(om) + +File :53, in int(self) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 159 print(type(C), C) + 160 print(type(C._element_constructor), C._element_constructor) +--> 161 raise + 162 + 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:456, in PolynomialRing_general._element_constructor_(self, x, check, is_gen, construct, **kwds) + 454 x = x.numerator() * x.denominator().inverse_of_unit() + 455 else: +--> 456 raise TypeError("denominator must be a unit") + 457 elif isinstance(x, pari_gen): + 458 if x.type() == 't_RFRAC': + +TypeError: denominator must be a unit +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om) +[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy +result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x +(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx +W 0 +numerator x^6 + x^4 + x^2 + 1 +a 4 +2*f*W.derivative() + W*f.derivative(), numerator x^6 x^6 + x^4 + x^2 + 1 +(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx +W 2*x^4 +numerator x^4 + x^2 + 1 +a 2 +2*f*W.derivative() + W*f.derivative(), numerator x^6 + x^4 + x^2 x^4 + x^2 + 1 +(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx +W 2*x^4 + x^2 +numerator 1 +(2*x^4 + x^2 + 2)*y + x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om +[?7h[?12l[?25h[?2004l[?7h(2*x^4 + x^2 + 2)*y + x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.cartier()[?7h[?12l[?25h[?25l[?7lint().diffn() == om.form()[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lregular_form().int()[?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_form().int()[?7h[?12l[?25h[?25l[?7lsage: om.regular_form().int() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [57], in () +----> 1 om.regular_form().int() + +AttributeError: 'superelliptic_function' object has no attribute 'regular_form' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form().int()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form().int(); print(om)[?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[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form().int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lint().difn() == om.form()[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ldiffn() == om.form()[?7h[?12l[?25h[?25l[?7lsage: om.int().diffn() == om.form() +[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy +result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x +(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx +W 0 +numerator x^6 + x^4 + x^2 + 1 +a 4 +2*f*W.derivative() + W*f.derivative(), numerator x^6 x^6 + x^4 + x^2 + 1 +(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx +W 2*x^4 +numerator x^4 + x^2 + 1 +a 2 +2*f*W.derivative() + W*f.derivative(), numerator x^6 + x^4 + x^2 x^4 + x^2 + 1 +(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx +W 2*x^4 + x^2 +numerator 1 +[?7hTrue +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int().diffn() == om.form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int() +[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy +result przed x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x +(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx +W 0 +numerator x^6 + x^4 + x^2 + 1 +a 4 +2*f*W.derivative() + W*f.derivative(), numerator x^6 x^6 + x^4 + x^2 + 1 +(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx +W 2*x^4 +numerator x^4 + x^2 + 1 +a 2 +2*f*W.derivative() + W*f.derivative(), numerator x^6 + x^4 + x^2 x^4 + x^2 + 1 +(superelliptic_function(C, numerator)*(C.y)^(-1)*C.dx).cartier() 0 dx +W 2*x^4 + x^2 +numerator 1 +[?7h(2*x^4 + x^2 + 2)*y + x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l().diffn() == om.form()[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 +2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form()[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lint()[?7h[?12l[?25h[?25l[?7lsage: om.int() +[?7h[?12l[?25h[?2004l[?7h(2*x^4 + x^2 + 2)*y + x^19 + 2*x^17 + 2*x^13 + x^11 + 2*x +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l().diffn() == om.form()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l() == om.form()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l om.form()[?7h[?12l[?25h[?25l[?7lsage: om.int().diffn() == om.form() +[?7h[?12l[?25h[?2004l[?7hTrue +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int().diffn() == om.form()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgom.int()[?7h[?12l[?25h[?25l[?7l om.int()[?7h[?12l[?25h[?25l[?7l-om.int()[?7h[?12l[?25h[?25l[?7l om.int()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g - om.int() +[?7h[?12l[?25h[?2004l[?7h0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2) +....: sage: B = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystaline_cohomology_basis(prec = 10); autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lB = C.crystaline_cohomology_basis(prec = 10); autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lB = C.crystaline_cohomology_basis(prec = 10); autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lB = C.crystaline_cohomology_basis(prec = 10); autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lB = C.crystaline_cohomology_basis(prec = 10); autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lB = C.crystaline_cohomology_basis(prec = 10); autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2) +....: B = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B) +[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y]) +result.omega8 == compare True +result.omega8 - compare 0 +omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y]) +result.omega8 == compare True +result.omega8 - compare 0 +omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y]) +result.omega8 == compare True +result.omega8 - compare 0 +omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y]) +result.omega8 == compare True +result.omega8 - compare 0 +omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y]) +result.omega8 == compare True +result.omega8 - compare 0 +omega0_lift, omega8_lift [(2*x^5/(x^8 + 2))*y] d[x] + V(((-x^27 - x^19)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]) 0 +result.omega8 == compare True +result.omega8 - compare 0 +omega0_lift, omega8_lift 0 [(1/(x^12 + 2*x^4))*y] d[x] + V(((x^8 + 1)/(x^24*y - x^16*y)) dx) + dV([(1/(x^32 + 2*x^24))*y]) +result.omega8 == compare True +result.omega8 - compare 0 +omega0_lift, omega8_lift [(x^3/(x^8 + 2))*y] d[x] + V(((-x^29 - x^21 + x^13)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]) [(2/(x^13 + 2*x^5))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^35*y - x^27*y)) dx) + dV([(2/(x^35 + 2*x^27))*y]) +result.omega8 == compare True +result.omega8 - compare 0 +(1, 0, 0, 1, 0, 0, 0, 0) +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [66], in () + 1 C = superelliptic((x**Integer(3) - x)**Integer(3) + x**Integer(3) - x, Integer(2)) +----> 2 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(3)]).coordinates(basis=B) + +File :107, in coordinates(self, basis) + +File :94, in div_by_p(self) + +ValueError: ('aux.omega0.h2.function not in Rxy:', ((2*x^74 + x^73 + x^71 + 2*x^70 + 2*x^65 + x^64 + x^62 + 2*x^61 + 2*x^56 + x^55 + x^53 + 2*x^52 + x^50 + 2*x^49 + 2*x^47 + x^46 + x^44 + 2*x^43 + 2*x^38 + x^37 + x^32 + 2*x^31 + 2*x^29 + x^28 + x^26 + 2*x^25 + x^23 + 2*x^22 + 2*x^17 + x^16 + x^14 + 2*x^13 + 2*x^8 + x^7 + x^5 + 2*x^4 + 2*x^2 + x)/(x^35 + 2*x^34 + 2*x^32 + x^31 + x^27 + 2*x^25 + 2*x^24 + x^22 + x^19 + x^16 + x^13 + 2*x^11 + 2*x^10 + x^8 + x^4 + 2*x^3 + 2*x + 1))*y) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.coordinates()[?7h[?12l[?25h[?25l[?7lfff.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = ((C.x^2 + 2*C.x + C.one)/(C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsage: ff = ((2*C.x^74 + C.x^73 + C.x^71 + 2*C.x^70 + 2*C.x^65 + C.x^64 + C.x^62 + 2*C.x^61 + 2*C.x^56 + C.x^55 + C.x^53 + 2*C.x^52 + C.x^50 + 2*C.x^49 + 2*C.x^47 + +....:  C.x^46 + C.x^44 + 2*C.x^43 + 2*C.x^38 + C.x^37 + C.x^32 + 2*C.x^31 + 2*C.x^29 + C.x^28 + C.x^26 + 2*C.x^25 + C.x^23 + 2*C.x^22 + 2*C.x^17 + C.x^16 + C.x^14 +....: + 2*C.x^13 + 2*C.x^8 + C.x^7 + C.x^5 + 2*C.x^4 + 2*C.x^2 + C.x)/(C.x^35 + 2*C.x^34 + 2*C.x^32 + C.x^31 + C.x^27 + 2*C.x^25 + 2*C.x^24 + C.x^22 + C.x^19 + C. x +....: ^16 + C.x^13 + 2*C.x^11 + 2*C.x^10 + C.x^8 + C.x^4 + 2*C.x^3 + 2*C.x + C.one))*C.y[?7h[?12l[?25h[?25l[?7lsage: ff = ((2*C.x^74 + C.x^73 + C.x^71 + 2*C.x^70 + 2*C.x^65 + C.x^64 + C.x^62 + 2*C.x^61 + 2*C.x^56 + C.x^55 + C.x^53 + 2*C.x^52 + C.x^50 + 2*C.x^49 + 2*C.x^47 + +....:  C.x^46 + C.x^44 + 2*C.x^43 + 2*C.x^38 + C.x^37 + C.x^32 + 2*C.x^31 + 2*C.x^29 + C.x^28 + C.x^26 + 2*C.x^25 + C.x^23 + 2*C.x^22 + 2*C.x^17 + C.x^16 + C.x^14 +....: + 2*C.x^13 + 2*C.x^8 + C.x^7 + C.x^5 + 2*C.x^4 + 2*C.x^2 + C.x)/(C.x^35 + 2*C.x^34 + 2*C.x^32 + C.x^31 + C.x^27 + 2*C.x^25 + 2*C.x^24 + C.x^22 + C.x^19 + C. x +....: ^16 + C.x^13 + 2*C.x^11 + 2*C.x^10 + C.x^8 + C.x^4 + 2*C.x^3 + 2*C.x + C.one))*C.y +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ff = ((2*C.x^74 + C.x^73 + C.x^71 + 2*C.x^70 + 2*C.x^65 + C.x^64 + C.x^62 + 2*C.x^61 + 2*C.x^56 + C.x^55 + C.x^53 + 2*C.x^52 + C.x^50 + 2*C.x^49 + 2*C.x^47 + +....:  C.x^46 + C.x^44 + 2*C.x^43 + 2*C.x^38 + C.x^37 + C.x^32 + 2*C.x^31 + 2*C.x^29 + C.x^28 + C.x^26 + 2*C.x^25 + C.x^23 + 2*C.x^22 + 2*C.x^17 + C.x^16 + C.x^14   +....: + 2*C.x^13 + 2*C.x^8 + C.x^7 + C.x^5 + 2*C.x^4 + 2*C.x^2 + C.x)/(C.x^35 + 2*C.x^34 + 2*C.x^32 + C.x^31 + C.x^27 + 2*C.x^25 + 2*C.x^24 + C.x^22 + C.x^19 + C. x +....: ^16 + C.x^13 + 2*C.x^11 + 2*C.x^10 + C.x^8 + C.x^4 + 2*C.x^3 + 2*C.x + C.one))*C.y[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.diffn() +  +  + [?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7lsage: ff.diffn() +[?7h[?12l[?25h[?2004l[?7h0 dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + [?7h[?12l[?25h[?25l[?7lff.diffn()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ff.pth_root() +[?7h[?12l[?25h[?2004l[?7h((2*x^24 + x^23 + 2*x^21 + x^20 + 2*x^18 + x^17 + x^16 + 2*x^15 + x^14 + 2*x^12 + x^10 + 2*x^9 + x^8 + x^7 + 2*x^5 + x^4 + 2*x^2 + x + 2)/(x^14 + 2*x^13 + x^11 + 2*x^10 + x^8 + 2*x^7 + x^6 + 2*x^4 + x^3 + 2*x + 1))*y +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(xi.f)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: decomposition + decomposition decomposition_g0_g8_pth_power + decomposition_g0_g8 decomposition_omega0_omega8  + + + [?7h[?12l[?25h[?25l[?7l_g0_g8(xi.f)[?7h[?12l[?25h[?25l[?7l + decomposition  + + [?7h[?12l[?25h[?25l[?7l_g0_g8_pth_power + decomposition  decomposition_g0_g8_pth_power[?7h[?12l[?25h[?25l[?7lomea0_omega8 + decomposition_g0_g8_pth_power + decomposition_omega0_omega8 [?7h[?12l[?25h[?25l[?7lg0_8 + + decomposition_g0_g8  decomposition_omega0_omega8 [?7h[?12l[?25h[?25l[?7l + decomposition  + decomposition_g0_g8 [?7h[?12l[?25h[?25l[?7l + + +[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lff.pth_root()[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7l = ((2*C.x^74 + C.x^73 + C.x^71 + 2*C.x^70 + 2*C.x^65 + C.x^64 + C.x^62 + 2*C.x^61 + 2*C.x^56 + C.x^55 + C.x^53 + 2*C.x^52 + C.x^50 + 2*C.x^49 + 2*C.x^47 + +....:  C.x^46 + C.x^44 + 2*C.x^43 + 2*C.x^38 + C.x^37 + C.x^32 + 2*C.x^31 + 2*C.x^29 + C.x^28 + C.x^26 + 2*C.x^25 + C.x^23 + 2*C.x^22 + 2*C.x^17 + C.x^16 + C.x^14 +....: + 2*C.x^13 + 2*C.x^8 + C.x^7 + C.x^5 + 2*C.x^4 + 2*C.x^2 + C.x)/(C.x^35 + 2*C.x^34 + 2*C.x^32 + C.x^31 + C.x^27 + 2*C.x^25 + 2*C.x^24 + C.x^22 + C.x^19 + C. x +....: ^16 + C.x^13 + 2*C.x^11 + 2*C.x^10 + C.x^8 + C.x^4 + 2*C.x^3 + 2*C.x + C.one))*C.y[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 -x)^3 + x^3- x, 2) +B = C.crystalline_cohomology_basis(prec = 100);autom(B[3]).coordinates(basis=B) +  + [?7h[?12l[?25h[?25l[?7l() +()[?7h[?12l[?25h[?25l[?7l() + +....: B = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7l() +B = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B) + [?7h[?12l[?25h[?25l[?7l() +[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2) +....: B = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B) +[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y]) +result.omega8 == compare True +result.omega8 - compare 0 +omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y]) +result.omega8 == compare True +result.omega8 - compare 0 +omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y]) +result.omega8 == compare True +result.omega8 - compare 0 +omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y]) +result.omega8 == compare True +result.omega8 - compare 0 +omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y]) +result.omega8 == compare True +result.omega8 - compare 0 +omega0_lift, omega8_lift [(2*x^5/(x^8 + 2))*y] d[x] + V(((-x^27 - x^19)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]) 0 +result.omega8 == compare True +result.omega8 - compare 0 +omega0_lift, omega8_lift 0 [(1/(x^12 + 2*x^4))*y] d[x] + V(((x^8 + 1)/(x^24*y - x^16*y)) dx) + dV([(1/(x^32 + 2*x^24))*y]) +result.omega8 == compare True +result.omega8 - compare 0 +omega0_lift, omega8_lift [(x^3/(x^8 + 2))*y] d[x] + V(((-x^29 - x^21 + x^13)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]) [(2/(x^13 + 2*x^5))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^35*y - x^27*y)) dx) + dV([(2/(x^35 + 2*x^27))*y]) +result.omega8 == compare True +result.omega8 - compare 0 +(1, 0, 0, 1, 0, 0, 0, 0) +h2 ((2*x^74 + x^73 + x^71 + 2*x^70 + 2*x^65 + x^64 + x^62 + 2*x^61 + 2*x^56 + x^55 + x^53 + 2*x^52 + x^50 + 2*x^49 + 2*x^47 + x^46 + x^44 + 2*x^43 + 2*x^38 + x^37 + x^32 + 2*x^31 + 2*x^29 + x^28 + x^26 + 2*x^25 + x^23 + 2*x^22 + 2*x^17 + x^16 + x^14 + 2*x^13 + 2*x^8 + x^7 + x^5 + 2*x^4 + 2*x^2 + x)/(x^35 + 2*x^34 + 2*x^32 + x^31 + x^27 + 2*x^25 + 2*x^24 + x^22 + x^19 + x^16 + x^13 + 2*x^11 + 2*x^10 + x^8 + x^4 + 2*x^3 + 2*x + 1))*y +aux (V(((x^63 - x^55 - x^39 - x^36 + x^31 + x^28 + x^12 - x^4)/y) dx), V(((x^53 + x^52 + 2*x^50 + 2*x^49 + x^47 + x^46 + 2*x^44 + 2*x^43 + x^41 + x^40 + 2*x^38 + 2*x^37 + x^35 + x^34 + 2*x^32 + 2*x^31 + x^29 + x^28 + x^26 + x^25 + x^23 + x^22 + 2*x^20 + 2*x^19 + x^17 + x^16 + x^14 + x^13 + 2*x^11 + 2*x^10 + x^8 + x^7 + 2*x^5 + 2*x^4 + 2*x^2 + 2*x)/(x^14 + x^13 + 2*x^11 + 2*x^10 + x^8 + x^7 + x^6 + 2*x^4 + 2*x^3 + x + 1))*y), V(((-x^16 - x^14 - x^13 - x^11 - x^10 - x^8 + x^7 - x^5 - x^4 - x^3 + x - 1)/(x^15*y + x^14*y - x^12*y - x^11*y + x^9*y + x^8*y + x^7*y - x^5*y - x^4*y + x^2*y + x*y)) dx)) +aux_divided_by_p (((x^18 - x^10 - x^9 + x)/y) dx, ((x^17 + 2*x^16 + x^15 + 2*x^14 + x^13 + 2*x^12 + x^11 + 2*x^10 + x^9 + x^8 + x^7 + 2*x^6 + x^5 + x^4 + 2*x^3 + x^2 + 2*x + 2)/(x^7 + 2*x^6 + x^5 + 2*x^4 + x^3 + 2*x^2 + x + 2))*y, ((x^9 - x^4 + x^3 - x^2 + x + 1)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx) +is regular True True +aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True +[?7h[4, 3, 3, 1, 0, 0, 3, 0] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2) +....: B = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l()autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l(autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lutom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lutom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lautom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l()autom(B[3]).coordinates(basis=B) 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autom(B[4]).coordinates(basis=B) +[?7h[?12l[?25h[?2004l(1, 1, 0, 2, 1, 2, 1, 2) +h2 ((2*x^69 + x^67 + x^63 + 2*x^61 + x^48 + 2*x^46 + x^45 + 2*x^43 + 2*x^42 + x^40 + 2*x^39 + x^37 + x^33 + 2*x^31 + x^30 + 2*x^28 + x^27 + 2*x^25 + 2*x^21 + x^19 + 2*x^18 + x^16 + x^15 + 2*x^13 + x^12 + 2*x^10 + x^9 + 2*x^7 + x^3 + 2*x)/(x^30 + 2*x^28 + 2*x^24 + 2*x^22 + 2*x^20 + 2*x^16 + 2*x^14 + 2*x^10 + 2*x^8 + 2*x^6 + 2*x^2 + 1))*y +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [72], in () +----> 1 autom(B[Integer(4)]).coordinates(basis=B) + +File :114, in coordinates(self, basis) + +File :99, in div_by_p(self) + +ValueError: ('aux.omega8.h2.expansion_at_infty().valuation() < 0:', 2*t^-15 + t^-3 + 2*t + 2*t^3 + O(t^5)) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lautom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2) +....: B = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l4]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2) +....: B = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B) +[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y]) +result.omega8 == compare True +result.omega8 - compare 0 +omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y]) +result.omega8 == compare True +result.omega8 - compare 0 +omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y]) +result.omega8 == compare True +result.omega8 - compare 0 +omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y]) +result.omega8 == compare True +result.omega8 - compare 0 +omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y]) +result.omega8 == compare True +result.omega8 - compare 0 +omega0_lift, omega8_lift [(2*x^5/(x^8 + 2))*y] d[x] + V(((-x^27 - x^19)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]) 0 +result.omega8 == compare True +result.omega8 - compare 0 +omega0_lift, omega8_lift 0 [(1/(x^12 + 2*x^4))*y] d[x] + V(((x^8 + 1)/(x^24*y - x^16*y)) dx) + dV([(1/(x^32 + 2*x^24))*y]) +result.omega8 == compare True +result.omega8 - compare 0 +omega0_lift, omega8_lift [(x^3/(x^8 + 2))*y] d[x] + V(((-x^29 - x^21 + x^13)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]) [(2/(x^13 + 2*x^5))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^35*y - x^27*y)) dx) + dV([(2/(x^35 + 2*x^27))*y]) +result.omega8 == compare True +result.omega8 - compare 0 +(1, 1, 0, 2, 1, 2, 1, 2) +h2 ((2*x^69 + x^67 + x^63 + 2*x^61 + x^48 + 2*x^46 + x^45 + 2*x^43 + 2*x^42 + x^40 + 2*x^39 + x^37 + x^33 + 2*x^31 + x^30 + 2*x^28 + x^27 + 2*x^25 + 2*x^21 + x^19 + 2*x^18 + x^16 + x^15 + 2*x^13 + x^12 + 2*x^10 + x^9 + 2*x^7 + x^3 + 2*x)/(x^30 + 2*x^28 + 2*x^24 + 2*x^22 + 2*x^20 + 2*x^16 + 2*x^14 + 2*x^10 + 2*x^8 + 2*x^6 + 2*x^2 + 1))*y +aux.omega8.h2 ((2*x^30 + x^24 + 2*x^21 + 2*x^18 + x^17 + x^16 + x^15 + x^14 + 2*x^12 + 2*x^11 + x^10 + 2*x^9 + 2*x^8 + x^7 + x^6 + 2*x^5 + 2*x^4 + 2*x^2 + 2*x + 1)/(x^27 + x^19 + x^11))*y +second_patch(aux.omega8.h2.diffn()).is_regular_on_U0() False +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [74], in () + 1 C = superelliptic((x**Integer(3) - x)**Integer(3) + x**Integer(3) - x, Integer(2)) +----> 2 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(4)]).coordinates(basis=B) + +File :116, in coordinates(self, basis) + +File :101, in div_by_p(self) + +ValueError: ('aux.omega8.h2.expansion_at_infty().valuation() < 0:', 2*t^-15 + t^-3 + 2*t + 2*t^3 + O(t^5)) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.nb_of_pts_at_nfty[?7h[?12l[?25h[?25l[?7lx.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-2 + t^14 + O(t^18) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lyx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.y.expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-9 + 2*t^7 + O(t^11) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu = C.one/C.x[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l C.one/C.x[?7h[?12l[?25h[?25l[?7lsage: u = C.one/C.x +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg - om.int()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y; om = g.diffn().regular_form()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g = C.genus() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv = C.y/(C.x)^2[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.y/(C.x)^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()_[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: v = C.y/(C.x)^(g+1) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu = C.one/C.x[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: u.expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^2 + 2*t^18 + O(t^22) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv = C.y/(C.x)^(g+1)[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: v.expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht + O(t^21) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((2*C.x^30 + C.x^24 + 2*C.x^21 + 2*C.x^18 + C.x^17 + C.x^16 + C.x^15 + C.x^14 + 2*C.x^12 + 2*C.x^11 + C.x^10 + 2*C.x^9 + 2*C.x^8 + C.x^7 + C.x^6 + 2*C.x^5 + +....: 2*C.x^4 + 2*C.x^2 + 2*C.x + 1)/(C.x^27 + C.x^19 + C.x^11))*C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l( +)[?7h[?12l[?25h[?25l[?7l( +)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l( +)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg((2*C.x^30 + C.x^24 + 2*C.x^21 + 2*C.x^18 + C.x^17 + C.x^16 + C.x^15 + C.x^14 + 2*C.x^12 + 2*C.x^1 + C.x^10 + 2*C.x^9 + 2*C.x^8 + C.x^7 + C.x^6 + 2*C.x^5 + + 2*C.x^4 + 2*C.x^2 + 2*C.x + 1)/(C.x^27 + C.x^19 + C.x^1))*C.y[?7h[?12l[?25h[?25l[?7lg((2*C.x^30 + C.x^24 + 2*C.x^21 + 2*C.x^18 + C.x^17 + C.x^16 + C.x^15 + C.x^14 + 2*C.x^12 + 2*C.x^1 + C.x^10 + 2*C.x^9 + 2*C.x^8 + C.x^7 + C.x^6 + 2*C.x^5  ++ 2*C.x^4 + 2*C.x^2 + 2*C.x + 1)/(C.x^27 + C.x^19 + C.x^1))*C.y[?7h[?12l[?25h[?25l[?7l ((2*C.x^30 + C.x^24 + 2*C.x^21 + 2*C.x^18 + C.x^17 + C.x^16 + C.x^15 + C.x^14 + 2*C.x^12 + 2*C.x^1 + C.x^10 + 2*C.x^9 + 2*C.x^8 + C.x^7 + C.x^6 + 2*C.x^ 5 + + 2*C.x^4 + 2*C.x^2 + 2*C.x + 1)/(C.x^27 + C.x^19 + C.x^1))*C.y[?7h[?12l[?25h[?25l[?7l=((2*C.x^30 + C.x^24 + 2*C.x^21 + 2*C.x^18 + C.x^17 + C.x^16 + C.x^15 + C.x^14 + 2*C.x^12 + 2*C.x^1 + C.x^10 + 2*C.x^9 + 2*C.x^8 + C.x^7 + C.x^6 + 2*C.x ^ +5 + 2*C.x^4 + 2*C.x^2 + 2*C.x + 1)/(C.x^27 + C.x^19 + C.x^1))*C.y[?7h[?12l[?25h[?25l[?7l ((2*C.x^30 + C.x^24 + 2*C.x^21 + 2*C.x^18 + C.x^17 + C.x^16 + C.x^15 + C.x^14 + 2*C.x^12 + 2*C.x^1 + C.x^10 + 2*C.x^9 + 2*C.x^8 + C.x^7 + C.x^6 + 2*C. x +^5 + 2*C.x^4 + 2*C.x^2 + 2*C.x + 1)/(C.x^27 + C.x^19 + C.x^1))*C.y[?7h[?12l[?25h[?25l[?7lsage: gg = ((2*C.x^30 + C.x^24 + 2*C.x^21 + 2*C.x^18 + C.x^17 + C.x^16 + C.x^15 + C.x^14 + 2*C.x^12 + 2*C.x^11 + C.x^10 + 2*C.x^9 + 2*C.x^8 + C.x^7 + C.x^6 + 2*C. x +....: ^5 + 2*C.x^4 + 2*C.x^2 + 2*C.x + 1)/(C.x^27 + C.x^19 + C.x^11))*C.y +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [82], in () +----> 1 gg = ((Integer(2)*C.x**Integer(30) + C.x**Integer(24) + Integer(2)*C.x**Integer(21) + Integer(2)*C.x**Integer(18) + C.x**Integer(17) + C.x**Integer(16) + C.x**Integer(15) + C.x**Integer(14) + Integer(2)*C.x**Integer(12) + Integer(2)*C.x**Integer(11) + C.x**Integer(10) + Integer(2)*C.x**Integer(9) + Integer(2)*C.x**Integer(8) + C.x**Integer(7) + C.x**Integer(6) + Integer(2)*C.x**Integer(5) + Integer(2)*C.x**Integer(4) + Integer(2)*C.x**Integer(2) + Integer(2)*C.x + Integer(1))/(C.x**Integer(27) + C.x**Integer(19) + C.x**Integer(11)))*C.y + +File :38, in __add__(self, other) + +File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() + 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' + 493 """ +--> 494 return self.getattr_from_category(name) + 495 + 496 cdef getattr_from_category(self, name): + +File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() + 505 else: + 506 cls = P._abstract_element_class +--> 507 return getattr_from_other_class(self, cls, name) + 508 + 509 def __dir__(self): + +File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() + 359 dummy_error_message.cls = type(self) + 360 dummy_error_message.name = name +--> 361 raise AttributeError(dummy_error_message) + 362 attribute = attr + 363 # Check for a descriptor (__get__ in Python) + +AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: gg = ((2*C.x^30 + C.x^24 + 2*C.x^21 + 2*C.x^18 + C.x^17 + C.x^16 + C.x^15 + C.x^14 + 2*C.x^12 + 2*C.x^11 + C.x^10 + 2*C.x^9 + 2*C.x^8 + C.x^7 + C.x^6 + 2*C. x +....: ^5 + 2*C.x^4 + 2*C.x^2 + 2*C.x + 1)/(C.x^27 + C.x^19 + C.x^11))*C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l( +)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l( +())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l( +)()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l( +)[?7h[?12l[?25h[?25l[?7l( +)[?7h[?12l[?25h[?25l[?7l)/(C.x^27 + C.x^19 + C.x^1)*C.y[?7h[?12l[?25h[?25l[?7lC)/(C.x^27 + C.x^19 + C.x^1)*C.y[?7h[?12l[?25h[?25l[?7l.)/(C.x^27 + C.x^19 + C.x^1)*C.y[?7h[?12l[?25h[?25l[?7lon)/(C.x^27+ C.x^19+ C.x^11))*C.y[?7h[?12l[?25h[?25l[?7le)/(C.x^27 + C.x^19 + C.x^1)*C.y[?7h[?12l[?25h[?25l[?7l( +)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: gg = ((2*C.x^30 + C.x^24 + 2*C.x^21 + 2*C.x^18 + C.x^17 + C.x^16 + C.x^15 + C.x^14 + 2*C.x^12 + 2*C.x^11 + C.x^10 + 2*C.x^9 + 2*C.x^8 + C.x^7 + C.x^6 + 2*C. x +....: ^5 + 2*C.x^4 + 2*C.x^2 + 2*C.x + C.one)/(C.x^27 + C.x^19 + C.x^11))*C.y +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.pth_root()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: gg = ((2*C.x^30 + C.x^24 + 2*C.x^21 + 2*C.x^18 + C.x^17 + C.x^16 + C.x^15 + C.x^14 + 2*C.x^12 + 2*C.x^11 + C.x^10 + 2*C.x^9 + 2*C.x^8 + C.x^7 + C.x^6 + 2*C. x +....: ^5 + 2*C.x^4 + 2*C.x^2 + 2*C.x + C.one)/(C.x^27 + C.x^19 + C.x^11))*C.y[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.pth_root() + [?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: gg.expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7h2*t^-15 + t^-3 + 2*t + 2*t^3 + O(t^5) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: gg.diffn().expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7h2*t^10 + t^12 + 2*t^16 + O(t^20) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lgg.iffn().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lexpasion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: gg = ((2*C.x^30 + C.x^24 + 2*C.x^21 + 2*C.x^18 + C.x^17 + C.x^16 + C.x^15 + C.x^14 + 2*C.x^12 + 2*C.x^11 + C.x^10 + 2*C.x^9 + 2*C.x^8 + C.x^7 + C.x^6 + 2*C. x +....: ^5 + 2*C.x^4 + 2*C.x^2 + 2*C.x + C.one)/(C.x^27 + C.x^19 + C.x^11))*C.y[?7h[?12l[?25h[?25l[?7l1)/(C.x^27 + C.x^19 + C.x^11))*C.y[?7h[?12l[?25h[?25l[?7lv.expansion_at_infty() + [?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lv = C.y/(C.x)^(g+1)[?7h[?12l[?25h[?25l[?7lggenus()[?7h[?12l[?25h[?25l[?7luone/C.x[?7h[?12l[?25h[?25l[?7lC.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l = suerelliptic((x^3 - x)^3 + x^3 - x, 2) +....: B = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2) +....: B = C.crystalline_cohomology_basis(prec = 100); autom(B[4]).coordinates(basis=B) +[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^9 + 2*x))*y] d[x] + V(((x^9 + x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]) [(1/(x^9 + 2*x))*y] d[x] + V(((x^8 + 1)/(x^15*y - x^7*y)) dx) + dV([(1/(x^23 + 2*x^15))*y]) +result.omega8 == compare True +result.omega8 - compare 0 +omega0_lift, omega8_lift [(1/(x^8 + 2))*y] d[x] + V(((-x^20 - x^12 + x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]) [(1/(x^8 + 2))*y] d[x] + V(((x^16 + 1)/(x^20*y - x^12*y)) dx) + dV([(1/(x^20 + 2*x^12))*y]) +result.omega8 == compare True +result.omega8 - compare 0 +omega0_lift, omega8_lift [(x/(x^8 + 2))*y] d[x] + V(((x^23 + x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]) [(x/(x^8 + 2))*y] d[x] + V(((x^16 - x^8 - 1)/(x^17*y - x^9*y)) dx) + dV([(1/(x^17 + 2*x^9))*y]) +result.omega8 == compare True +result.omega8 - compare 0 +omega0_lift, omega8_lift [(x^2/(x^8 + 2))*y] d[x] + V(((x^18 + x^10)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]) [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(1/(x^14 + 2*x^6))*y]) +result.omega8 == compare True +result.omega8 - compare 0 +omega0_lift, omega8_lift [(x^6/(x^8 + 2))*y] d[x] + V(((-x^38 - x^30 + x^22)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]) [(2/(x^10 + 2*x^2))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^26*y - x^18*y)) dx) + dV([(2/(x^26 + 2*x^18))*y]) +result.omega8 == compare True +result.omega8 - compare 0 +omega0_lift, omega8_lift [(2*x^5/(x^8 + 2))*y] d[x] + V(((-x^27 - x^19)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]) 0 +result.omega8 == compare True +result.omega8 - compare 0 +omega0_lift, omega8_lift 0 [(1/(x^12 + 2*x^4))*y] d[x] + V(((x^8 + 1)/(x^24*y - x^16*y)) dx) + dV([(1/(x^32 + 2*x^24))*y]) +result.omega8 == compare True +result.omega8 - compare 0 +omega0_lift, omega8_lift [(x^3/(x^8 + 2))*y] d[x] + V(((-x^29 - x^21 + x^13)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]) [(2/(x^13 + 2*x^5))*y] d[x] + V(((-x^16 + x^8 + 1)/(x^35*y - x^27*y)) dx) + dV([(2/(x^35 + 2*x^27))*y]) +result.omega8 == compare True +result.omega8 - compare 0 +(1, 1, 0, 2, 1, 2, 1, 2) +h2 ((2*x^69 + x^67 + x^63 + 2*x^61 + x^48 + 2*x^46 + x^45 + 2*x^43 + 2*x^42 + x^40 + 2*x^39 + x^37 + x^33 + 2*x^31 + x^30 + 2*x^28 + x^27 + 2*x^25 + 2*x^21 + x^19 + 2*x^18 + x^16 + x^15 + 2*x^13 + x^12 + 2*x^10 + x^9 + 2*x^7 + x^3 + 2*x)/(x^30 + 2*x^28 + 2*x^24 + 2*x^22 + 2*x^20 + 2*x^16 + 2*x^14 + 2*x^10 + 2*x^8 + 2*x^6 + 2*x^2 + 1))*y +aux.omega8.omega ((x^28 - x^26 + x^25 - x^24 + x^23 - x^22 - x^21 + x^20 + x^19 + x^18 + x^17 + x^15 - x^14 + x^13 + x^12 + x^11 - x^10 - x^8 - x^7 + x^6 - x^5 + x^4 + x^2 + x - 1)/(x^16*y - x^15*y + x^14*y - x^13*y + x^12*y - x^11*y + x^10*y - x^9*y - x^8*y + x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y)) dx +aux.omega8.h2 ((2*x^30 + x^24 + 2*x^21 + 2*x^18 + x^17 + x^16 + x^15 + x^14 + 2*x^12 + 2*x^11 + x^10 + 2*x^9 + 2*x^8 + x^7 + x^6 + 2*x^5 + 2*x^4 + 2*x^2 + 2*x + 1)/(x^27 + x^19 + x^11))*y +second_patch(aux.omega8.h2.diffn()).is_regular_on_U0() False +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [87], in () + 1 C = superelliptic((x**Integer(3) - x)**Integer(3) + x**Integer(3) - x, Integer(2)) +----> 2 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(4)]).coordinates(basis=B) + +File :117, in coordinates(self, basis) + +File :102, in div_by_p(self) + +ValueError: ('aux.omega8.h2.expansion_at_infty().valuation() < 0:', 2*t^-15 + t^-3 + 2*t + 2*t^3 + O(t^5)) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int().diffn() == om.form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = (C.x^2 + C.one)/Cy * C.dx[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - 1)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C.x^ 9 +....: *C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - 1)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C.x^ 9 +....: *C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [88], in () +----> 1 om = ((C.x**Integer(28) - C.x**Integer(26) + C.x**Integer(25) - C.x**Integer(24) + C.x**Integer(23) - C.x**Integer(22) - C.x**Integer(21) + C.x**Integer(20) + C.x**Integer(19) + C.x**Integer(18) + C.x**Integer(17) + C.x**Integer(15) - C.x**Integer(14) + C.x**Integer(13) + C.x**Integer(12) + C.x**Integer(11) - C.x**Integer(10) - C.x**Integer(8) - C.x**Integer(7) + C.x**Integer(6) - C.x**Integer(5) + C.x**Integer(4) + C.x**Integer(2) + C.x - Integer(1))/(C.x**Integer(16)*C.y - C.x**Integer(15)*C.y + C.x**Integer(14)*C.y - C.x**Integer(13)*C.y + C.x**Integer(12)*C.y - C.x**Integer(11)*C.y + C.x**Integer(10)*C.y - C.x**Integer(9)*C.y - C.x**Integer(8)*C.y + C.x**Integer(7)*C.y - C.x**Integer(6)*C.y + C.x**Integer(5)*C.y - C.x**Integer(4)*C.y + C.x**Integer(3)*C.y - C.x**Integer(2)*C.y + C.x*C.y))*C.dx + +File :50, in __sub__(self, other) + +File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() + 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' + 493 """ +--> 494 return self.getattr_from_category(name) + 495 + 496 cdef getattr_from_category(self, name): + +File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() + 505 else: + 506 cls = P._abstract_element_class +--> 507 return getattr_from_other_class(self, cls, name) + 508 + 509 def __dir__(self): + +File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() + 359 dummy_error_message.cls = type(self) + 360 dummy_error_message.name = name +--> 361 raise AttributeError(dummy_error_message) + 362 attribute = attr + 363 # Check for a descriptor (__get__ in Python) + +AttributeError: 'sage.rings.integer.Integer' object has no attribute 'function' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - 1)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C.x^ 9 +....: *C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 + - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int)diffn() == om.form() +  + [?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion + om.expansion  +  om.expansion_at_infty + + + [?7h[?12l[?25h[?25l[?7l + om.expansion  + + [?7h[?12l[?25h[?25l[?7l_at_infty + om.expansion  + om.expansion_at_infty[?7h[?12l[?25h[?25l[?7l( + + +[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-18 + t^-16 + 2*t^-14 + O(t^-8) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + [?7h[?12l[?25h[?25l[?7lom.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcartier()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.cartier() +[?7h[?12l[?25h[?2004l[?7h((x^13 - x^12 - x^11 - x^10 - x^9 + x^8 - x^5 + x^4 - x^3 - x^2 + x - 1)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + [?7h[?12l[?25h[?25l[?7lom.cartier()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: om.cartier().expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-6 + t^-2 + 1 + t^2 + O(t^4) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: lau = om.cartier().expansion_at_infty() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau = om.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lsage: lau. + lau.O lau.additive_order lau.category lau.common_valuation lau.dump  + lau.V lau.base_extend lau.change_ring lau.degree lau.dumps  + lau.abs lau.base_ring lau.coefficients lau.denominator lau.euclidean_degree > + lau.add_bigoh lau.cartesian_product lau.common_prec lau.derivative lau.exponents  + [?7h[?12l[?25h[?25l[?7lO + lau.O  + + + + [?7h[?12l[?25h[?25l[?7ladditive_order + lau.O  lau.additive_order [?7h[?12l[?25h[?25l[?7lcategory + lau.additive_order  lau.category [?7h[?12l[?25h[?25l[?7lommon_valuation + lau.category  lau.common_valuation [?7h[?12l[?25h[?25l[?7ldup + lau.common_valuation  lau.dump [?7h[?12l[?25h[?25l[?7lfactor + additive_ordercategory ommon_valuationdup factor + base_extendchang_rigdegre umps gcd  +<bae_ringcoefficientsdenomnator eucliden_degreeintegral  + cartesian_productommon_prec derivativ exponents inverse [?7h[?12l[?25h[?25l[?7linverse_of_unit +category ommon_valuationdup factorinverse_of_unit +chang_rigdegre umps gcd is_idempotent +coefficientsdenomnator eucliden_degreeintegral s_monomial +ommon_prec derivativ exponents inverse s_nilpotent[?7h[?12l[?25h[?25l[?7ls_one +ommon_valuationdup factorinverse_of_units_one  +degre umps gcd is_idempotentprie  +denomnator eucliden_degreeintegral s_monomialunit  +derivativ exponents inverse s_nilpotentzero [?7h[?12l[?25h[?25l[?7llaurent_polynomial +dup factorinverse_of_units_one laurent_polynomial +umps gcd is_idempotentprie lcm  +eucliden_degreeintegral s_monomialunit lift_to_precision +exponents inverse s_nilpotentzero list [?7h[?12l[?25h[?25l[?7lmultiplicative_order +factorinverse_of_units_one laurent_polynomialmultiplicative_order +gcd is_idempotentprie lcm n  +integral s_monomialunit lift_to_precisionnth_rot  +inverse s_nilpotentzero list numerator[?7h[?12l[?25h[?25l[?7llaurent_polynomial + lau.laurent_polynomial  lau.multiplicative_order [?7h[?12l[?25h[?25l[?7lmultiplicative_order + lau.laurent_polynomial  lau.multiplicative_order [?7h[?12l[?25h[?25l[?7lnmerical_approx +inverse_of_units_one laurent_polynomialmultiplicative_ordernmerical_approx  +is_idempotentprie lcm n order +s_monomialunit lift_to_precisionnth_rot parent  +s_nilpotentzero list numeratorpow_seies[?7h[?12l[?25h[?25l[?7lpows +s_one laurent_polynomialmultiplicative_ordernmerical_approx pows  +prie lcm n orderpec  +unit lift_to_precisionnth_rot parent recision_absolute +zero list numeratorpow_seiesrecision_relative[?7h[?12l[?25h[?25l[?7lquo_em +laurent_polynomialmultiplicative_ordernmerical_approx pows quo_em +lcm n orderpec radical +lift_to_precisionnth_rot parent recision_absoluterename  +list numeratorpow_seiesrecision_relativereset_name [?7h[?12l[?25h[?25l[?7lresidue +multiplicative_ordernmerical_approx pows quo_emresidue +n orderpec radicaleverse +nth_rot parent recision_absoluterename save  +numeratorpow_seiesrecision_relativereset_name shif [?7h[?12l[?25h[?25l[?7lsquarefree_part +nmerical_approx pows quo_emresiduesquarefree_part +orderpec radicaleversesubs  +parent recision_absoluterename save ubstitute +pow_seiesrecision_relativereset_name shif truncate[?7h[?12l[?25h[?25l[?7ltrncate_laurentseries +pows quo_emresiduesquarefree_parttrncate_laurentseries +pec radicaleversesubs truncate_neg +recision_absoluterename save ubstitutevaluation  +recision_relativereset_name shif truncatevaluation_zero_part[?7h[?12l[?25h[?25l[?7lvariabl +quo_emresiduesquarefree_parttrncate_laurentseriesvariabl   +radicaleversesubs truncate_negvershibun  +rename save ubstitutevaluation xgcd   +reset_name shif truncatevaluation_zero_part  [?7h[?12l[?25h[?25l[?7ltruncat_laurentseries + lau.truncate_laurentseries lau.variable [?7h[?12l[?25h[?25l[?7l + lau.truncate_laurentseries + + + lau.truncate [?7h[?12l[?25h[?25l[?7lshift + + + + lau.shift  lau.truncate [?7h[?12l[?25h[?25l[?7lrese_name + + + + lau.reset_name  lau.shift [?7h[?12l[?25h[?25l[?7lprecision_relative +powes quo_remresidue sqarefree_part truncat_laurentseries  +prec adicalreversesubs trunat_ne  +precision_absoluterenameave substitutevaluation> +precision_relativerese_nameshift truncate  lau.valuation_zero_part  [?7h[?12l[?25h[?25l[?7lower_series +numical_approxpowes quo_remresidue sqarefree_part  +oderprec adicalreversesubs  +arent precision_absoluterenameave substitute +ower_series precision_relativerese_nameshift truncate [?7h[?12l[?25h[?25l[?7lnumato +mltiplicative_ordernumical_approxpowes quo_remresidue  +n oderprec adicalreverse +nth_rootarent precision_absoluterenameave  +numato ower_series precision_relativerese_nameshift [?7h[?12l[?25h[?25l[?7llist +laurent_polynomial mltiplicative_ordernumical_approxpowes quo_rem +lcmn oderprec adical +lift_t_precisionnth_rootarent precision_absoluterename +list numato ower_series precision_relativerese_name[?7h[?12l[?25h[?25l[?7lis_zero +is_one laurent_polynomial mltiplicative_ordernumical_approxpowes  +is_primelcmn oderprec  +is_unit lift_t_precisionnth_rootarent precision_absolute +is_zerolist numato ower_series precision_relative[?7h[?12l[?25h[?25l[?7lnilpotent +nverse_of_unitis_one laurent_polynomial mltiplicative_ordernumical_approx +idepotentis_primelcmn oder +monomialis_unit lift_t_precisionnth_rootarent  +nilpotentis_zerolist numato ower_series [?7h[?12l[?25h[?25l[?7lnverse +factor nverse_of_unitis_one laurent_polynomial mltiplicative_order +gcd idepotentis_primelcmn  +ntegral monomialis_unit lift_t_precisionnth_root +nverse nilpotentis_zerolist numato [?7h[?12l[?25h[?25l[?7lexponents +dump factor nverse_of_unitis_one laurent_polynomial  +dumpsgcd idepotentis_primelcm +euclidean_degreentegral monomialis_unit lift_t_precision +exponentsnverse nilpotentis_zerolist [?7h[?12l[?25h[?25l[?7lderivative +comon_valuationdump factor nverse_of_unitis_one  +egreedumpsgcd idepotentis_prime +denomintor euclidean_degreentegral monomialis_unit  +derivativeexponentsnverse nilpotentis_zero[?7h[?12l[?25h[?25l[?7lcommon_prc +ategory comon_valuationdump factor nverse_of_unit +chang_ringegreedumpsgcd idepotent +coeffcientsdenomintor euclidean_degreentegral monomial +common_prcderivativeexponentsnverse nilpotent[?7h[?12l[?25h[?25l[?7lartesian_product +additive_orderategory comon_valuationdump factor  +base_xtedchang_ringegreedumpsgcd  +base_ring coeffcientsdenomintor euclidean_degreentegral  +artesian_productcommon_prcderivativeexponentsnverse [?7h[?12l[?25h[?25l[?7ladd_bigoh + O additive_orderategory comon_valuationdump  + V base_xtedchang_ringegreedumps + ab base_ring coeffcientsdenomintor euclidean_degree + add_bigoh artesian_productcommon_prcderivativeexponents[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + + + + +[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lcate + lau.truncate  + lau.truncate_laurentseries + lau.truncate_neg [?7h[?12l[?25h[?25l[?7l + lau.truncate  + + + [?7h[?12l[?25h[?25l[?7l_laurentseries + lau.truncate  + lau.truncate_laurentseries[?7h[?12l[?25h[?25l[?7lneg + + lau.truncate_laurentseries + lau.truncate_neg [?7h[?12l[?25h[?25l[?7l + + + lau.truncate_neg  +[?7h[?12l[?25h[?25l[?7l_neg + + + lau.truncate_neg  + [?7h[?12l[?25h[?25l[?7l( + + + +[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: lau.truncate_neg() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [94], in () +----> 1 lau.truncate_neg() + +TypeError: LaurentSeries.truncate_neg() takes exactly one argument (0 given) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau.truncate_neg()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: lau.truncate_neg(3) +[?7h[?12l[?25h[?2004l[?7hO(t^4) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau.truncate_neg(3)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lsage: lau +[?7h[?12l[?25h[?2004l[?7ht^-6 + t^-2 + 1 + t^2 + O(t^4) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l.truncate_neg(3)[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lent_polynomial[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: lau.laurent_polynomial() +[?7h[?12l[?25h[?2004l[?7ht^-6 + t^-2 + 1 + t^2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau.laurent_polynomial()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lsage: lau.laurent_polynomial() + lau.O lau.additive_order lau.category lau.common_valuation lau.dump  + lau.V lau.base_extend lau.change_ring lau.degree lau.dumps  + lau.abs lau.base_ring lau.coefficients lau.denominator lau.euclidean_degree > + lau.add_bigoh lau.cartesian_product lau.common_prec lau.derivative lau.exponents  + [?7h[?12l[?25h[?25l[?7lO + lau.O  + + + + [?7h[?12l[?25h[?25l[?7ladditive_order + lau.O  lau.additive_order [?7h[?12l[?25h[?25l[?7lcategory + lau.additive_order  lau.category [?7h[?12l[?25h[?25l[?7lommon_valuation + lau.category  lau.common_valuation [?7h[?12l[?25h[?25l[?7lategory + lau.category  lau.common_valuation [?7h[?12l[?25h[?25l[?7lhane_ring + lau.category  + lau.change_ring [?7h[?12l[?25h[?25l[?7ldegre + + lau.change_ring  lau.degree [?7h[?12l[?25h[?25l[?7lumps + + lau.degree  lau.dumps [?7h[?12l[?25h[?25l[?7legree + + lau.degree  lau.dumps [?7h[?12l[?25h[?25l[?7lcommon_valuation + lau.common_valuation  + lau.degree [?7h[?12l[?25h[?25l[?7ldup + lau.common_valuation  lau.dump [?7h[?12l[?25h[?25l[?7ls + lau.dump  + lau.dumps [?7h[?12l[?25h[?25l[?7leclidean_degree + + lau.dumps  + lau.euclidean_degree [?7h[?12l[?25h[?25l[?7lxponents + + + lau.euclidean_degree  + lau.exponents [?7h[?12l[?25h[?25l[?7linverse + additive_ordercategory ommon_valuationdup factor + base_extendchang_rigdegre umps gcd  +<bae_ringcoefficientsdenomnator eucliden_degreeintegral  + cartesian_productommon_prec derivativ exponents inverse [?7h[?12l[?25h[?25l[?7ltgral + + + lau.integral  + lau.inverse [?7h[?12l[?25h[?25l[?7lgcd + + lau.gcd  + lau.integral [?7h[?12l[?25h[?25l[?7lfactor + lau.factor  + lau.gcd [?7h[?12l[?25h[?25l[?7lgcd + lau.factor  + lau.gcd [?7h[?12l[?25h[?25l[?7lintegral + + lau.gcd  + lau.integral [?7h[?12l[?25h[?25l[?7l( + + + + +[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: lau.integral() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ZeroDivisionError Traceback (most recent call last) +Input In [98], in () +----> 1 lau.integral() + +File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1654, in sage.rings.laurent_series_ring_element.LaurentSeries.integral() + 1652 + 1653 if n < 0: +-> 1654 v = [a[i]/(n+i+1) for i in range(min(-1-n,len(a)))] + [0] + 1655 else: + 1656 v = [] + +File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__() + 1740 + 1741 try: +-> 1742 return coercion_model.bin_op(left, right, truediv) + 1743 except TypeError: + 1744 return NotImplemented + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op() + 1202 self._record_exception() + 1203 else: +-> 1204 return PyObject_CallObject(op, xy) + 1205 + 1206 if op is mul: + +File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__() + 1735 cdef int cl = classify_elements(left, right) + 1736 if HAVE_SAME_PARENT(cl): +-> 1737 return (left)._div_(right) + 1738 if BOTH_ARE_ELEMENT(cl): + 1739 return coercion_model.bin_op(left, right, truediv) + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_() + 2621 right_inverse = self.__modulus.inverses[(right).ivalue] + 2622 if right_inverse is None: +-> 2623 raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist") + 2624 else: + 2625 return self._new_c((self.ivalue * (right_inverse).ivalue) % self.__modulus.int32) + +ZeroDivisionError: inverse of Mod(0, 3) does not exist +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau.integral()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: lau. + lau.O lau.additive_order lau.category lau.common_valuation lau.dump  + lau.V lau.base_extend lau.change_ring lau.degree lau.dumps  + lau.abs lau.base_ring lau.coefficients lau.denominator lau.euclidean_degree > + lau.add_bigoh lau.cartesian_product lau.common_prec lau.derivative lau.exponents  + [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lO + lau.O  + + + + [?7h[?12l[?25h[?25l[?7ladditive_order + lau.O  lau.additive_order [?7h[?12l[?25h[?25l[?7lcategory + lau.additive_order  lau.category [?7h[?12l[?25h[?25l[?7lommon_valuation + lau.category  lau.common_valuation [?7h[?12l[?25h[?25l[?7ldup + lau.common_valuation  lau.dump [?7h[?12l[?25h[?25l[?7lfactor + additive_ordercategory ommon_valuationdup factor + base_extendchang_rigdegre umps gcd  +<bae_ringcoefficientsdenomnator eucliden_degreeintegral  + cartesian_productommon_prec derivativ exponents inverse [?7h[?12l[?25h[?25l[?7linverse_of_unit +category ommon_valuationdup factorinverse_of_unit +chang_rigdegre umps gcd is_idempotent +coefficientsdenomnator eucliden_degreeintegral s_monomial +ommon_prec derivativ exponents inverse s_nilpotent[?7h[?12l[?25h[?25l[?7lfactor + lau.factor  lau.inverse_of_unit [?7h[?12l[?25h[?25l[?7lgcd + lau.factor  + lau.gcd [?7h[?12l[?25h[?25l[?7lintegral + + lau.gcd  + lau.integral [?7h[?12l[?25h[?25l[?7ls_monomial + + + lau.integral  lau.is_monomial [?7h[?12l[?25h[?25l[?7lidempotent + + lau.is_idempotent  + lau.is_monomial [?7h[?12l[?25h[?25l[?7lnverse_f_unit + lau.inverse_of_unit  + lau.is_idempotent [?7h[?12l[?25h[?25l[?7ls_one +ommon_valuationdup factorinverse_of_units_one  +degre umps gcd is_idempotentprie  +denomnator eucliden_degreeintegral s_monomialunit  +derivativ exponents inverse s_nilpotentzero [?7h[?12l[?25h[?25l[?7lprime + lau.is_one  + lau.is_prime [?7h[?12l[?25h[?25l[?7llcm +dup factorinverse_of_units_one laurent_polynomial +umps gcd is_idempotentprie lcm  +eucliden_degreeintegral s_monomialunit lift_to_precision +exponents inverse s_nilpotentzero list [?7h[?12l[?25h[?25l[?7laurent_polynomial + lau.laurent_polynomial  + lau.lcm [?7h[?12l[?25h[?25l[?7lcm + lau.laurent_polynomial  + lau.lcm [?7h[?12l[?25h[?25l[?7lift_to_precision + + lau.lcm  + lau.lift_to_precision [?7h[?12l[?25h[?25l[?7ls + + + lau.lift_to_precision  + lau.list [?7h[?12l[?25h[?25l[?7lf_to_precision + + + lau.lift_to_precision  + lau.list [?7h[?12l[?25h[?25l[?7l( + + + + +[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: lau.lift_to_precision(0) +[?7h[?12l[?25h[?2004l[?7ht^-6 + t^-2 + 1 + t^2 + O(t^4) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  + + + [?7h[?12l[?25h[?25l[?7llau.lift_to_precision(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 + lau.O lau.additive_order lau.category lau.common_valuation lau.dump  + lau.V lau.base_extend lau.change_ring lau.degree lau.dumps  +  lau.abs lau.base_ring lau.coefficients lau.denominator lau.euclidean_degree > + lau.add_bigoh lau.cartesian_product lau.common_prec lau.derivative lau.exponents  + [?7h[?12l[?25h[?25l[?7lO + lau.O  + + + + [?7h[?12l[?25h[?25l[?7ladditive_order + lau.O  lau.additive_order [?7h[?12l[?25h[?25l[?7lcategory + lau.additive_order  lau.category [?7h[?12l[?25h[?25l[?7lommon_valuation + lau.category  lau.common_valuation [?7h[?12l[?25h[?25l[?7ldup + lau.common_valuation  lau.dump [?7h[?12l[?25h[?25l[?7lfactor + additive_ordercategory ommon_valuationdup factor + base_extendchang_rigdegre umps gcd  +<bae_ringcoefficientsdenomnator eucliden_degreeintegral  + cartesian_productommon_prec derivativ exponents inverse [?7h[?12l[?25h[?25l[?7linverse_of_unit +category ommon_valuationdup factorinverse_of_unit +chang_rigdegre umps gcd is_idempotent +coefficientsdenomnator eucliden_degreeintegral s_monomial +ommon_prec derivativ exponents inverse s_nilpotent[?7h[?12l[?25h[?25l[?7ls_one +ommon_valuationdup factorinverse_of_units_one  +degre umps gcd is_idempotentprie  +denomnator eucliden_degreeintegral s_monomialunit  +derivativ exponents inverse s_nilpotentzero [?7h[?12l[?25h[?25l[?7llaurent_polynomial +dup factorinverse_of_units_one laurent_polynomial +umps gcd is_idempotentprie lcm  +eucliden_degreeintegral s_monomialunit lift_to_precision +exponents inverse s_nilpotentzero list [?7h[?12l[?25h[?25l[?7lmultiplicative_order +factorinverse_of_units_one laurent_polynomialmultiplicative_order +gcd is_idempotentprie lcm n  +integral s_monomialunit lift_to_precisionnth_rot  +inverse s_nilpotentzero list numerator[?7h[?12l[?25h[?25l[?7lnmerical_approx +inverse_of_units_one laurent_polynomialmultiplicative_ordernmerical_approx  +is_idempotentprie lcm n order +s_monomialunit lift_to_precisionnth_rot parent  +s_nilpotentzero list numeratorpow_seies[?7h[?12l[?25h[?25l[?7lmltiplicative_order + lau.multiplicative_order  lau.numerical_approx [?7h[?12l[?25h[?25l[?7llaurent_polynomial + lau.laurent_polynomial  lau.multiplicative_order [?7h[?12l[?25h[?25l[?7lis_one + lau.is_one  lau.laurent_polynomial [?7h[?12l[?25h[?25l[?7lnverse_of_unit + lau.inverse_of_unit  lau.is_one [?7h[?12l[?25h[?25l[?7lfactor +factor nverse_of_unitis_one laurent_polynomial mltiplicative_order +gcd idepotentis_primelcmn  +ntegral monomialis_unit lift_t_precisionnth_root +nverse nilpotentis_zerolist numato [?7h[?12l[?25h[?25l[?7ldump +dump factor nverse_of_unitis_one laurent_polynomial  +dumpsgcd idepotentis_primelcm +euclidean_degreentegral monomialis_unit lift_t_precision +exponentsnverse nilpotentis_zerolist [?7h[?12l[?25h[?25l[?7lcomon_valuation +comon_valuationdump factor nverse_of_unitis_one  +egreedumpsgcd idepotentis_prime +denomintor euclidean_degreentegral monomialis_unit  +derivativeexponentsnverse nilpotentis_zero[?7h[?12l[?25h[?25l[?7lategory +ategory comon_valuationdump factor nverse_of_unit +chang_ringegreedumpsgcd idepotent +coeffcientsdenomintor euclidean_degreentegral monomial +common_prcderivativeexponentsnverse nilpotent[?7h[?12l[?25h[?25l[?7ladditive_order +additive_orderategory comon_valuationdump factor  +base_xtedchang_ringegreedumpsgcd  +base_ring coeffcientsdenomintor euclidean_degreentegral  +artesian_productcommon_prcderivativeexponentsnverse [?7h[?12l[?25h[?25l[?7lO + O additive_orderategory comon_valuationdump  + V base_xtedchang_ringegreedumps + ab base_ring coeffcientsdenomintor euclidean_degree + add_bigoh artesian_productcommon_prcderivativeexponents[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + + + + +[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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.pth_root()[?7h[?12l[?25h[?25l[?7lor a in range(0, 9):[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7l +....: [?7h[?12l[?25h[?25l[?7lprint(a*(C.x.teichmuller().diffn()) == a*(C.x.teichmuller()).diffn())[?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[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l() +....: [?7h[?12l[?25h[?25l[?7lsage: for i in lau.exponents(): +....:  print(lau.coefficient(t^i)) +....:  +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [100], in () + 1 for i in lau.exponents(): +----> 2 print(lau.coefficient(t**i)) + +File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() + 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' + 493 """ +--> 494 return self.getattr_from_category(name) + 495 + 496 cdef getattr_from_category(self, name): + +File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() + 505 else: + 506 cls = P._abstract_element_class +--> 507 return getattr_from_other_class(self, cls, name) + 508 + 509 def __dir__(self): + +File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() + 359 dummy_error_message.cls = type(self) + 360 dummy_error_message.name = name +--> 361 raise AttributeError(dummy_error_message) + 362 attribute = attr + 363 # Check for a descriptor (__get__ in Python) + +AttributeError: 'sage.rings.laurent_series_ring_element.LaurentSeries' object has no attribute 'coefficient' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau.lift_to_precision(0)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lsage: lau.lift_to_precision(0) + lau.O lau.additive_order lau.category lau.common_valuation lau.dump  + lau.V lau.base_extend lau.change_ring lau.degree lau.dumps  + lau.abs lau.base_ring lau.coefficients lau.denominator lau.euclidean_degree > + lau.add_bigoh lau.cartesian_product lau.common_prec lau.derivative lau.exponents  + [?7h[?12l[?25h[?25l[?7lO + lau.O  + + + + [?7h[?12l[?25h[?25l[?7ladditive_order + lau.O  lau.additive_order [?7h[?12l[?25h[?25l[?7lO + lau.O  lau.additive_order [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + + + + +[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in lau.exponents(): +....:  print(lau.coefficient(t^i))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?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([i])[?7h[?12l[?25h[?25l[?7l)[i])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l() +....: [?7h[?12l[?25h[?25l[?7lsage: for i in lau.exponents(): +....:  print(lau.coefficient()[i]) +....:  +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [101], in () + 1 for i in lau.exponents(): +----> 2 print(lau.coefficient()[i]) + +File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() + 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' + 493 """ +--> 494 return self.getattr_from_category(name) + 495 + 496 cdef getattr_from_category(self, name): + +File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() + 505 else: + 506 cls = P._abstract_element_class +--> 507 return getattr_from_other_class(self, cls, name) + 508 + 509 def __dir__(self): + +File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() + 359 dummy_error_message.cls = type(self) + 360 dummy_error_message.name = name +--> 361 raise AttributeError(dummy_error_message) + 362 attribute = attr + 363 # Check for a descriptor (__get__ in Python) + +AttributeError: 'sage.rings.laurent_series_ring_element.LaurentSeries' object has no attribute 'coefficient' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for i in lau.exponents(): +....:  print(lau.coefficient()[i])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[i])[?7h[?12l[?25h[?25l[?7l[i])[?7h[?12l[?25h[?25l[?7l[i])[?7h[?12l[?25h[?25l[?7l[i])[?7h[?12l[?25h[?25l[?7l[i])[?7h[?12l[?25h[?25l[?7l[i])[?7h[?12l[?25h[?25l[?7l[i])[?7h[?12l[?25h[?25l[?7l[i])[?7h[?12l[?25h[?25l[?7l[i])[?7h[?12l[?25h[?25l[?7l[i])[?7h[?12l[?25h[?25l[?7l[i])[?7h[?12l[?25h[?25l[?7l[i])[?7h[?12l[?25h[?25l[?7l[i])[?7h[?12l[?25h[?25l[?7l[i])[?7h[?12l[?25h[?25l[?7l[][?7h[?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(lau[i]) +....: [?7h[?12l[?25h[?25l[?7lsage: for i in lau.exponents(): +....:  print(lau[i]) +....:  +[?7h[?12l[?25h[?2004l1 +1 +1 +1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for i in lau.exponents(): +....:  print(lau[i])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lilau[i])[?7h[?12l[?25h[?25l[?7l,lau[i])[?7h[?12l[?25h[?25l[?7l lau[i])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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(i, lau[i]) +....: [?7h[?12l[?25h[?25l[?7lsage: for i in lau.exponents(): +....:  print(i, lau[i]) +....:  +[?7h[?12l[?25h[?2004l-6 1 +-2 1 +0 1 +2 1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om +[?7h[?12l[?25h[?2004l[?7h((x^28 - x^26 + x^25 - x^24 + x^23 - x^22 - x^21 + x^20 + x^19 + x^18 + x^17 + x^15 - x^14 + x^13 + x^12 + x^11 - x^10 - x^8 - x^7 + x^6 - x^5 + x^4 + x^2 + x - 1)/(x^16*y - x^15*y + x^14*y - x^13*y + x^12*y - x^11*y + x^10*y - x^9*y - x^8*y + x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y)) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.cartier().cartier() +[?7h[?12l[?25h[?2004l[?7h(x^3/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().cartier()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.cartier().cartier().expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7h1 + O(t^10) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: om.cartier().cartier().expansion_at_infty(prec = 100) +[?7h[?12l[?25h[?2004l[?7h1 + 2*t^16 + 2*t^48 + t^64 + O(t^100) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().cartier().expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1.diffn()[?7h[?12l[?25h[?25l[?7l = om1.pth_root()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.pth_rot()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1 = om.cartier().cartier() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = om.cartier().cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7lint().diffn()[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7linv[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrtier[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.inv_cartier() +[?7h[?12l[?25h[?2004l[?7h((x^18 - x^10)/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.inv_cartier()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7linv[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.inv_cartier().inv_cartier() +[?7h[?12l[?25h[?2004l[?7h((x^63 - x^55 - x^39 + x^31)/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.inv_cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.inv_cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7lmom1.inv_cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7l2om1.inv_cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7l om1.inv_cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7l=om1.inv_cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7l om1.inv_cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om2 = om1.inv_cartier().inv_cartier() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpip install -U sage[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2 = om1.inv_cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1.inv_cartier().nv_cartier()[?7h[?12l[?25h[?25l[?7l = om.cartier().cartier()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2 = om1.inv_cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.expansonat_infty()[?7h[?12l[?25h[?25l[?7lcartier().expasion_at_infty()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(B[1].omega8.r())[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l_patch(B[1].omega8.r())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7lm)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7losecond_patch(om)[?7h[?12l[?25h[?25l[?7lmsecond_patch(om)[?7h[?12l[?25h[?25l[?7l1second_patch(om)[?7h[?12l[?25h[?25l[?7l second_patch(om)[?7h[?12l[?25h[?25l[?7l=second_patch(om)[?7h[?12l[?25h[?25l[?7l second_patch(om)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om1 = second_patch(om) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = second_patch(om)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.inv_artier().inv_cartier()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.cartier().cartier() +[?7h[?12l[?25h[?2004l[?7h((-1)/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.cartier().cartier()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7linv[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7linv[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.cartier().cartier().inv_cartier().inv_cartier() +[?7h[?12l[?25h[?2004l[?7h((-x^36 + x^28 + x^12 - x^4)/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau.lift_to_precision(0)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lplau[?7h[?12l[?25h[?25l[?7lalau[?7h[?12l[?25h[?25l[?7lrlau[?7h[?12l[?25h[?25l[?7lelau[?7h[?12l[?25h[?25l[?7lnlau[?7h[?12l[?25h[?25l[?7ltlau[?7h[?12l[?25h[?25l[?7l(lau[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: parent(lau) +[?7h[?12l[?25h[?2004l[?7hLaurent Series Ring in t over Finite Field of size 3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(lau)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lparent(lau)[?7h[?12l[?25h[?25l[?7laparent(lau)[?7h[?12l[?25h[?25l[?7lrparent(lau)[?7h[?12l[?25h[?25l[?7leparent(lau)[?7h[?12l[?25h[?25l[?7lntparent(lau)[?7h[?12l[?25h[?25l[?7l(parent(lau)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: parent(parent(lau)) +[?7h[?12l[?25h[?2004l[?7h +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(parent(lau))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(parent(lau))[?7h[?12l[?25h[?25l[?7l(parent(lau))[?7h[?12l[?25h[?25l[?7l(parent(lau))[?7h[?12l[?25h[?25l[?7l(parent(lau))[?7h[?12l[?25h[?25l[?7l(parent(lau))[?7h[?12l[?25h[?25l[?7l(parent(lau))[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb(parent(lau))[?7h[?12l[?25h[?25l[?7la(parent(lau))[?7h[?12l[?25h[?25l[?7ls(parent(lau))[?7h[?12l[?25h[?25l[?7le(parent(lau))[?7h[?12l[?25h[?25l[?7l_(parent(lau))[?7h[?12l[?25h[?25l[?7lr(parent(lau))[?7h[?12l[?25h[?25l[?7li(parent(lau))[?7h[?12l[?25h[?25l[?7ln(parent(lau))[?7h[?12l[?25h[?25l[?7lg(parent(lau))[?7h[?12l[?25h[?25l[?7l(())[?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: base_ring(parent(lau)) +[?7h[?12l[?25h[?2004l[?7hFinite Field of size 3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau.lift_to_precision(0)[?7h[?12l[?25h[?25l[?7load('ini.sag')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: load('auxilliar + auxilliaries/  + auxilliary_derivative + + + [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lies/ + auxilliaries/  + + [?7h[?12l[?25h[?25l[?7ll + + +[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lrent_analytic_part.sage[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('auxilliaries/laurent_analytic_part.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  + + + + [?7h[?12l[?25h[?25l[?7lload('auxilliaries/laurent_analytic_part.sage')[?7h[?12l[?25h[?25l[?7lau.lift_to_preciion(0)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lanalytic_part[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: laurent_analytic_part(lau) +[?7h[?12l[?25h[?2004l[?7ht^-6 + t^-2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + [?7h[?12l[?25h[?25l[?7llaurent_analytic_part(lau)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lsage: lau +[?7h[?12l[?25h[?2004l[?7ht^-6 + t^-2 + 1 + t^2 + O(t^4) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau[?7h[?12l[?25h[?25l[?7lrent_analytic_part(lau)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: laurent_analytic_part(lau).integral() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ZeroDivisionError Traceback (most recent call last) +Input In [121], in () +----> 1 laurent_analytic_part(lau).integral() + +File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1654, in sage.rings.laurent_series_ring_element.LaurentSeries.integral() + 1652 + 1653 if n < 0: +-> 1654 v = [a[i]/(n+i+1) for i in range(min(-1-n,len(a)))] + [0] + 1655 else: + 1656 v = [] + +File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__() + 1740 + 1741 try: +-> 1742 return coercion_model.bin_op(left, right, truediv) + 1743 except TypeError: + 1744 return NotImplemented + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op() + 1202 self._record_exception() + 1203 else: +-> 1204 return PyObject_CallObject(op, xy) + 1205 + 1206 if op is mul: + +File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__() + 1735 cdef int cl = classify_elements(left, right) + 1736 if HAVE_SAME_PARENT(cl): +-> 1737 return (left)._div_(right) + 1738 if BOTH_ARE_ELEMENT(cl): + 1739 return coercion_model.bin_op(left, right, truediv) + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_() + 2621 right_inverse = self.__modulus.inverses[(right).ivalue] + 2622 if right_inverse is None: +-> 2623 raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist") + 2624 else: + 2625 return self._new_c((self.ivalue * (right_inverse).ivalue) % self.__modulus.int32) + +ZeroDivisionError: inverse of Mod(0, 3) does not exist +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.cartier().cartier().inv_cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om +[?7h[?12l[?25h[?2004l[?7h((x^28 - x^26 + x^25 - x^24 + x^23 - x^22 - x^21 + x^20 + x^19 + x^18 + x^17 + x^15 - x^14 + x^13 + x^12 + x^11 - x^10 - x^8 - x^7 + x^6 - x^5 + x^4 + x^2 + x - 1)/(x^16*y - x^15*y + x^14*y - x^13*y + x^12*y - x^11*y + x^10*y - x^9*y - x^8*y + x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y)) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1.cartier().cartier().inv_cartier().inv_cartier()[?7h[?12l[?25h[?25l[?7l = second_patch(om)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lom.cartier().cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1 = om.cartier() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llaurent_analytic_part(lau).integral()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l = om.crtier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsage: lau = om1.expansion + om1.expansion  + om1.expansion_at_infty + + + [?7h[?12l[?25h[?25l[?7l + om1.expansion  + + [?7h[?12l[?25h[?25l[?7l_at_infty + om1.expansion  + om1.expansion_at_infty[?7h[?12l[?25h[?25l[?7l( + + +[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: lau = om1.expansion_at_infty() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + [?7h[?12l[?25h[?25l[?7llau = om1.expansion_at_infty()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l.lift_to_recsion(0)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: lau.analytic_part().integral() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [125], in () +----> 1 lau.analytic_part().integral() + +File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() + 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' + 493 """ +--> 494 return self.getattr_from_category(name) + 495 + 496 cdef getattr_from_category(self, name): + +File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() + 505 else: + 506 cls = P._abstract_element_class +--> 507 return getattr_from_other_class(self, cls, name) + 508 + 509 def __dir__(self): + +File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() + 359 dummy_error_message.cls = type(self) + 360 dummy_error_message.name = name +--> 361 raise AttributeError(dummy_error_message) + 362 attribute = attr + 363 # Check for a descriptor (__get__ in Python) + +AttributeError: 'sage.rings.laurent_series_ring_element.LaurentSeries' object has no attribute 'analytic_part' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau.analytic_part().integral()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lanalytic_part().integral()[?7h[?12l[?25h[?25l[?7lranalytic_part().integral()[?7h[?12l[?25h[?25l[?7leanalytic_part().integral()[?7h[?12l[?25h[?25l[?7lnanalytic_part().integral()[?7h[?12l[?25h[?25l[?7ltanalytic_part().integral()[?7h[?12l[?25h[?25l[?7l_analytic_part().integral()[?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).integral()[?7h[?12l[?25h[?25l[?7la).integral()[?7h[?12l[?25h[?25l[?7lu).integral()[?7h[?12l[?25h[?25l[?7l()[?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: laurent_analytic_part(lau).integral() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ZeroDivisionError Traceback (most recent call last) +Input In [126], in () +----> 1 laurent_analytic_part(lau).integral() + +File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1654, in sage.rings.laurent_series_ring_element.LaurentSeries.integral() + 1652 + 1653 if n < 0: +-> 1654 v = [a[i]/(n+i+1) for i in range(min(-1-n,len(a)))] + [0] + 1655 else: + 1656 v = [] + +File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__() + 1740 + 1741 try: +-> 1742 return coercion_model.bin_op(left, right, truediv) + 1743 except TypeError: + 1744 return NotImplemented + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op() + 1202 self._record_exception() + 1203 else: +-> 1204 return PyObject_CallObject(op, xy) + 1205 + 1206 if op is mul: + +File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__() + 1735 cdef int cl = classify_elements(left, right) + 1736 if HAVE_SAME_PARENT(cl): +-> 1737 return (left)._div_(right) + 1738 if BOTH_ARE_ELEMENT(cl): + 1739 return coercion_model.bin_op(left, right, truediv) + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_() + 2621 right_inverse = self.__modulus.inverses[(right).ivalue] + 2622 if right_inverse is None: +-> 2623 raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist") + 2624 else: + 2625 return self._new_c((self.ivalue * (right_inverse).ivalue) % self.__modulus.int32) + +ZeroDivisionError: inverse of Mod(0, 3) does not exist +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llaurent_analytic_part(lau).integral()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l.aalytic_part().integral()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lrt().integral()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: lau.analytic_part() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [127], in () +----> 1 lau.analytic_part() + +File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() + 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' + 493 """ +--> 494 return self.getattr_from_category(name) + 495 + 496 cdef getattr_from_category(self, name): + +File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() + 505 else: + 506 cls = P._abstract_element_class +--> 507 return getattr_from_other_class(self, cls, name) + 508 + 509 def __dir__(self): + +File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() + 359 dummy_error_message.cls = type(self) + 360 dummy_error_message.name = name +--> 361 raise AttributeError(dummy_error_message) + 362 attribute = attr + 363 # Check for a descriptor (__get__ in Python) + +AttributeError: 'sage.rings.laurent_series_ring_element.LaurentSeries' object has no attribute 'analytic_part' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau.analytic_part()[?7h[?12l[?25h[?25l[?7lret_analytic_part(lau).integral()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: laurent_analytic_part(lau) +[?7h[?12l[?25h[?2004l[?7ht^-6 + t^-2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = om.cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.7, Release Date: 2022-09-19 │ +│ Using Python 3.10.5. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llaurent_analytic_part(lau)[?7h[?12l[?25h[?25l[?7load('auxiliaries/laurent_analytic_part.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7l(nit.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004llo[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lafty/[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliaries/laurent_analytic_part.sage')[?7h[?12l[?25h[?25l[?7l(uxilliaries/laurent_analytic_part.sage')[?7h[?12l[?25h[?25l[?7lsage: load('auxilliaries/laurent_analytic_part.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = om.cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l +  + [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + [?7h[?12l[?25h[?25l[?7l((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^10 - C . +....: x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C.x^9 * +....: C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^10 - C . +....: x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C.x^9 * +....: C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx +[?7h[?12l[?25h[?2004l[?7h((x^28 - x^26 + x^25 - x^24 + x^23 - x^22 - x^21 + x^20 + x^19 + x^18 + x^17 + x^15 - x^14 + x^13 + x^12 + x^11 - x^10 - x^8 - x^7 + x^6 - x^5 + x^4 + x^2 + x - 1)/(x^16*y - x^15*y + x^14*y - x^13*y + x^12*y - x^11*y + x^10*y - x^9*y - x^8*y + x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y)) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = om.cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 + - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.cartier().cartier().expansion_at_infty(prec = 100) +  + [?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ltier().cartier().expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lsage: om.cartier().cartier().expansion_at_infty(prec = 100) +[?7h[?12l[?25h[?2004l[?7h1 + 2*t^16 + 2*t^48 + t^64 + O(t^100) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().cartier().expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.cartier() +[?7h[?12l[?25h[?2004l[?7h((x^13 - x^12 - x^11 - x^10 - x^9 + x^8 - x^5 + x^4 - x^3 - x^2 + x - 1)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier()[?7h[?12l[?25h[?25l[?7l().cartier().expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lexpansion_at_ifty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: om.cartier().expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-6 + t^-2 + 1 + t^2 + O(t^4) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llom.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7laom.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7luom.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l om.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l=om.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l om.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()\[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: lau = om.cartier().expansion_at_infty() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7ln[?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[?7llau = om.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lrent_anlytic_part(lau)[?7h[?12l[?25h[?25l[?7lent_analytic_part(lau)[?7h[?12l[?25h[?25l[?7lsage: laurent_analytic_part(lau) +[?7h[?12l[?25h[?2004l[?7ht^-6 + t^-2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llaurent_analytic_part(lau)[?7h[?12l[?25h[?25l[?7l().integral()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lintegral()[?7h[?12l[?25h[?25l[?7lsage: laurent_analytic_part(lau).integral() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ZeroDivisionError Traceback (most recent call last) +Input In [11], in () +----> 1 laurent_analytic_part(lau).integral() + +File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1654, in sage.rings.laurent_series_ring_element.LaurentSeries.integral() + 1652 + 1653 if n < 0: +-> 1654 v = [a[i]/(n+i+1) for i in range(min(-1-n,len(a)))] + [0] + 1655 else: + 1656 v = [] + +File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__() + 1740 + 1741 try: +-> 1742 return coercion_model.bin_op(left, right, truediv) + 1743 except TypeError: + 1744 return NotImplemented + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op() + 1202 self._record_exception() + 1203 else: +-> 1204 return PyObject_CallObject(op, xy) + 1205 + 1206 if op is mul: + +File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__() + 1735 cdef int cl = classify_elements(left, right) + 1736 if HAVE_SAME_PARENT(cl): +-> 1737 return (left)._div_(right) + 1738 if BOTH_ARE_ELEMENT(cl): + 1739 return coercion_model.bin_op(left, right, truediv) + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_() + 2621 right_inverse = self.__modulus.inverses[(right).ivalue] + 2622 if right_inverse is None: +-> 2623 raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist") + 2624 else: + 2625 return self._new_c((self.ivalue * (right_inverse).ivalue) % self.__modulus.int32) + +ZeroDivisionError: inverse of Mod(0, 3) does not exist +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llaurent_analytic_part(lau).integral()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.7, Release Date: 2022-09-19 │ +│ Using Python 3.10.5. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llaurent_analytic_part(lau).integral()[?7h[?12l[?25h[?25l[?7load('auxiliaries/laurent_aalytic_part.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l(t.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7lauxilliaries/laurent_analytic_part.sage')[?7h[?12l[?25h[?25l[?7l(uxilliaries/laurent_analytic_part.sage')[?7h[?12l[?25h[?25l[?7lsage: load('auxilliaries/laurent_analytic_part.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^10 - C . +....: x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C.x^9 * +....: C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l( + +)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l( +( +))[?7h[?12l[?25h[?25l[?7l( +)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l 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+ +)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^2 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^1 - C.x^10 - C +.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^1*C.y + C.x^10*C.y - C.x^ 9 +*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^2 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^1 - C.x^10 -  +C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^1*C.y + C.x^10*C.y - C.x ^ +9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^2 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^1 - C.x^10 - + C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^1*C.y + C.x^10*C.y - C. x +^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l=((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^2 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^1 - C.x^10  +- C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^1*C.y + C.x^10*C.y - C . +x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^2 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^1 - C.x^1 0 + - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^1*C.y + C.x^10*C.y - C +.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.cartier().expansion_at_infty() +  + [?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrtier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llom.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7laom.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7luom.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsom.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l om.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l=om.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l om.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = om.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: lau = om.cartier().expansion_at_infty() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + [?7h[?12l[?25h[?25l[?7llau = om.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lsage: lau +[?7h[?12l[?25h[?2004l[?7ht^-8 + t^-6 + t^-4 + 1 + O(t^2) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l.analytic_part()[?7h[?12l[?25h[?25l[?7litegral()[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lintegral()[?7h[?12l[?25h[?25l[?7lsage: lau.integral() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ZeroDivisionError Traceback (most recent call last) +Input In [6], in () +----> 1 lau.integral() + +File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1654, in sage.rings.laurent_series_ring_element.LaurentSeries.integral() + 1652 + 1653 if n < 0: +-> 1654 v = [a[i]/(n+i+1) for i in range(min(-1-n,len(a)))] + [0] + 1655 else: + 1656 v = [] + +File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__() + 1740 + 1741 try: +-> 1742 return coercion_model.bin_op(left, right, truediv) + 1743 except TypeError: + 1744 return NotImplemented + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op() + 1202 self._record_exception() + 1203 else: +-> 1204 return PyObject_CallObject(op, xy) + 1205 + 1206 if op is mul: + +File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__() + 1735 cdef int cl = classify_elements(left, right) + 1736 if HAVE_SAME_PARENT(cl): +-> 1737 return (left)._div_(right) + 1738 if BOTH_ARE_ELEMENT(cl): + 1739 return coercion_model.bin_op(left, right, truediv) + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_() + 2621 right_inverse = self.__modulus.inverses[(right).ivalue] + 2622 if right_inverse is None: +-> 2623 raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist") + 2624 else: + 2625 return self._new_c((self.ivalue * (right_inverse).ivalue) % self.__modulus.int32) + +ZeroDivisionError: inverse of Mod(0, 3) does not exist +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR == gg.pth_root().diffn()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y=C.fct_field[?7h[?12l[?25h[?25l[?7lsage: F +[?7h[?12l[?25h[?2004l[?7hFinite Field of size 3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR == gg.pth_root().diffn()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l<[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l>[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lL[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: Rt. = LaurentSeries + LaurentSeries  + LaurentSeriesRing + + + [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + LaurentSeries  + + [?7h[?12l[?25h[?25l[?7lRing + LaurentSeries  + LaurentSeriesRing[?7h[?12l[?25h[?25l[?7l( + + +[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: Rt. = LaurentSeriesRing(F) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  + + + + [?7h[?12l[?25h[?25l[?7ltest[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: t.integral() +[?7h[?12l[?25h[?2004l[?7h2*t^2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + [?7h[?12l[?25h[?25l[?7llau.integral()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lsage: lau +[?7h[?12l[?25h[?2004l[?7ht^-8 + t^-6 + t^-4 + 1 + O(t^2) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt.integral()[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: t^(-8).integral() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [11], in () +----> 1 t**(-Integer(8)).integral() + +File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() + 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' + 493 """ +--> 494 return self.getattr_from_category(name) + 495 + 496 cdef getattr_from_category(self, name): + +File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() + 505 else: + 506 cls = P._abstract_element_class +--> 507 return getattr_from_other_class(self, cls, name) + 508 + 509 def __dir__(self): + +File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() + 359 dummy_error_message.cls = type(self) + 360 dummy_error_message.name = name +--> 361 raise AttributeError(dummy_error_message) + 362 attribute = attr + 363 # Check for a descriptor (__get__ in Python) + +AttributeError: 'sage.rings.integer.Integer' object has no attribute 'integral' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt^(-8).integral()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()).integral()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(t^(-8).integral()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: (t^(-8)).integral() +[?7h[?12l[?25h[?2004l[?7h2*t^-7 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(t^(-8)).integral()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)).integral()[?7h[?12l[?25h[?25l[?7l6)).integral()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l([?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: (t^(-6)).integral() +[?7h[?12l[?25h[?2004l[?7ht^-5 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: lau +[?7h[?12l[?25h[?2004l[?7ht^-8 + t^-6 + t^-4 + 1 + O(t^2) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(t^(-6)).integral()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)).integral()[?7h[?12l[?25h[?25l[?7l4)).integral()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?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: (t^(-4)).integral() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ZeroDivisionError Traceback (most recent call last) +Input In [15], in () +----> 1 (t**(-Integer(4))).integral() + +File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1654, in sage.rings.laurent_series_ring_element.LaurentSeries.integral() + 1652 + 1653 if n < 0: +-> 1654 v = [a[i]/(n+i+1) for i in range(min(-1-n,len(a)))] + [0] + 1655 else: + 1656 v = [] + +File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__() + 1740 + 1741 try: +-> 1742 return coercion_model.bin_op(left, right, truediv) + 1743 except TypeError: + 1744 return NotImplemented + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op() + 1202 self._record_exception() + 1203 else: +-> 1204 return PyObject_CallObject(op, xy) + 1205 + 1206 if op is mul: + +File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__() + 1735 cdef int cl = classify_elements(left, right) + 1736 if HAVE_SAME_PARENT(cl): +-> 1737 return (left)._div_(right) + 1738 if BOTH_ARE_ELEMENT(cl): + 1739 return coercion_model.bin_op(left, right, truediv) + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_() + 2621 right_inverse = self.__modulus.inverses[(right).ivalue] + 2622 if right_inverse is None: +-> 2623 raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist") + 2624 else: + 2625 return self._new_c((self.ivalue * (right_inverse).ivalue) % self.__modulus.int32) + +ZeroDivisionError: inverse of Mod(0, 3) does not exist +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(t^(-4)).integral()[?7h[?12l[?25h[?25l[?7llau[?7h[?12l[?25h[?25l[?7l(t^(-6)).integral()[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lt^(-8).integral()[?7h[?12l[?25h[?25l[?7llau[?7h[?12l[?25h[?25l[?7lt.integral()[?7h[?12l[?25h[?25l[?7lRt.<> = LaurentSeriesRing(F)[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7llau.integral()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = om.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.integral()[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7lRt. = LaurentSeriesRing(F)[?7h[?12l[?25h[?25l[?7lt.inegral()[?7h[?12l[?25h[?25l[?7llau[?7h[?12l[?25h[?25l[?7lt^(-8).integral()[?7h[?12l[?25h[?25l[?7l(t^(-8)).integral()[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7llau[?7h[?12l[?25h[?25l[?7l(t^(-4)).integral()[?7h[?12l[?25h[?25l[?7l[?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: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.cartier().expansion_at_infty() +  + [?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lcartier().expasion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.cartier().cartier() +[?7h[?12l[?25h[?2004l[?7h((x^6 + x^3 - x^2 - 1)/(x^6*y + x^4*y + x^2*y + y)) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().cartier()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lpansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lsage: om.cartier().cartier().expansion_at_infty(prec = 100) +[?7h[?12l[?25h[?2004l[?7h1 + t^4 + t^6 + 2*t^8 + t^10 + 2*t^20 + t^22 + 2*t^26 + 2*t^28 + t^30 + 2*t^34 + t^36 + t^38 + t^40 + t^42 + 2*t^46 + t^52 + t^54 + 2*t^56 + t^58 + t^60 + 2*t^64 + t^66 + t^68 + 2*t^72 + t^74 + t^76 + 2*t^80 + t^82 + t^84 + 2*t^88 + t^90 + t^92 + 2*t^96 + t^98 + O(t^100) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().cartier().expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lexpansion_at_ifty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lpansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: om.cartier().expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-8 + t^-6 + t^-4 + 1 + O(t^2) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = C.y/(C.x)^(g+1)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.y/(C.x)^(g+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[?7lgg.diffn().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = C.genus()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7lsage: g = C.genus() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = C.y/(C.x)^(g+1)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.y/(C.x)^(g+1)[?7h[?12l[?25h[?25l[?7lsage: v = C.y/(C.x)^(g+1) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv = C.y/(C.x)^(g+1)[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lxpansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: v.expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht + O(t^21) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l^2 - u + u^3[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lov^(-4)*[?7h[?12l[?25h[?25l[?7lmv^(-4)*[?7h[?12l[?25h[?25l[?7l v^(-4)*[?7h[?12l[?25h[?25l[?7l=v^(-4)*[?7h[?12l[?25h[?25l[?7l v^(-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[?7lv[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om = v^(-4)*v.diffn() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = v^(-4)*v.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lexpansion_at_ifty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lpansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: om.expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-4 + t^4 + O(t^6) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcartier().expasion_at_infty()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.cartier() +[?7h[?12l[?25h[?2004l[?7h(x^3/(x^2*y - y)) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lpansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: om.cartier().expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-2 + t^2 + O(t^8) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrtier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: om.cartier().expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-2 + t^2 + O(t^8) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lcartier().expasion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrtier().expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lsage: om.cartier().cartier().expansion_at_infty(prec = 100) +[?7h[?12l[?25h[?2004l[?7h0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().cartier().expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: om.cartier().cartier() +[?7h[?12l[?25h[?2004l[?7h0 dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om +[?7h[?12l[?25h[?2004l[?7h(x^6/(x^4*y + x^2*y + y)) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.cartier().cartier()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrtier().cartier()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.cartier() +[?7h[?12l[?25h[?2004l[?7h(x^3/(x^2*y - y)) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = v^(-4)*v.diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.cartier() +  + [?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrtier()[?7h[?12l[?25h[?25l[?7lsage: om.cartier() +[?7h[?12l[?25h[?2004l[?7h((x^11 + x^9 - x^7 - x^4 - x)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier()[?7h[?12l[?25h[?25l[?7l().cartier()[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: om.cartier().expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-8 + t^-6 + t^-4 + 1 + O(t^2) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcartier()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrtier()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lexpansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lsage: om.cartier().cartier().expansion_at_infty(prec = 100) +[?7h[?12l[?25h[?2004l[?7h1 + t^4 + t^6 + 2*t^8 + t^10 + 2*t^20 + t^22 + 2*t^26 + 2*t^28 + t^30 + 2*t^34 + t^36 + t^38 + t^40 + t^42 + 2*t^46 + t^52 + t^54 + 2*t^56 + t^58 + t^60 + 2*t^64 + t^66 + t^68 + 2*t^72 + t^74 + t^76 + 2*t^80 + t^82 + t^84 + 2*t^88 + t^90 + t^92 + 2*t^96 + t^98 + O(t^100) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit() +[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.7, Release Date: 2022-09-19 │ +│ Using Python 3.10.5. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau[?7h[?12l[?25h[?25l[?7load('auxilliaries/laurent_analytic_part.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l('auxilliaries/laurent_analytic_part.sage')[?7h[?12l[?25h[?25l[?7lsage: load('auxilliaries/laurent_analytic_part.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('auxilliaries/laurent_analytic_part.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l(it.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^10 - C . +....: x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C.x^9 * +....: C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^10 - C . +....: x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C.x^9 * +....: C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx +[?7h[?12l[?25h[?2004l[?7h((x^28 - x^26 + x^25 - x^24 + x^23 - x^22 - x^21 + x^20 + x^19 + x^18 + x^17 + x^15 - x^14 + x^13 + x^12 + x^11 - x^10 - x^8 - x^7 + x^6 - x^5 + x^4 + x^2 + x - 1)/(x^16*y - x^15*y + x^14*y - x^13*y + x^12*y - x^11*y + x^10*y - x^9*y - x^8*y + x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y)) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().cartier().expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 + - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.cartier().cartier().expansion_at_infty(prec = 100) +  + [?7h[?12l[?25h[?25l[?7lc[?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.cartier().cartier().expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: om.expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-18 + t^-16 + 2*t^-14 + O(t^-8) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l5)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: om.expansion_at_infty(prec = 50) +[?7h[?12l[?25h[?2004l[?7ht^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2 + 2 + 2*t^4 + t^6 + t^8 + 2*t^14 + 2*t^16 + t^24 + t^28 + 2*t^30 + O(t^32) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcartier().cartier().expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: om.cartier().expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-6 + t^-2 + 1 + t^2 + O(t^4) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om +[?7h[?12l[?25h[?2004l[?7h((x^28 - x^26 + x^25 - x^24 + x^23 - x^22 - x^21 + x^20 + x^19 + x^18 + x^17 + x^15 - x^14 + x^13 + x^12 + x^11 - x^10 - x^8 - x^7 + x^6 - x^5 + x^4 + x^2 + x - 1)/(x^16*y - x^15*y + x^14*y - x^13*y + x^12*y - x^11*y + x^10*y - x^9*y - x^8*y + x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y)) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l= g.diffn() +  + [?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^ 1 +....: 0 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - +....: C.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om == ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^ 1 +....: 0 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - +....: C.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx +[?7h[?12l[?25h[?2004l[?7hTrue +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om == ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^ 1 +....: 0 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y -   +....: C.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.cartier().expansion_at_infty() +  + [?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: om.cartier().expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-6 + t^-2 + 1 + t^2 + O(t^4) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lau[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l = om.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: lau = om.cartier().expansion_at_infty(prec = 30) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau = om.cartier().expansion_at_infty(prec = 30)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: laux +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Input In [13], in () +----> 1 laux + +NameError: name 'laux' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llaux[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lsage: lau +[?7h[?12l[?25h[?2004l[?7ht^-6 + t^-2 + 1 + t^2 + t^6 + 2*t^10 + t^14 + t^16 + 2*t^18 + 2*t^22 + O(t^24) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7ln[?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[?7llau[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lrent_analytic_part(lau).integral()[?7h[?12l[?25h[?25l[?7lent_analytic_part(lau).integral()[?7h[?12l[?25h[?25l[?7lsage: laurent_analytic_part(lau).integral() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ZeroDivisionError Traceback (most recent call last) +Input In [15], in () +----> 1 laurent_analytic_part(lau).integral() + +File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1654, in sage.rings.laurent_series_ring_element.LaurentSeries.integral() + 1652 + 1653 if n < 0: +-> 1654 v = [a[i]/(n+i+1) for i in range(min(-1-n,len(a)))] + [0] + 1655 else: + 1656 v = [] + +File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__() + 1740 + 1741 try: +-> 1742 return coercion_model.bin_op(left, right, truediv) + 1743 except TypeError: + 1744 return NotImplemented + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op() + 1202 self._record_exception() + 1203 else: +-> 1204 return PyObject_CallObject(op, xy) + 1205 + 1206 if op is mul: + +File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__() + 1735 cdef int cl = classify_elements(left, right) + 1736 if HAVE_SAME_PARENT(cl): +-> 1737 return (left)._div_(right) + 1738 if BOTH_ARE_ELEMENT(cl): + 1739 return coercion_model.bin_op(left, right, truediv) + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_() + 2621 right_inverse = self.__modulus.inverses[(right).ivalue] + 2622 if right_inverse is None: +-> 2623 raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist") + 2624 else: + 2625 return self._new_c((self.ivalue * (right_inverse).ivalue) % self.__modulus.int32) + +ZeroDivisionError: inverse of Mod(0, 3) does not exist +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llaurent_analytic_part(lau).integral()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lsage: lau +[?7h[?12l[?25h[?2004l[?7ht^-6 + t^-2 + 1 + t^2 + t^6 + 2*t^10 + t^14 + t^16 + 2*t^18 + 2*t^22 + O(t^24) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llau[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lrent_analytic_part(lau).integral()[?7h[?12l[?25h[?25l[?7lent_analytic_part(lau).integral()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: laurent_analytic_part(lau) +[?7h[?12l[?25h[?2004l[?7ht^-6 + t^-2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRt. = LaurentSeriesRing(F)[?7h[?12l[?25h[?25l[?7lt. = LaurentSeriesRing(F)[?7h[?12l[?25h[?25l[?7lsage: Rt. = LaurentSeriesRing(F) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^10 - C . +....: x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C.x^9 * +....: C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lt^(-4)).integral() +  + [?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l().integral()[?7h[?12l[?25h[?25l[?7lsage: (t^(-6)).integral() +[?7h[?12l[?25h[?2004l[?7ht^-5 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(t^(-6)).integral()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)).integral()[?7h[?12l[?25h[?25l[?7l2)).integral()[?7h[?12l[?25h[?25l[?7l()[?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: (t^(-2)).integral() +[?7h[?12l[?25h[?2004l[?7h2*t^-1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(t^(-2)).integral()[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7lR. = LaurentSeriesRing(F)[?7h[?12l[?25h[?25l[?7llaurent_anlytic_part(lau)[?7h[?12l[?25h[?25l[?7lsage: laurent_analytic_part(lau) +[?7h[?12l[?25h[?2004l[?7ht^-6 + t^-2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llaurent_analytic_part(lau)[?7h[?12l[?25h[?25l[?7l().integral()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lintegral()[?7h[?12l[?25h[?25l[?7lsage: laurent_analytic_part(lau).integral() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ZeroDivisionError Traceback (most recent call last) +Input In [22], in () +----> 1 laurent_analytic_part(lau).integral() + +File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1654, in sage.rings.laurent_series_ring_element.LaurentSeries.integral() + 1652 + 1653 if n < 0: +-> 1654 v = [a[i]/(n+i+1) for i in range(min(-1-n,len(a)))] + [0] + 1655 else: + 1656 v = [] + +File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__() + 1740 + 1741 try: +-> 1742 return coercion_model.bin_op(left, right, truediv) + 1743 except TypeError: + 1744 return NotImplemented + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op() + 1202 self._record_exception() + 1203 else: +-> 1204 return PyObject_CallObject(op, xy) + 1205 + 1206 if op is mul: + +File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__() + 1735 cdef int cl = classify_elements(left, right) + 1736 if HAVE_SAME_PARENT(cl): +-> 1737 return (left)._div_(right) + 1738 if BOTH_ARE_ELEMENT(cl): + 1739 return coercion_model.bin_op(left, right, truediv) + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_() + 2621 right_inverse = self.__modulus.inverses[(right).ivalue] + 2622 if right_inverse is None: +-> 2623 raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist") + 2624 else: + 2625 return self._new_c((self.ivalue * (right_inverse).ivalue) % self.__modulus.int32) + +ZeroDivisionError: inverse of Mod(0, 3) does not exist +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llaurent_analytic_part(lau).integral()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?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: laurent_analytic_part(lau).int() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [23], in () +----> 1 laurent_analytic_part(lau).int() + +File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() + 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' + 493 """ +--> 494 return self.getattr_from_category(name) + 495 + 496 cdef getattr_from_category(self, name): + +File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() + 505 else: + 506 cls = P._abstract_element_class +--> 507 return getattr_from_other_class(self, cls, name) + 508 + 509 def __dir__(self): + +File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() + 359 dummy_error_message.cls = type(self) + 360 dummy_error_message.name = name +--> 361 raise AttributeError(dummy_error_message) + 362 attribute = attr + 363 # Check for a descriptor (__get__ in Python) + +AttributeError: 'sage.rings.laurent_series_ring_element.LaurentSeries' object has no attribute 'int' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llaurent_analytic_part(lau).int()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7le()[?7h[?12l[?25h[?25l[?7lg()[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7la()[?7h[?12l[?25h[?25l[?7ll()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: laurent_analytic_part(lau).integral() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ZeroDivisionError Traceback (most recent call last) +Input In [24], in () +----> 1 laurent_analytic_part(lau).integral() + +File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1654, in sage.rings.laurent_series_ring_element.LaurentSeries.integral() + 1652 + 1653 if n < 0: +-> 1654 v = [a[i]/(n+i+1) for i in range(min(-1-n,len(a)))] + [0] + 1655 else: + 1656 v = [] + +File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__() + 1740 + 1741 try: +-> 1742 return coercion_model.bin_op(left, right, truediv) + 1743 except TypeError: + 1744 return NotImplemented + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op() + 1202 self._record_exception() + 1203 else: +-> 1204 return PyObject_CallObject(op, xy) + 1205 + 1206 if op is mul: + +File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__() + 1735 cdef int cl = classify_elements(left, right) + 1736 if HAVE_SAME_PARENT(cl): +-> 1737 return (left)._div_(right) + 1738 if BOTH_ARE_ELEMENT(cl): + 1739 return coercion_model.bin_op(left, right, truediv) + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_() + 2621 right_inverse = self.__modulus.inverses[(right).ivalue] + 2622 if right_inverse is None: +-> 2623 raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist") + 2624 else: + 2625 return self._new_c((self.ivalue * (right_inverse).ivalue) % self.__modulus.int32) + +ZeroDivisionError: inverse of Mod(0, 3) does not exist +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llaurent_analytic_part(lau).integral()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7legral()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().integral()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7legral()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(t^(-2)).integral()[?7h[?12l[?25h[?25l[?7lt[?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[?7l2)).integral()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (t^(-2) + t^(-6)).integral() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ZeroDivisionError Traceback (most recent call last) +Input In [25], in () +----> 1 (t**(-Integer(2)) + t**(-Integer(6))).integral() + +File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1654, in sage.rings.laurent_series_ring_element.LaurentSeries.integral() + 1652 + 1653 if n < 0: +-> 1654 v = [a[i]/(n+i+1) for i in range(min(-1-n,len(a)))] + [0] + 1655 else: + 1656 v = [] + +File /ext/sage/9.7/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__() + 1740 + 1741 try: +-> 1742 return coercion_model.bin_op(left, right, truediv) + 1743 except TypeError: + 1744 return NotImplemented + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op() + 1202 self._record_exception() + 1203 else: +-> 1204 return PyObject_CallObject(op, xy) + 1205 + 1206 if op is mul: + +File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__() + 1735 cdef int cl = classify_elements(left, right) + 1736 if HAVE_SAME_PARENT(cl): +-> 1737 return (left)._div_(right) + 1738 if BOTH_ARE_ELEMENT(cl): + 1739 return coercion_model.bin_op(left, right, truediv) + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:2623, in sage.rings.finite_rings.integer_mod.IntegerMod_int._div_() + 2621 right_inverse = self.__modulus.inverses[(right).ivalue] + 2622 if right_inverse is None: +-> 2623 raise ZeroDivisionError(f"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist") + 2624 else: + 2625 return self._new_c((self.ivalue * (right_inverse).ivalue) % self.__modulus.int32) + +ZeroDivisionError: inverse of Mod(0, 3) does not exist +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(t^(-2) + t^(-6)).integral()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()) + t^(-6).integral()[?7h[?12l[?25h[?25l[?7l(). + t^(-6).integral()[?7h[?12l[?25h[?25l[?7li + t^(-6).integral()[?7h[?12l[?25h[?25l[?7lin + t^(-6).integral()[?7h[?12l[?25h[?25l[?7lint + t^(-6).integral()[?7h[?12l[?25h[?25l[?7le + t^(-6).integral()[?7h[?12l[?25h[?25l[?7lg + t^(-6).integral()[?7h[?12l[?25h[?25l[?7lr + t^(-6).integral()[?7h[?12l[?25h[?25l[?7la + t^(-6).integral()[?7h[?12l[?25h[?25l[?7ll + t^(-6).integral()[?7h[?12l[?25h[?25l[?7l( + t^(-6).integral()[?7h[?12l[?25h[?25l[?7l() + t^(-6).integral()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(t^(-6).integral()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: (t^(-2)).integral() + (t^(-6)).integral() +[?7h[?12l[?25h[?2004l[?7ht^-5 + 2*t^-1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llaurent_analytic_part(lau).integral()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliaries/laurent_analytic_part.sage')[?7h[?12l[?25h[?25l[?7l(uxilliaries/laurent_analytic_part.sage')[?7h[?12l[?25h[?25l[?7lsage: load('auxilliaries/laurent_analytic_part.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('auxilliaries/laurent_analytic_part.sage')[?7h[?12l[?25h[?25l[?7l(t^(-2)).integral() + (t^(-6)).integral()[?7h[?12l[?25h[?25l[?7lload('auxilliaries/laurent_analytic_part.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('auxilliaries/laurent_analytic_part.sage')[?7h[?12l[?25h[?25l[?7laurent_anaytic_part(lau).itegral()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7llytic_part[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: laurent_integral(laurent_analytic_part(lau)) +[?7h[?12l[?25h[?2004l[?7ht^-5 + 2*t^-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$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.7, Release Date: 2022-09-19 │ +│ Using Python 3.10.5. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRt. = LaurentSeriesRing(F)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llaurent_integral(laurent_analytic_part(lau))[?7h[?12l[?25h[?25l[?7load('auxilliaries/laurent_nalytic_part.sage')[?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'auxilliaries/laurent_analytic_part.sage')[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l(t.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +OSError Traceback (most recent call last) +Input In [1], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:244, in load(filename, globals, attach) + 242 break + 243 else: +--> 244 raise IOError('did not find file %r to load or attach' % filename) + 246 ext = os.path.splitext(fpath)[1].lower() + 247 if ext == '.py': + +OSError: did not find file 'sage/superelliptic_drw/superelliptic_drw_auxilliaries.sage' to load or attach +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRt. = LaurentSeriesRing(F)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: Rx +[?7h[?12l[?25h[?2004l[?7hUnivariate Polynomial Ring in x over Finite Field of size 3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i in lau.exponents():[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.genus()[?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[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: g = x^3 - x +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = x^3 - x[?7h[?12l[?25h[?25l[?7l(x+1) - g[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g(x = C.x/C.y) +[?7h[?12l[?25h[?2004lsage/rings/polynomial/polynomial_zmod_flint.pyx:7: DeprecationWarning: invalid escape sequence '\Z' + """ +sage/rings/polynomial/polynomial_zmod_flint.pyx:7: DeprecationWarning: invalid escape sequence '\Z' + """ +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [5], in () +----> 1 g(x = C.x/C.y) + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zmod_flint.pyx:332, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint.__call__() + 330 nmod_poly_compose(&t.x, &self.x, &y.x) + 331 return t +--> 332 return Polynomial.__call__(self, *x, **kwds) + 333 + 334 @coerce_binop + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:870, in sage.rings.polynomial.polynomial_element.Polynomial.__call__() + 868 # This can save lots of coercions when the common parent is the + 869 # polynomial's base ring (e.g., for evaluations at integers). +--> 870 cst, aa = coercion_model.canonical_coercion(cst, a) + 871 # Use fast multiplication actions like matrix × scalar. + 872 # If there is no action, replace a by an element of the + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1393, in sage.structure.coerce.CoercionModel.canonical_coercion() + 1391 self._record_exception() + 1392 +-> 1393 raise TypeError("no common canonical parent for objects with parents: '%s' and '%s'"%(xp, yp)) + 1394 + 1395 + +TypeError: no common canonical parent for objects with parents: 'Finite Field of size 3' and '' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 +....: ....: 0 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10 * +....: C.y - +....: ....: C.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 +....: ....: 0 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10 * +....: C.y - +....: ....: C.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx +[?7h[?12l[?25h[?2004l Input In [8] + ((C.x**Integer(28) - C.x**Integer(26) + C.x**Integer(25) - C.x**Integer(24) + C.x**Integer(23) - C.x**Integer(22) - C.x**Integer(21) + C.x**Integer(20) + C.x**Integer(19) + C.x**Integer(18) + C.x**Integer(17) + C.x**Integer(15) - C.x**Integer(14) + C.x**Integer(13) + C.x**Integer(12) + C.x**Integer(11) - C.x**Integer(1) + ^ +SyntaxError: invalid syntax. Perhaps you forgot a comma? + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om == ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^ 1 +....: 0 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y -   +....: C.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l (C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^2 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^1 - C.x^1 0 + - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^1*C.y + C.x^10*C.y - C +.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y)*C.dx[?7h[?12l[?25h[?25l[?7l + %%! AbelianGroupWithValues AdditiveAbelianGroupWrapperElement  +....: .x^9* AA AbelianVariety AdditiveMagmas  + AbelianGroup AdditiveAbelianGroup AffineCryptosystem > + AbelianGroupMorphism AdditiveAbelianGroupWrapper AffineGroup  + [?7h[?12l[?25h[?25l[?7l((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 + - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx + +[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + [?7h[?12l[?25h[?25l[?7lom = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l +  + [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(xi.f)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmposition + decomposition decomposition_g0_pth_power decomposition_omega8_hpdh  +  decomposition_g0_g8 decomposition_omega0_hpdh  + decomposition_g0_p2th_power decomposition_omega0_omega8  + + [?7h[?12l[?25h[?25l[?7l + decomposition  + + + [?7h[?12l[?25h[?25l[?7l_g0_g8 + decomposition  + decomposition_g0_g8 [?7h[?12l[?25h[?25l[?7lp2th_power + + decomposition_g0_g8  + decomposition_g0_p2th_power[?7h[?12l[?25h[?25l[?7lomega0_omega8 + + + decomposition_g0_p2th_power decomposition_omega0_omega8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lhpdh + + decomposition_omega0_hpdh  + decomposition_omega0_omega8[?7h[?12l[?25h[?25l[?7lg0_pthpower + decomposition_g0_pth_power  + decomposition_omega0_hpdh [?7h[?12l[?25h[?25l[?7lomega8hpdh + decomposition_g0_pth_power  decomposition_omega8_hpdh [?7h[?12l[?25h[?25l[?7l( + + + +[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega8_hpdh(om) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Input In [10], in () +----> 1 decomposition_omega8_hpdh(om) + +File :32, in decomposition_omega8_hpdh(omega, prec) + +NameError: name 'laurent_analytic_part' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 + - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3-x)^3 +x^3 - x,2) +  + [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lom = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om) +  + [?7h[?12l[?25h[?25l[?7lsage: decomposition_omega8_hpdh(om) +[?7h[?12l[?25h[?2004l[?7h(((x^37 + x^36 - x^35 - x^31 + x^30 + x^29 + x^28 - x^26 + x^25 + x^24 - x^22 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^25*y - x*y)) dx, + 0) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.cartier().expansion_at_infty() +  + [?7h[?12l[?25h[?25l[?7lexpansion_at_ifty(prec = 50)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7lsage: om.expansion_at_infty(prec = 50) +[?7h[?12l[?25h[?2004l[?7ht^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2 + 2 + 2*t^4 + t^6 + t^8 + 2*t^14 + 2*t^16 + t^24 + t^28 + 2*t^30 + O(t^32) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 + - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega8_hpdh(om) +[?7h[?12l[?25h[?2004lomega_analytic t^-6 + t^-2 +omega_analytic (x^30 + x^10*y^4)/y^6 +omega_analytic ((x^30 + x^28 + x^20 + x^12)/(x^24*y - y)) dx +omega8 ((x^37 + x^36 - x^35 - x^31 + x^30 + x^29 + x^28 - x^26 + x^25 + x^24 - x^22 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^25*y - x*y)) dx +dh 0 dx +[?7h(((x^37 + x^36 - x^35 - x^31 + x^30 + x^29 + x^28 - x^26 + x^25 + x^24 - x^22 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^25*y - x*y)) dx, + 0) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l= superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 + - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lw[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lcomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega8_hpdh(om) +[?7h[?12l[?25h[?2004lomega_analytic t^-6 + t^-2 +omega_analytic, superelliptic_function(C, omega_analytic), Cv.diffn() (x^30 + x^10*y^4)/y^6 (x^27 + x^25 + x^17 + x^9)/(x^24 + 2) (x^3/y) dx +omega_analytic ((x^30 + x^28 + x^20 + x^12)/(x^24*y - y)) dx +omega8 ((x^37 + x^36 - x^35 - x^31 + x^30 + x^29 + x^28 - x^26 + x^25 + x^24 - x^22 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^25*y - x*y)) dx +dh 0 dx +[?7h(((x^37 + x^36 - x^35 - x^31 + x^30 + x^29 + x^28 - x^26 + x^25 + x^24 - x^22 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^25*y - x*y)) dx, + 0) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 + - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega8_hpdh(om) +[?7h[?12l[?25h[?2004lomega_analytic t^-6 + t^-2 +omega_analytic, superelliptic_function(C, omega_analytic), Cv.diffn() (x^30 + x^10*y^4)/y^6 (x^27 + x^25 + x^17 + x^9)/(x^24 + 2) (x^3/y) dx +omega_analytic ((x^30 + x^28 + x^20 + x^12)/(x^24*y - y)) dx +omega8 ((x^37 + x^36 - x^35 - x^31 + x^30 + x^29 + x^28 - x^26 + x^25 + x^24 - x^22 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^25*y - x*y)) dx +dh 0 dx +omega8.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + O(t^-8) +[?7h(((x^37 + x^36 - x^35 - x^31 + x^30 + x^29 + x^28 - x^26 + x^25 + x^24 - x^22 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^25*y - x*y)) dx, + 0) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.expansion_at_infty(prec = 50) +  + [?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7lsage: om.expansion_at_infty(prec = 50) +[?7h[?12l[?25h[?2004l[?7ht^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2 + 2 + 2*t^4 + t^6 + t^8 + 2*t^14 + 2*t^16 + t^24 + t^28 + 2*t^30 + O(t^32) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7laom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7luom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7lrom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7leom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7lnom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7ltom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7l_om.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7laom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7lnom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7laom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7llom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7lyom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7ltom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7liom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7lcom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7l_om.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7lpom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7laom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7lrom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7ltom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7l(om.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: laurent_analytic_part(om.expansion_at_infty(prec = 50)) +[?7h[?12l[?25h[?2004l[?7ht^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llaurent_analytic_part(om.expansion_at_infty(prec = 50))[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l-auxf.t.teichmuller()diffn() +  + [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l= ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 + - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega8_hpdh(om) +[?7h[?12l[?25h[?2004lomega_analytic t^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2 +omega_analytic, superelliptic_function(C, omega_analytic), Cv.diffn() (x^90 + x^80*y^2 - x^70*y^4 + x^20*y^14 + x^10*y^16)/y^18 (x^81 + x^80 + 2*x^79 + x^74 + x^73 + 2*x^72 + 2*x^71 + 2*x^66 + x^65 + 2*x^63 + x^57 + x^50 + x^49 + 2*x^42 + x^41 + x^33 + x^26 + x^25 + 2*x^18 + x^17 + x^9)/(x^72 + 2) (x^3/y) dx +omega_analytic ((x^84 + x^83 - x^82 + x^77 + x^76 - x^75 - x^74 - x^69 + x^68 - x^66 + x^60 + x^53 + x^52 - x^45 + x^44 + x^36 + x^29 + x^28 - x^21 + x^20 + x^12)/(x^72*y - y)) dx +omega8 ((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx +dh ((x^30 + x^28 + x^20 + x^12)/(x^24*y - y)) dx +omega8.expansion_at_infty() t^-2 + 2 + t^2 + 2*t^4 + t^6 + O(t^8) +[?7h(((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx, + ((x^38 + 2*x^36 + x^30 + x^12)/(x^40 + x^32 + x^24 + 2*x^16 + 2*x^8 + 2))*y) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = C.y/(C.x)^(g+1)[?7h[?12l[?25h[?25l[?7l= C.y/(C.x)^(g+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[?7lg(x = C.x/C.y)[?7h[?12l[?25h[?25l[?7l =x^3 - x[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7lsage: g = C.genus() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = C.y/(C.x)^(g+1)[?7h[?12l[?25h[?25l[?7l= C.y/(C.x)^(g+1)[?7h[?12l[?25h[?25l[?7lsage: v = C.y/(C.x)^(g+1) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv = C.y/(C.x)^(g+1)[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: v.expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht + O(t^21) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldexpansion_at_infty()[?7h[?12l[?25h[?25l[?7liexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lfexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lfexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lnexpansion_at_infty()[?7h[?12l[?25h[?25l[?7l(expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()expansion_at_infty()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: v.diffn().expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7h1 + O(t^10) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 + - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega8_hpdh(om) +[?7h[?12l[?25h[?2004lomega_analytic t^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2 +omega_analytic, superelliptic_function(C, omega_analytic), Cv.diffn() (x^90 + x^80*y^2 - x^70*y^4 + x^20*y^14 + x^10*y^16)/y^18 (x^81 + x^80 + 2*x^79 + x^74 + x^73 + 2*x^72 + 2*x^71 + 2*x^66 + x^65 + 2*x^63 + x^57 + x^50 + x^49 + 2*x^42 + x^41 + x^33 + x^26 + x^25 + 2*x^18 + x^17 + x^9)/(x^72 + 2) (x^3/y) dx +omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + O(t^-8) +omega_analytic ((x^84 + x^83 - x^82 + x^77 + x^76 - x^75 - x^74 - x^69 + x^68 - x^66 + x^60 + x^53 + x^52 - x^45 + x^44 + x^36 + x^29 + x^28 - x^21 + x^20 + x^12)/(x^72*y - y)) dx +omega8 ((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx +dh ((x^30 + x^28 + x^20 + x^12)/(x^24*y - y)) dx +omega8.expansion_at_infty() t^-2 + 2 + t^2 + 2*t^4 + t^6 + O(t^8) +[?7h(((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx, + ((x^38 + 2*x^36 + x^30 + x^12)/(x^40 + x^32 + x^24 + 2*x^16 + 2*x^8 + 2))*y) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l= superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 + - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega8_hpdh(om) +[?7h[?12l[?25h[?2004lomega_analytic t^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2 +omega_analytic, superelliptic_function(C, omega_analytic), Cv.diffn() (x^90 + x^80*y^2 - x^70*y^4 + x^20*y^14 + x^10*y^16)/y^18 (x^81 + x^80 + 2*x^79 + x^74 + x^73 + 2*x^72 + 2*x^71 + 2*x^66 + x^65 + 2*x^63 + x^57 + x^50 + x^49 + 2*x^42 + x^41 + x^33 + x^26 + x^25 + 2*x^18 + x^17 + x^9)/(x^72 + 2) (x^3/y) dx +omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + 2*t^2 + t^14 + t^16 + t^28 + 2*t^30 + O(t^32) +omega_analytic ((x^84 + x^83 - x^82 + x^77 + x^76 - x^75 - x^74 - x^69 + x^68 - x^66 + x^60 + x^53 + x^52 - x^45 + x^44 + x^36 + x^29 + x^28 - x^21 + x^20 + x^12)/(x^72*y - y)) dx +omega8 ((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx +dh ((x^30 + x^28 + x^20 + x^12)/(x^24*y - y)) dx +omega8.expansion_at_infty() t^-2 + 2 + t^2 + 2*t^4 + t^6 + t^8 + t^14 + t^16 + t^24 + t^34 + 2*t^36 + t^38 + t^40 + 2*t^46 + O(t^48) +[?7h(((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx, + ((x^38 + 2*x^36 + x^30 + x^12)/(x^40 + x^32 + x^24 + 2*x^16 + 2*x^8 + 2))*y) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 + - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega8_hpdh(om) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +KeyError Traceback (most recent call last) +File /ext/sage/9.7/src/sage/structure/category_object.pyx:839, in sage.structure.category_object.CategoryObject.getattr_from_category() + 838 try: +--> 839 return self.__cached_methods[name] + 840 except KeyError: + +KeyError: 'integer_ring' + +During handling of the above exception, another exception occurred: + +AttributeError Traceback (most recent call last) +File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce) + 705 try: +--> 706 x, y = resolve_fractions(x0, y0) + 707 except (AttributeError, TypeError): + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:683, in FractionField_generic._element_constructor_..resolve_fractions(x, y) + 682 def resolve_fractions(x, y): +--> 683 xn = x.numerator() + 684 xd = x.denominator() + +File /ext/sage/9.7/src/sage/categories/complete_discrete_valuation.py:281, in CompleteDiscreteValuationFields.ElementMethods.numerator(self) + 252 """ + 253 Return the numerator of this element, normalized in such a + 254 way that `x = x.numerator() / x.denominator()` always holds + (...) + 279  7^5 + O(7^10) + 280 """ +--> 281 R = self.parent().integer_ring() + 282 return R(self * self.denominator()) + +File /ext/sage/9.7/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/9.7/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/9.7/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: 'PolynomialRing_dense_mod_p_with_category' object has no attribute '_cached_repr' + +During handling of the above exception, another exception occurred: + +TypeError Traceback (most recent call last) +Input In [49], in () +----> 1 decomposition_omega8_hpdh(om) + +File :34, in decomposition_omega8_hpdh(omega, prec) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 159 print(type(C), C) + 160 print(type(C._element_constructor), C._element_constructor) +--> 161 raise + 162 + 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:708, in FractionField_generic._element_constructor_(self, x, y, coerce) + 706 x, y = resolve_fractions(x0, y0) + 707 except (AttributeError, TypeError): +--> 708 raise TypeError("cannot convert {!r}/{!r} to an element of {}".format( + 709 x0, y0, self)) + 710 try: + 711 return self._element_class(self, x, y, coerce=coerce) + +TypeError: cannot convert t^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2/1 to an element of Fraction Field of Univariate Polynomial Ring in T over Finite Field of size 3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 + - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega8_hpdh(om) +[?7h[?12l[?25h[?2004lomega_analytic (T^16 + T^14 + 2*T^4 + T^2 + 1)/T^18 +omega_analytic, superelliptic_function(C, omega_analytic), Cv.diffn() (x^90 + x^80*y^2 - x^70*y^4 + x^20*y^14 + x^10*y^16)/y^18 (x^81 + x^80 + 2*x^79 + x^74 + x^73 + 2*x^72 + 2*x^71 + 2*x^66 + x^65 + 2*x^63 + x^57 + x^50 + x^49 + 2*x^42 + x^41 + x^33 + x^26 + x^25 + 2*x^18 + x^17 + x^9)/(x^72 + 2) (x^3/y) dx +omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + 2*t^2 + t^14 + t^16 + t^28 + 2*t^30 + O(t^32) +omega_analytic ((x^84 + x^83 - x^82 + x^77 + x^76 - x^75 - x^74 - x^69 + x^68 - x^66 + x^60 + x^53 + x^52 - x^45 + x^44 + x^36 + x^29 + x^28 - x^21 + x^20 + x^12)/(x^72*y - y)) dx +omega8 ((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx +dh ((x^30 + x^28 + x^20 + x^12)/(x^24*y - y)) dx +omega8.expansion_at_infty() t^-2 + 2 + t^2 + 2*t^4 + t^6 + t^8 + t^14 + t^16 + t^24 + t^34 + 2*t^36 + t^38 + t^40 + 2*t^46 + O(t^48) +[?7h(((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx, + ((x^38 + 2*x^36 + x^30 + x^12)/(x^40 + x^32 + x^24 + 2*x^16 + 2*x^8 + 2))*y) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 + - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega8_hpdh(om) +[?7h[?12l[?25h[?2004lomega_analytic (T^16 + T^14 + 2*T^4 + T^2 + 1)/T^18 +--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [57], in () +----> 1 decomposition_omega8_hpdh(om) + +File :39, in decomposition_omega8_hpdh(omega, prec) + +AttributeError: 'superelliptic_function' object has no attribute 'expanstion_at_infty' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 + - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega8_hpdh(om) +[?7h[?12l[?25h[?2004lomega_analytic (T^16 + T^14 + 2*T^4 + T^2 + 1)/T^18 +omega_analytic, superelliptic_function(C, omega_analytic), Cv.diffn() (x^90 + x^80*y^2 - x^70*y^4 + x^20*y^14 + x^10*y^16)/y^18 (x^81 + x^80 + 2*x^79 + x^74 + x^73 + 2*x^72 + 2*x^71 + 2*x^66 + x^65 + 2*x^63 + x^57 + x^50 + x^49 + 2*x^42 + x^41 + x^33 + x^26 + x^25 + 2*x^18 + x^17 + x^9)/(x^72 + 2) (x^3/y) dx t^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2 + 1 + t^2 + t^12 + 2*t^14 + 2*t^16 + t^18 + 2*t^28 + 2*t^30 + O(t^32) +omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + 2*t^2 + t^14 + t^16 + t^28 + 2*t^30 + O(t^32) +omega_analytic ((x^84 + x^83 - x^82 + x^77 + x^76 - x^75 - x^74 - x^69 + x^68 - x^66 + x^60 + x^53 + x^52 - x^45 + x^44 + x^36 + x^29 + x^28 - x^21 + x^20 + x^12)/(x^72*y - y)) dx +omega8 ((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx +dh ((x^30 + x^28 + x^20 + x^12)/(x^24*y - y)) dx +omega8.expansion_at_infty() t^-2 + 2 + t^2 + 2*t^4 + t^6 + t^8 + t^14 + t^16 + t^24 + t^34 + 2*t^36 + t^38 + t^40 + 2*t^46 + O(t^48) +[?7h(((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx, + ((x^38 + 2*x^36 + x^30 + x^12)/(x^40 + x^32 + x^24 + 2*x^16 + 2*x^8 + 2))*y) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 + - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega8_hpdh(om) +[?7h[?12l[?25h[?2004lomega_analytic (T^16 + T^14 + 2*T^4 + T^2 + 1)/T^18 +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [65], in () +----> 1 decomposition_omega8_hpdh(om) + +File :39, in decomposition_omega8_hpdh(omega, prec) + +TypeError: superelliptic_function.diffn() got an unexpected keyword argument 'prec' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 + - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega8_hpdh(om) +[?7h[?12l[?25h[?2004lomega_analytic (T^16 + T^14 + 2*T^4 + T^2 + 1)/T^18 +expansions t^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2 + 1 + t^2 + t^12 + 2*t^14 + 2*t^16 + t^18 + 2*t^28 + 2*t^30 + O(t^32) + 1 + 2*t^16 + 2*t^48 + O(t^50) + t^-18 + t^-16 + 2*t^-14 + t^-4 + 2*t^2 + t^14 + t^16 + t^28 + 2*t^30 + O(t^32) +omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + 2*t^2 + t^14 + t^16 + t^28 + 2*t^30 + O(t^32) +omega_analytic ((x^84 + x^83 - x^82 + x^77 + x^76 - x^75 - x^74 - x^69 + x^68 - x^66 + x^60 + x^53 + x^52 - x^45 + x^44 + x^36 + x^29 + x^28 - x^21 + x^20 + x^12)/(x^72*y - y)) dx +omega8 ((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx +dh ((x^30 + x^28 + x^20 + x^12)/(x^24*y - y)) dx +omega8.expansion_at_infty() t^-2 + 2 + t^2 + 2*t^4 + t^6 + t^8 + t^14 + t^16 + t^24 + t^34 + 2*t^36 + t^38 + t^40 + 2*t^46 + O(t^48) +[?7h(((x^77 - x^76 + x^75 - x^74 + x^73 + x^72 + x^69 - x^67 + x^65 + x^61 + x^57 + x^56 + x^53 - x^51 + x^49 - x^48 + x^45 + x^43 + x^41 + x^37 + x^33 + x^32 + x^29 - x^27 + x^25 - x^24 + x^21 + x^19 + x^17 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx, + ((x^38 + 2*x^36 + x^30 + x^12)/(x^40 + x^32 + x^24 + 2*x^16 + 2*x^8 + 2))*y) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lloal[?7h[?12l[?25h[?25l[?7lsage: loal + + + + + + + + + [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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('init.sage')[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l:218: DeprecationWarning: invalid escape sequence '\s' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + + + + [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l:218: DeprecationWarning: invalid escape sequence '\s' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + + [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l:218: DeprecationWarning: invalid escape sequence '\s' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + [?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  + + [?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.y.exansion_at_infty()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.uniformizer() +[?7h[?12l[?25h[?2004l[?7h(x^4/(x^8 + 2))*y +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.uniformizer().expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-1 + 2*t^15 + O(t^19) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.uniformizer() +[?7h[?12l[?25h[?2004l[?7h(x^4/(x^8 + 2))*y +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C.uniformizer().expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-1 + 2*t^15 + O(t^19) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l= superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.uniformizer().expansion_at_infty()[?7h[?12l[?25h[?25l[?7luniformizer().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C.uniformizer().expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-1 + 2*t^15 + O(t^19) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l:218: DeprecationWarning: invalid escape sequence '\s' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l= superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.uniformizer().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lformizer().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C.uniformizer().expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-1 + 2*t^15 + O(t^19) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?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[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: C.uniformizer().expansion_at_infty(prec = 200) +[?7h[?12l[?25h[?2004l[?7ht^-1 + 2*t^15 + 2*t^31 + 2*t^47 + 2*t^111 + 2*t^127 + 2*t^143 + 2*t^159 + t^191 + O(t^199) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l:219: DeprecationWarning: invalid escape sequence '\s' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().expansion_at_infty(prec = 200)[?7h[?12l[?25h[?25l[?7l.uniformizer().expansion_at_infty(prec = 200)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().expansion_at_infty(prec = 200)[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l= superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.uniformizer().expansion_at_infty(prec = 200)[?7h[?12l[?25h[?25l[?7luniformizer().expansion_at_infty(prec = 200)[?7h[?12l[?25h[?25l[?7lsage: C.uniformizer().expansion_at_infty(prec = 200) +[?7h[?12l[?25h[?2004la, b, delta, M, R 5 1 1 2 9 +[?7ht^-1 + 2*t^15 + 2*t^31 + 2*t^47 + 2*t^111 + 2*t^127 + 2*t^143 + 2*t^159 + t^191 + O(t^199) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().expansion_at_infty(prec = 200)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-2 + t^14 + O(t^18) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l:219: DeprecationWarning: invalid escape sequence '\s' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = suerelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l= superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.x.exansion_at_infty()[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.x.exansion_at_infty()[?7h[?12l[?25h[?25l[?7luniformizer().expansion_at_infty(prec = 200)[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lformizer().expansion_at_infty(prec = 200)[?7h[?12l[?25h[?25l[?7lsage: C.uniformizer().expansion_at_infty(prec = 200) +[?7h[?12l[?25h[?2004la, b, delta, M, R 5 1 1 2 9 +[?7ht + O(t^201) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().expansion_at_infty(prec = 200)[?7h[?12l[?25h[?25l[?7lsage: C.uniformizer().expansion_at_infty(prec = 200) +[?7h[?12l[?25h[?2004la, b, delta, M, R 5 1 1 2 9 +[?7ht + O(t^201) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().expansion_at_infty(prec = 200)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l20)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.uniformizer().expansion_at_infty(prec = 220) +[?7h[?12l[?25h[?2004la, b, delta, M, R 5 1 1 2 9 +[?7ht + O(t^221) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.uniformizer().expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()).expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l()^.expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l(.expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l().expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l-).expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l1).expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()).expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.uniformizer())^(-1).expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7lsage: ((C.uniformizer())^(-1)).expansion_at_infty(prec = 220) +[?7h[?12l[?25h[?2004la, b, delta, M, R 5 1 1 2 9 +[?7ht^-1 + 2*t^15 + 2*t^31 + 2*t^47 + 2*t^111 + 2*t^127 + 2*t^143 + 2*t^159 + t^191 + O(t^219) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.uniformizer())^(-1)).expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l320)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.uniformizer())^(-1)).expansion_at_infty(prec = 320) +[?7h[?12l[?25h[?2004la, b, delta, M, R 5 1 1 2 9 +[?7ht^-1 + 2*t^15 + 2*t^31 + 2*t^47 + 2*t^111 + 2*t^127 + 2*t^143 + 2*t^159 + t^191 + t^255 + 2*t^271 + O(t^319) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.uniformizer())^(-1)).expansion_at_infty(prec = 320)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l10)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.uniformizer())^(-1)).expansion_at_infty(prec = 1000) +[?7h[?12l[?25h[?2004la, b, delta, M, R 5 1 1 2 9 +[?7ht^-1 + 2*t^15 + 2*t^31 + 2*t^47 + 2*t^111 + 2*t^127 + 2*t^143 + 2*t^159 + t^191 + t^255 + 2*t^271 + 2*t^319 + 2*t^431 + 2*t^447 + 2*t^463 + 2*t^479 + t^559 + t^575 + t^591 + t^623 + t^751 + 2*t^975 + O(t^999) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty(prec = 20) +[?7h[?12l[?25h[?2004l[?7ht^-2 + t^14 + O(t^18) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l30)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l10)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty(prec = 100) +[?7h[?12l[?25h[?2004l[?7ht^-2 + t^14 + 2*t^30 + 2*t^46 + 2*t^62 + O(t^98) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7luniformizer().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lformizer().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.uniformizer() +[?7h[?12l[?25h[?2004la, b, delta, M, R 5 1 1 2 9 +[?7h1/x^5*y +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lpansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7lsage: C.uniformizer().expansion_at_infty(prec = 220) +[?7h[?12l[?25h[?2004la, b, delta, M, R 5 1 1 2 9 +[?7ht + O(t^221) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lformizer[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a = C.uniformizer() +[?7h[?12l[?25h[?2004la, b, delta, M, R 5 1 1 2 9 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = C.uniformizer()[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()).expansion_at_infty(prec = 10)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a^(-1).expansion_at_infty(prec = 10)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l20)[?7h[?12l[?25h[?25l[?7l()[?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[?7l10)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (a^(-1)).expansion_at_infty(prec = 100) +[?7h[?12l[?25h[?2004l[?7ht^-1 + 2*t^15 + 2*t^31 + 2*t^47 + O(t^99) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = C.uniformizer()[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a^(-1) +[?7h[?12l[?25h[?2004l[?7h(x^4/(x^8 + 2))*y +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: C.y^2 +[?7h[?12l[?25h[?2004l[?7hx^9 + 2*x +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y^2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexpansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty(prec = 100) +[?7h[?12l[?25h[?2004l[?7ht^-2 + t^14 + 2*t^30 + 2*t^46 + 2*t^62 + O(t^98) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx[?7h[?12l[?25h[?25l[?7lt. = LaurentSeriesRing(F)[?7h[?12l[?25h[?25l[?7l. = LaurentSeriesRing(F)[?7h[?12l[?25h[?25l[?7lsage: Rt. = LaurentSeriesRing(F) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly^2[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: C.y.expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-9 + 2*t^7 + O(t^11) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.y.expansion_at_infty(prec = 100) +[?7h[?12l[?25h[?2004l[?7ht^-9 + 2*t^7 + 2*t^23 + 2*t^55 + 2*t^71 + t^87 + O(t^91) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a^(-1)).expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lt2integral() + (t^(-6)).integral()[?7h[?12l[?25h[?25l[?7l^[?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)).integral() + (t^(-6)).integral()[?7h[?12l[?25h[?25l[?7l()).integral() + (t^(-6)).integral()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()).integral() + (t^(-6)).integral()[?7h[?12l[?25h[?25l[?7l() + t^(-6)).integral()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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.coordinates()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?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[?7lt[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: xx = t^(-2) + t^(14) + 2*t^(30) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lt[?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[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: yy = t^(-9) + 2*t^7 + 2*t^23 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx = t^(-2) + t^(14) + 2*t^(30)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l8)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: xx^4*yy/(xx^8 - 1) +[?7h[?12l[?25h[?2004l[?7ht^-1 + 2*t^15 + O(t^19) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la^(-1)[?7h[?12l[?25h[?25l[?7l = C.uniformizer()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx^4*yy/(xx^8 - 1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?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(x - a^(-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[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCx - a^(-2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.x - a^(-2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.x - a^(-2)).expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7h2*t^14 + O(t^34) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x - a^(-2)).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.x - a^(-2)).expansion_at_infty(prec = 100) +[?7h[?12l[?25h[?2004l[?7h2*t^14 + 2*t^62 + t^110 + O(t^114) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexpansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty(prec = 100) +[?7h[?12l[?25h[?2004l[?7ht^-2 + t^14 + 2*t^30 + 2*t^46 + 2*t^62 + O(t^98) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la^(-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[?7lxx^4*yy/(xx^8 - 1)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: xx^8 - 1 +[?7h[?12l[?25h[?2004l[?7ht^-16 + 1 + 2*t^16 + 2*t^48 + t^64 + t^80 + t^112 + t^144 + 2*t^160 + 2*t^176 + 2*t^208 + t^224 + t^240 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx^8 - 1[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy = t^(-9) + 2*t^7 + 2*t^23[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: yy/xx^5 +[?7h[?12l[?25h[?2004l[?7ht + O(t^21) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy/xx^5[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRt. = LaurentSeriesRing(F)[?7h[?12l[?25h[?25l[?7lt. = LaurentSeriesRing(F)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: Rt. = LaurentSeriesRing(F, prec = 100) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [116], in () +----> 1 Rt = LaurentSeriesRing(F, prec = Integer(100), names=('t',)); (t,) = Rt._first_ngens(1) + +File /ext/sage/9.7/src/sage/misc/classcall_metaclass.pyx:320, in sage.misc.classcall_metaclass.ClasscallMetaclass.__call__() + 318 """ + 319 if cls.classcall is not None: +--> 320 return cls.classcall(cls, *args, **kwds) + 321 else: + 322 # Fast version of type.__call__(cls, *args, **kwds) + +File /ext/sage/9.7/src/sage/rings/laurent_series_ring.py:201, in LaurentSeriesRing.__classcall__(cls, *args, **kwds) + 199 power_series = args[0] + 200 else: +--> 201 power_series = PowerSeriesRing(*args, **kwds) + 203 return UniqueRepresentation.__classcall__(cls, power_series) + +TypeError: PowerSeriesRing() got an unexpected keyword argument 'prec' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRt. = LaurentSeriesRing(F, prec = 100)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldprec = 10)[?7h[?12l[?25h[?25l[?7leprec = 10)[?7h[?12l[?25h[?25l[?7lfprec = 10)[?7h[?12l[?25h[?25l[?7laprec = 10)[?7h[?12l[?25h[?25l[?7luprec = 10)[?7h[?12l[?25h[?25l[?7llprec = 10)[?7h[?12l[?25h[?25l[?7ltprec = 10)[?7h[?12l[?25h[?25l[?7l_prec = 10)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li = 10)[?7h[?12l[?25h[?25l[?7ls = 10)[?7h[?12l[?25h[?25l[?7li = 10)[?7h[?12l[?25h[?25l[?7lo = 10)[?7h[?12l[?25h[?25l[?7ln = 10)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: Rt. = LaurentSeriesRing(F, default_precision = 100) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [117], in () +----> 1 Rt = LaurentSeriesRing(F, default_precision = Integer(100), names=('t',)); (t,) = Rt._first_ngens(1) + +File /ext/sage/9.7/src/sage/misc/classcall_metaclass.pyx:320, in sage.misc.classcall_metaclass.ClasscallMetaclass.__call__() + 318 """ + 319 if cls.classcall is not None: +--> 320 return cls.classcall(cls, *args, **kwds) + 321 else: + 322 # Fast version of type.__call__(cls, *args, **kwds) + +File /ext/sage/9.7/src/sage/rings/laurent_series_ring.py:201, in LaurentSeriesRing.__classcall__(cls, *args, **kwds) + 199 power_series = args[0] + 200 else: +--> 201 power_series = PowerSeriesRing(*args, **kwds) + 203 return UniqueRepresentation.__classcall__(cls, power_series) + +TypeError: PowerSeriesRing() got an unexpected keyword argument 'default_precision' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRt. = LaurentSeriesRing(F, default_precision = 100)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = 10)[?7h[?12l[?25h[?25l[?7l = 10)[?7h[?12l[?25h[?25l[?7l = 10)[?7h[?12l[?25h[?25l[?7l = 10)[?7h[?12l[?25h[?25l[?7l = 10)[?7h[?12l[?25h[?25l[?7lsage: Rt. = LaurentSeriesRing(F, default_prec = 100) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRt. = LaurentSeriesRing(F, default_prec = 100)[?7h[?12l[?25h[?25l[?7lision = 100)[?7h[?12l[?25h[?25l[?7lprec = 100)[?7h[?12l[?25h[?25l[?7lyy/xx^5[?7h[?12l[?25h[?25l[?7lxx^8 - 1[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l(C.x - ^(-2)).expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lxx^4*yy/(xx^8 - 1)[?7h[?12l[?25h[?25l[?7lyy = t^(-9) +2*t^7 + 2*t^23[?7h[?12l[?25h[?25l[?7lxx2t^(14) + 2*t^(30)[?7h[?12l[?25h[?25l[?7lsage: xx = t^(-2) + t^(14) + 2*t^(30) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy/xx^5[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l = t^(-9) + 2*t^7 + 2*t^23[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l t^(-9) + 2*t^7 + 2*t^23[?7h[?12l[?25h[?25l[?7lsage: yy = t^(-9) + 2*t^7 + 2*t^23 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx = t^(-2) + t^(14) + 2*t^(30)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy = t^(-9) + 2*t^7 + 2*t^23[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/xx^5[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7lsage: yy/xx^5 +[?7h[?12l[?25h[?2004l[?7ht + t^49 + t^65 + 2*t^97 + O(t^101) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx = t^(-2) + t^(14) + 2*t^(30)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^8- 1[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: xx^5/yy +[?7h[?12l[?25h[?2004l[?7ht^-1 + 2*t^47 + 2*t^63 + 2*t^95 + O(t^99) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx^5/yy[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l4*/(xx^8 - 1)[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l8[?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: xx^4*yy/(xx^8 - 1) +[?7h[?12l[?25h[?2004l[?7ht^-1 + 2*t^15 + 2*t^31 + t^47 + 2*t^79 + 2*t^95 + O(t^99) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx^4*yy/(xx^8 - 1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(x^8 - 1)[?7h[?12l[?25h[?25l[?7l(x^8 - 1)[?7h[?12l[?25h[?25l[?7l(x^8 - 1)[?7h[?12l[?25h[?25l[?7l(x^8 - 1)[?7h[?12l[?25h[?25l[?7l(x^8 - 1)[?7h[?12l[?25h[?25l[?7l(x^8 - 1)[?7h[?12l[?25h[?25l[?7l(x^8 - 1)[?7h[?12l[?25h[?25l[?7l(x^8 - 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[?7lx)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l4)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l*)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7ly)[?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[?7lsage: (xx^8 - 1)/(xx^4 * yy) +[?7h[?12l[?25h[?2004l[?7ht + t^17 + 2*t^33 + 2*t^49 + t^81 + t^97 + O(t^101) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^2[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: C.y^2 +[?7h[?12l[?25h[?2004l[?7hx^9 + 2*x +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy/xx^5[?7h[?12l[?25h[?25l[?7ly[?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[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: yy^2 - xx^9 + xx +[?7h[?12l[?25h[?2004l[?7h2*t^-2 + t^30 + t^46 + 2*t^126 + t^270 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y^2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: C.y^2 +[?7h[?12l[?25h[?2004l[?7hx^9 + 2*x +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy^2 - xx^9 + xx[?7h[?12l[?25h[?25l[?7ly[?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[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l&[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: yy^2 - (xx^9 +2*xx) +[?7h[?12l[?25h[?2004l[?7h2*t^-2 + t^30 + t^46 + 2*t^126 + t^270 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy^2 - (xx^9 +2*xx)[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: yy +[?7h[?12l[?25h[?2004l[?7ht^-9 + 2*t^7 + 2*t^23 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx^4*yy/(xx^8 - 1)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: xx +[?7h[?12l[?25h[?2004l[?7ht^-2 + t^14 + 2*t^30 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^2 - (xx^9 +2*xx)[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: yy^2 +[?7h[?12l[?25h[?2004l[?7ht^-18 + t^-2 + 2*t^14 + 2*t^30 + t^46 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^4*yy/(xx^8 - 1)[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: xx^9 + 2*xx +[?7h[?12l[?25h[?2004l[?7ht^-18 + 2*t^-2 + 2*t^14 + t^30 + t^126 + 2*t^270 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y^2[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx^3 - x, 2)[?7h[?12l[?25h[?25l[?7lx^3 - x, 2)[?7h[?12l[?25h[?25l[?7lx^3 - x, 2)[?7h[?12l[?25h[?25l[?7lx^3 - x, 2)[?7h[?12l[?25h[?25l[?7l()x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l^3 - x, 2)[?7h[?12l[?25h[?25l[?7lx^3 - x, 2)[?7h[?12l[?25h[?25l[?7lx^3 - x, 2)[?7h[?12l[?25h[?25l[?7lx^3 - x, 2)[?7h[?12l[?25h[?25l[?7lx^3 - x, 2)[?7h[?12l[?25h[?25l[?7lx^3 - x, 2)[?7h[?12l[?25h[?25l[?7l^3 - x, 2)[?7h[?12l[?25h[?25l[?7lx^3 - x, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 - x, 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx^9 + 2*xx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l =t^(-2) + t^(14) + 2*t^(30)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: xx = C.x.expansion_at_infty(prec = 100) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy^2[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l = t^(-9) + 2*t^7 + 2*t^23[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7la[?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[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: yy = C.y.expanstion_at_infty(prec = 100) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [135], in () +----> 1 yy = C.y.expanstion_at_infty(prec = Integer(100)) + +AttributeError: 'superelliptic_function' object has no attribute 'expanstion_at_infty' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy = C.y.expanstion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lion_at_infty(prec = 10)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: yy = C.y.expansion_at_infty(prec = 100) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy = C.y.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^2[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l - (xx^9 +2*xx)[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: yy^2 - (xx^3 - xx) +[?7h[?12l[?25h[?2004l[?7h2*t^-2 + t^6 + t^10 + 2*t^14 + t^18 + t^34 + 2*t^38 + t^42 + t^46 + 2*t^50 + t^54 + O(t^94) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy^2 - (xx^3 - xx)[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: yy +[?7h[?12l[?25h[?2004l[?7ht^-3 + 2*t + 2*t^5 + 2*t^9 + t^13 + 2*t^17 + 2*t^33 + t^37 + 2*t^41 + 2*t^45 + t^49 + 2*t^53 + O(t^97) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx = C.x.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: xx +[?7h[?12l[?25h[?2004l[?7ht^-2 + t^2 + 2*t^6 + 2*t^10 + t^14 + 2*t^18 + 2*t^34 + t^38 + 2*t^42 + 2*t^46 + t^50 + 2*t^54 + O(t^98) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l , 2)[?7h[?12l[?25h[?25l[?7l+, 2)[?7h[?12l[?25h[?25l[?7l , 2)[?7h[?12l[?25h[?25l[?7l1, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 - x + 1, 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x + 1, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(xx^8 - 1)/(xx^4 * yy)[?7h[?12l[?25h[?25l[?7lC.x - a^(-2)).expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly*v^2 - C.y^2*v).cordinates()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.genus()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?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[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x + 1, 2)[?7h[?12l[?25h[?25l[?7l.y^2[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*v^2 - C.y^2*v).coordinates()[?7h[?12l[?25h[?25l[?7l*v^2 - C.y^2*v).coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.y^2).expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-6 + 2*t^-2 + 1 + 2*t^2 + t^4 + 2*t^6 + O(t^14) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l = C.y.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l= C.y.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lsage: yy = C.y.expansion_at_infty(prec = 100) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l = C.x.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l= C.x.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lsage: xx = C.x.expansion_at_infty(prec = 100) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy = C.y.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^2- (xx^3 - xx)[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l - (xx^3 - xx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l+)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: yy^2 - (xx^3 - xx + 1) +[?7h[?12l[?25h[?2004l[?7h2*t^-2 + 1 + 2*t^4 + 2*t^6 + 2*t^8 + 2*t^10 + 2*t^12 + 2*t^14 + t^28 + t^30 + t^32 + 2*t^40 + 2*t^42 + 2*t^44 + 2*t^46 + 2*t^48 + 2*t^50 + t^52 + t^54 + t^56 + t^82 + t^84 + t^86 + 2*t^88 + 2*t^90 + 2*t^92 + O(t^94) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x + 1, 2)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x^3 - x + 1, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 - x, 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx = C.x.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l = C.x.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lsage: xx = C.x.expansion_at_infty(prec = 100) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy^2 - (xx^3 - xx + 1)[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^2 - (xx^3 - xx + 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[?7lyy^2 - (xx^3 - xx + 1)[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l =C.y.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.y.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lsage: yy = C.y.expansion_at_infty(prec = 100) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxx = C.x.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: xx +[?7h[?12l[?25h[?2004l[?7ht^-2 + t^2 + 2*t^6 + 2*t^10 + t^14 + 2*t^18 + 2*t^34 + t^38 + 2*t^42 + 2*t^46 + t^50 + 2*t^54 + O(t^98) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lyy = C.y.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: yy +[?7h[?12l[?25h[?2004l[?7ht^-3 + 2*t + 2*t^5 + 2*t^9 + t^13 + 2*t^17 + 2*t^33 + t^37 + 2*t^41 + 2*t^45 + t^49 + 2*t^53 + O(t^97) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: 1/xx +[?7h[?12l[?25h[?2004l[?7ht^2 + 2*t^6 + 2*t^10 + t^14 + 2*t^18 + 2*t^34 + t^38 + 2*t^42 + 2*t^46 + t^50 + 2*t^54 + O(t^102) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*((C.x.teichmuller()).diffn())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la^(-1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbase_ring(parent(lau))[?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[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: b = F(2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = F(2)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lot([?7h[?12l[?25h[?25l[?7lrot([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: b.nth_root(2) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [152], in () +----> 1 b.nth_root(Integer(2)) + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:1572, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.nth_root() + 1570 else: + 1571 return sign[0] * K(R.teichmuller(modp) * (plog // n).exp()) +-> 1572 return self._nth_root_common(n, all, algorithm, cunningham) + 1573 + 1574 def _nth_root_naive(self, n): + +File /ext/sage/9.7/src/sage/rings/finite_rings/element_base.pyx:74, in sage.rings.finite_rings.element_base.FiniteRingElement._nth_root_common() + 72 if n == 0: + 73 if all: return [] +---> 74 else: raise ValueError("no nth root") + 75 gcd, alpha, beta = n.xgcd(q-1) # gcd = alpha*n + beta*(q-1), so 1/n = alpha/gcd (mod q-1) + 76 if gcd == 1: + +ValueError: no nth root +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb.nth_root(2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: b.nth_root(3) +[?7h[?12l[?25h[?2004l[?7h2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l:219: DeprecationWarning: invalid escape sequence '\s' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.y^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 - x, 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.y^2[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.y^2[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexpansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty(prec = 100) +[?7h[?12l[?25h[?2004lww 1 + 2*t^4 + 2*t^8 + t^12 + 2*t^16 + 2*t^32 + t^36 + 2*t^40 + 2*t^44 + t^48 + 2*t^52 + O(t^100) +[?7ht^-2 + t^2 + 2*t^6 + 2*t^10 + t^14 + 2*t^18 + 2*t^34 + t^38 + 2*t^42 + 2*t^46 + t^50 + 2*t^54 + O(t^98) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7luniformizer().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lformizer().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7lsage: C.uniformizer().expansion_at_infty(prec = 220) +[?7h[?12l[?25h[?2004la, b, delta, M, R 2 1 1 2 3 +ww 1 + 2*t^4 + 2*t^8 + t^12 + 2*t^16 + 2*t^32 + t^36 + 2*t^40 + 2*t^44 + t^48 + 2*t^52 + 2*t^104 + t^108 + 2*t^112 + 2*t^116 + t^120 + 2*t^124 + 2*t^140 + t^144 + 2*t^148 + 2*t^152 + t^156 + 2*t^160 + O(t^220) +[?7ht + O(t^221) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l:219: DeprecationWarning: invalid escape sequence '\s' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty(prec = 100) +[?7h[?12l[?25h[?2004lww 1 + 2*t^4 + 2*t^8 + t^12 + 2*t^16 + 2*t^32 + t^36 + 2*t^40 + 2*t^44 + t^48 + 2*t^52 + O(t^100) +[?7ht^-2 + t^2 + 2*t^6 + 2*t^10 + t^14 + 2*t^18 + 2*t^34 + t^38 + 2*t^42 + 2*t^46 + t^50 + 2*t^54 + O(t^98) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l:219: DeprecationWarning: invalid escape sequence '\s' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty(prec = 100)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7luniformizer().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lformizer().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7lsage: C.uniformizer().expansion_at_infty(prec = 220) +[?7h[?12l[?25h[?2004la, b, delta, M, R 1 1 1 2 3 +ww 1 + 2*t^4 + 2*t^8 + t^12 + 2*t^16 + 2*t^32 + t^36 + 2*t^40 + 2*t^44 + t^48 + 2*t^52 + 2*t^104 + t^108 + 2*t^112 + 2*t^116 + t^120 + 2*t^124 + 2*t^140 + t^144 + 2*t^148 + 2*t^152 + t^156 + 2*t^160 + O(t^220) +[?7ht + O(t^221) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.uniformizer().expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()).expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l()^.expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l(.expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l().expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l-).expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l1).expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()).expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.uniformizer())^(-1).expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.uniformizer())^(-1)).expansion_at_infty(prec = 220) +[?7h[?12l[?25h[?2004la, b, delta, M, R 1 1 1 2 3 +ww 1 + 2*t^4 + 2*t^8 + t^12 + 2*t^16 + 2*t^32 + t^36 + 2*t^40 + 2*t^44 + t^48 + 2*t^52 + 2*t^104 + t^108 + 2*t^112 + 2*t^116 + t^120 + 2*t^124 + 2*t^140 + t^144 + 2*t^148 + 2*t^152 + t^156 + 2*t^160 + O(t^220) +[?7ht^-1 + O(t^219) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l:218: DeprecationWarning: invalid escape sequence '\s' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l +  + [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?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[?7l[?7h[?12l[?25h[?25l[?7l(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l(x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l(x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + [?7h[?12l[?25h[?25l[?7lom = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 + - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega8_hpdh(om) +[?7h[?12l[?25h[?2004lomega_analytic (T^14 + 2*T^4 + T^2 + 1)/T^18 +expansions t^-18 + t^-16 + 2*t^-14 + t^-4 + 1 + t^2 + t^12 + 2*t^16 + t^18 + 2*t^28 + O(t^32) + 1 + t^16 + t^48 + O(t^50) + t^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2 + 2 + 2*t^12 + 2*t^18 + t^30 + O(t^32) +omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + t^-2 + 2 + 2*t^12 + 2*t^18 + t^30 + O(t^32) +omega_analytic ((x^84 + x^83 - x^82 + x^77 - x^75 - x^74 - x^69 - x^66 + x^53 - x^45 + x^29 - x^21)/(x^72*y - y)) dx +omega8 ((-x^77 - x^76 + x^75 - x^74 + x^73 + x^72 - x^69 - x^67 + x^65 - x^61 + x^57 + x^56 - x^53 - x^51 + x^49 - x^48 - x^45 + x^43 + x^41 - x^37 + x^33 + x^32 - x^29 - x^27 + x^25 - x^24 - x^21 + x^19 + x^17 + x^13 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx +dh ((x^30 + x^28 + x^20 + x^12)/(x^24*y - y)) dx +omega8.expansion_at_infty() 2*t^-2 + 2 + t^2 + 2*t^4 + t^6 + t^8 + 2*t^16 + 2*t^18 + t^20 + 2*t^22 + 2*t^30 + 2*t^40 + t^46 + O(t^48) +[?7h(((-x^77 - x^76 + x^75 - x^74 + x^73 + x^72 - x^69 - x^67 + x^65 - x^61 + x^57 + x^56 - x^53 - x^51 + x^49 - x^48 - x^45 + x^43 + x^41 - x^37 + x^33 + x^32 - x^29 - x^27 + x^25 - x^24 - x^21 + x^19 + x^17 + x^13 - x^12 + x^11 + x^9 + x^8 - x^4 - x^3 + x^2 + 1)/(x^73*y - x*y)) dx, + ((x^38 + 2*x^36 + x^30 + x^12)/(x^40 + x^32 + x^24 + 2*x^16 + 2*x^8 + 2))*y) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.uniformizer().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lformizer().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7lsage: C.uniformizer().expansion_at_infty(prec = 220) +[?7h[?12l[?25h[?2004l[?7ht + O(t^221) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.uniformizer().expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()).expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l()^.expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l().expansion_at_infty(prec= 220)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l-).expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l0).expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l).expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l1).expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()).expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.uniformizer())^(-1).expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.uniformizer())^(-1)).expansion_at_infty(prec = 220) +[?7h[?12l[?25h[?2004l[?7ht^-1 + O(t^219) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.expansion_at_infty(prec = 50) +  + [?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lpansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7lsage: om.expansion_at_infty(prec = 50) +[?7h[?12l[?25h[?2004l[?7ht^-18 + t^-16 + 2*t^-14 + t^-4 + 1 + t^2 + 2*t^4 + t^6 + t^8 + 2*t^12 + 2*t^16 + t^18 + t^20 + 2*t^22 + O(t^32) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7luniformizer().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldexpansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7liexpansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7lfexpansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7lfexpansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7lnexpansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l(expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l()expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l().expansion_at_infty(prec = 20)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.uniformizer().diffn().expansion_at_infty(prec = 220) +[?7h[?12l[?25h[?2004l[?7h1 + O(t^220) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l:218: DeprecationWarning: invalid escape sequence '\s' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.uniformizer().diffn().expansion_at_infty(prec = 220)[?7h[?12l[?25h[?25l[?7l = superelliptic((x^3 - )^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l= superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.expansion_at_infty(prec = 50)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 + - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega8_hpdh(om) +[?7h[?12l[?25h[?2004lomega_analytic (T^14 + 2*T^4 + T^2 + 1)/T^18 +expansions t^-18 + t^-16 + 2*t^-14 + t^-4 + O(t^32) + 1 + O(t^50) + t^-18 + t^-16 + 2*t^-14 + t^-4 + O(t^32) +omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + O(t^32) +omega_analytic ((x^72 + x^71 - x^70 + x^65 - x^64 - x^62 - x^56 - x^55 - x^49 - x^48 + x^47 - x^46 - x^40 - x^38 - x^32 - x^31 - x^24 + x^23 - x^22 - x^16 - x^14 - x^8 - x^7 + 1)/(x^60*y)) dx +omega8 ((x^78 - x^76 - x^75 - x^74 + x^73 + x^72 - x^71 - x^69 - x^67 - x^66 + x^65 - x^64 + x^63 - x^60 + x^59 + x^58 - x^57 - x^56 + x^55 - x^54 + x^48 - x^47 + x^46 + x^45 - x^44 + x^43 - x^42 + x^41 - x^40 + x^39 - x^38 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 + x^21 - x^20 + x^19 - x^18 + x^17 - x^16 - x^15 - x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1)/(x^75*y - x^74*y + x^73*y - x^72*y + x^71*y - x^70*y + x^69*y - x^68*y - x^67*y + x^66*y - x^65*y + x^64*y - x^63*y + x^62*y - x^61*y + x^60*y)) dx +dh ((x^24 + x^22 - x^16 + x^14 - x^8 + 1)/(x^18*y)) dx +omega8.expansion_at_infty() 1 + t^2 + 2*t^4 + t^6 + t^8 + 2*t^12 + 2*t^16 + t^18 + t^20 + 2*t^22 + t^32 + 2*t^40 + t^48 + O(t^50) +[?7h(((x^78 - x^76 - x^75 - x^74 + x^73 + x^72 - x^71 - x^69 - x^67 - x^66 + x^65 - x^64 + x^63 - x^60 + x^59 + x^58 - x^57 - x^56 + x^55 - x^54 + x^48 - x^47 + x^46 + x^45 - x^44 + x^43 - x^42 + x^41 - x^40 + x^39 - x^38 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 + x^21 - x^20 + x^19 - x^18 + x^17 - x^16 - x^15 - x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1)/(x^75*y - x^74*y + x^73*y - x^72*y + x^71*y - x^70*y + x^69*y - x^68*y - x^67*y + x^66*y - x^65*y + x^64*y - x^63*y + x^62*y - x^61*y + x^60*y)) dx, + ((x^32 + 2*x^30 + 2*x^24 + 2*x^14 + 2*x^8 + 1)/(x^34 + x^26 + x^18))*y) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lodecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lmdecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7l8decomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7l,decomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7l decomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lAdecomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7l decomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7l=decomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7l decomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?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: om8, A = decomposition_omega8_hpdh(om) +[?7h[?12l[?25h[?2004lomega_analytic (T^14 + 2*T^4 + T^2 + 1)/T^18 +expansions t^-18 + t^-16 + 2*t^-14 + t^-4 + O(t^32) + 1 + O(t^50) + t^-18 + t^-16 + 2*t^-14 + t^-4 + O(t^32) +omega_analytic.expansion_at_infty() t^-18 + t^-16 + 2*t^-14 + t^-4 + O(t^32) +omega_analytic ((x^72 + x^71 - x^70 + x^65 - x^64 - x^62 - x^56 - x^55 - x^49 - x^48 + x^47 - x^46 - x^40 - x^38 - x^32 - x^31 - x^24 + x^23 - x^22 - x^16 - x^14 - x^8 - x^7 + 1)/(x^60*y)) dx +omega8 ((x^78 - x^76 - x^75 - x^74 + x^73 + x^72 - x^71 - x^69 - x^67 - x^66 + x^65 - x^64 + x^63 - x^60 + x^59 + x^58 - x^57 - x^56 + x^55 - x^54 + x^48 - x^47 + x^46 + x^45 - x^44 + x^43 - x^42 + x^41 - x^40 + x^39 - x^38 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 + x^21 - x^20 + x^19 - x^18 + x^17 - x^16 - x^15 - x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1)/(x^75*y - x^74*y + x^73*y - x^72*y + x^71*y - x^70*y + x^69*y - x^68*y - x^67*y + x^66*y - x^65*y + x^64*y - x^63*y + x^62*y - x^61*y + x^60*y)) dx +dh ((x^24 + x^22 - x^16 + x^14 - x^8 + 1)/(x^18*y)) dx +omega8.expansion_at_infty() 1 + t^2 + 2*t^4 + t^6 + t^8 + 2*t^12 + 2*t^16 + t^18 + t^20 + 2*t^22 + t^32 + 2*t^40 + t^48 + O(t^50) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom8, A = decomposition_omega8_hpdh(om)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om = ((C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^22 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^11 - C.x^1 0 +....:  - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^11*C.y + C.x^10*C.y - C +....: .x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l= (C.x^28 - C.x^26 + C.x^25 - C.x^24 + C.x^23 - C.x^2 - C.x^21 + C.x^20 + C.x^19 + C.x^18 + C.x^17 + C.x^15 - C.x^14 + C.x^13 + C.x^12 + C.x^1 - C.x^ 1 +0 - C.x^8 - C.x^7 + C.x^6 - C.x^5 + C.x^4 + C.x^2 + C.x - C.one)/(C.x^16*C.y - C.x^15*C.y + C.x^14*C.y - C.x^13*C.y + C.x^12*C.y - C.x^1*C.y + C.x^10*C.y -   +C.x^9*C.y - C.x^8*C.y + C.x^7*C.y - C.x^6*C.y + C.x^5*C.y - C.x^4*C.y + C.x^3*C.y - C.x^2*C.y + C.x*C.y)*C.dx[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l +  + [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l. =[?7h[?12l[?25h[?25l[?7lca ==[?7h[?12l[?25h[?25l[?7lr =[?7h[?12l[?25h[?25l[?7lt =[?7h[?12l[?25h[?25l[?7le =[?7h[?12l[?25h[?25l[?7l =[?7h[?12l[?25h[?25l[?7li =[?7h[?12l[?25h[?25l[?7le =[?7h[?12l[?25h[?25l[?7lr =[?7h[?12l[?25h[?25l[?7l( =[?7h[?12l[?25h[?25l[?7l() =[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.cartier() == om8.cartier() + A.diffn() +[?7h[?12l[?25h[?2004l[?7hTrue +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.cartier() == om8.cartier() + A.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l8, A = decomposition_omga8_hpdh(om)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l;[?7h[?12l[?25h[?25l[?7lsage: om8.is_regu; + %%! AbelianGroupMorphism AdditiveAbelianGroupWrapper  + A AbelianGroupWithValues AdditiveAbelianGroupWrapperElement  + AA AbelianVariety AdditiveMagmas > + AbelianGroup AdditiveAbelianGroup AffineCryptosystem  + [?7h[?12l[?25h[?25l[?7l + + + +[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lar_on_U + om8.is_regular_on_U0  + om8.is_regular_on_Uinfty[?7h[?12l[?25h[?25l[?7l0 + om8.is_regular_on_U0  + + [?7h[?12l[?25h[?25l[?7linfty + om8.is_regular_on_U0  + om8.is_regular_on_Uinfty[?7h[?12l[?25h[?25l[?7l( + + +[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om8.is_regular_on_Uinfty() +[?7h[?12l[?25h[?2004l[?7hTrue +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + [?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$ gigit add auxsuperelliptic_arbitrary_field.ipynb age/superelliptic_drw/superelliptic_drw_auxilliaries.sage diff --git a/sage/init.sage b/sage/init.sage index f4efe85..2ea9902 100644 --- a/sage/init.sage +++ b/sage/init.sage @@ -18,12 +18,14 @@ load('superelliptic_drw/decomposition_into_g0_g8.sage') load('superelliptic_drw/superelliptic_witt.sage') load('superelliptic_drw/superelliptic_drw_form.sage') load('superelliptic_drw/superelliptic_drw_cech.sage') +load('superelliptic_drw/superelliptic_drw_auxilliaries.sage') load('superelliptic_drw/regular_form.sage') load('superelliptic_drw/de_rham_witt_lift.sage') load('superelliptic_drw/automorphism.sage') load('auxilliaries/reverse.sage') load('auxilliaries/hensel.sage') load('auxilliaries/linear_combination_polynomials.sage') +load('auxilliaries/laurent_analytic_part.sage') ############## ############## load('drafty/convert_superelliptic_into_AS.sage') diff --git a/sage/superelliptic/superelliptic_class.sage b/sage/superelliptic/superelliptic_class.sage index 1a43896..7b3fd1d 100644 --- a/sage/superelliptic/superelliptic_class.sage +++ b/sage/superelliptic/superelliptic_class.sage @@ -201,10 +201,22 @@ class superelliptic: basis += [superelliptic_function(self, Fxy(m*y^(m-j)/x^i))] return basis -#Auxilliary. Given a superelliptic curve C : y^m = f(x) and a polynomial g(x, y) -#it replaces repeteadly all y^m's in g(x, y) by f(x). As a result -#you obtain \sum_{i = 0}^{m-1} y^i g_i(x). + def uniformizer(self): + m = self.exponent + r = self.polynomial.degree() + delta, a, b = xgcd(m, r) + a = -a + M = m/delta + R = r/delta + while a<0: + a += R + b += M + return (C.x)^a/(C.y)^b + def reduction(C, g): + '''Auxilliary. Given a superelliptic curve C : y^m = f(x) and a polynomial g(x, y) + it replaces repeteadly all y^m's in g(x, y) by f(x). As a result + you obtain \sum_{i = 0}^{m-1} y^i g_i(x).''' p = C.characteristic F = C.base_ring Rxy. = PolynomialRing(F, 2) diff --git a/sage/superelliptic/superelliptic_function_class.sage b/sage/superelliptic/superelliptic_function_class.sage index f93f91c..63b0f6d 100644 --- a/sage/superelliptic/superelliptic_function_class.sage +++ b/sage/superelliptic/superelliptic_function_class.sage @@ -122,13 +122,12 @@ class superelliptic_function: fct = RxyQ(fct) r = f.degree() delta, a, b = xgcd(m, r) - b = -b + a = -a M = m/delta R = r/delta while a<0: a += R b += M - g = (x^r*f(x = 1/x)) gW = RptWQ(g(x = t^M * W^b)) - W^(delta) ww = naive_hensel(gW, F, start = root_of_unity(F, delta)^place, prec = prec) diff --git a/sage/superelliptic_drw/decomposition_into_g0_g8.sage b/sage/superelliptic_drw/decomposition_into_g0_g8.sage index e83858c..d9e5134 100644 --- a/sage/superelliptic_drw/decomposition_into_g0_g8.sage +++ b/sage/superelliptic_drw/decomposition_into_g0_g8.sage @@ -57,11 +57,4 @@ def decomposition_omega0_omega8(omega, prec=50): #Rx. = PolynomialRing(F) #aux_fct = (g0.form)*y else: - raise ValueError("Something went wrong for "+str(omega) +". Result would be "+str(g0)+ " and " + str(g8)) - - -def decomposition_g0_g8_pth_power(fct): - '''Decompose fct as g0 - g8 + A^p, if possible. Output: (g0, g8, A).''' - coor = fct.coordinates() - C = fct.curve - return 0 \ No newline at end of file + raise ValueError("Something went wrong for "+str(omega) +". Result would be "+str(g0)+ " and " + str(g8)) \ No newline at end of file diff --git a/sage/superelliptic_drw/superelliptic_drw_auxilliaries.sage b/sage/superelliptic_drw/superelliptic_drw_auxilliaries.sage new file mode 100644 index 0000000..7061da7 --- /dev/null +++ b/sage/superelliptic_drw/superelliptic_drw_auxilliaries.sage @@ -0,0 +1,49 @@ +def decomposition_g0_pth_power(fct): + '''Decompose fct as g0 + A^p, if possible. Output: (g0, A).''' + omega = fct.diffn().regular_form() + g0 = omega.int() + A = (fct - g0).pth_root() + return (g0, A) + +def decomposition_g0_p2th_power(fct): + '''Decompose fct as g0 + A^(p^2), if possible. Output: (g0, A).''' + g0, A = decomposition_g0_pth_power(fct) + A0, A1 = decomposition_g0_pth_power(A) + return (g0 + A0^p, A1) + +def decomposition_omega0_hpdh(omega): + '''Decompose omega = (regular on U0) + h^(p-1) dh, so that Cartier(omega) = (regular on U0) + dh. + Result: (regular on U0, h)''' + omega1 = omega.cartier().cartier() + omega1 = omega1.inv_cartier().inv_cartier() + fct = (omega.cartier() - omega1.cartier()).int() + return (omega1, fct) + +def decomposition_omega8_hpdh(omega, prec = 50): + '''Decompose omega = (regular on U8) + h^(p-1) dh, so that Cartier(omega) = (regular on U8) + dh. + Result: (regular on U8, h)''' + C = omega.curve + g = C.genus() + Fxy, Rxy, x, y = C.fct_field + F = C.base_ring + p = C.characteristic + Rt. = LaurentSeriesRing(F) + RT. = PolynomialRing(F) + FT = FractionField(RT) + omega_analytic = FT(laurent_analytic_part(omega.expansion_at_infty(prec = prec))(t = T)) + print('omega_analytic', omega_analytic) + Cv = C.uniformizer() + v = Fxy(Cv.function) + omega_analytic = Fxy(omega_analytic(T = v)) + print('expansions', superelliptic_function(C, omega_analytic).expansion_at_infty(prec = prec), '\n', Cv.diffn().expansion_at_infty(prec = prec), + '\n', (superelliptic_function(C, omega_analytic)*Cv.diffn()).expansion_at_infty(prec = prec)) + omega_analytic = superelliptic_function(C, omega_analytic)*Cv.diffn() + print('omega_analytic.expansion_at_infty()', omega_analytic.expansion_at_infty(prec = prec)) + print('omega_analytic', omega_analytic) + omega8 = omega - omega_analytic + print('omega8', omega8) + dh = omega.cartier() - omega8.cartier() + print('dh', dh) + h = dh.int() + print('omega8.expansion_at_infty()', omega8.expansion_at_infty(prec = prec)) + return (omega8, h) \ No newline at end of file diff --git a/sage/superelliptic_drw/superelliptic_drw_cech.sage b/sage/superelliptic_drw/superelliptic_drw_cech.sage index 80ed151..04ec0e0 100644 --- a/sage/superelliptic_drw/superelliptic_drw_cech.sage +++ b/sage/superelliptic_drw/superelliptic_drw_cech.sage @@ -67,30 +67,34 @@ class superelliptic_drw_cech: aux.omega0 -= aux_f_t_0.teichmuller().diffn() aux.omega8 = aux.omega0 - aux.f.diffn() # + # Now omega = (regular on U0) + h^(p-1) dh, so that Cartier(omega) = (regular on U0) + dh. + # We replace omega by regular on U0 omega = aux.omega0.omega - omega1 = omega.cartier().cartier() - omega1 = omega1.inv_cartier().inv_cartier() - fct = (omega.cartier() - omega1.cartier()).int() + aux.omega0.omega, fct = decomposition_omega0_hpdh(aux.omega0.omega) aux.omega0.h2 += fct^p - aux.omega0.omega = omega1 - if aux.omega0.h2.function in Rxy: - aux.f -= aux.omega0.h2.verschiebung() - aux.omega0.h2 = 0*C.x - if aux.omega8.h2.expansion_at_infty().valuation() >= 0: - aux.f += aux.omega8.h2.verschiebung() - aux.omega8.h2 = 0*C.x - print('aux', aux) - # Now aux should be of the form (V(omega1), V(f), V(omega2)) - # Thus aux = p*(Cartier(omega1), p-th_root(f), Cartier(omega2)) - aux_divided_by_p = superelliptic_cech(C, aux.omega0.omega.cartier(), aux.f.f.pth_root()) - print('aux_divided_by_p', aux_divided_by_p) - print('is regular', aux_divided_by_p.omega0.is_regular_on_U0(), aux_divided_by_p.omega8.is_regular_on_Uinfty()) - print('aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier()', aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier()) - return aux_divided_by_p - else: - raise ValueError("aux.omega8.h2.expansion_at_infty().valuation() < 0:", aux.omega8.h2.expansion_at_infty()) + # Now we have to ensure that aux.omega0.h2.function in Rxy... + # In other words, we decompose h2 = (regular on U0) + A^(p^2). + aux.omega0.h2 = decomposition_g0_p2th_power(aux.omega0.h2)[0] + # Now we can reduce: (... + dV(h2), V(f), ...) --> (..., V(f - h2), ...) + aux.f -= aux.omega0.h2.verschiebung() + aux.omega0.h2 = 0*C.x + + if aux.omega8.h2.expansion_at_infty().valuation() >= 0: + aux.f += aux.omega8.h2.verschiebung() + aux.omega8.h2 = 0*C.x + print('aux', aux) + # Now aux should be of the form (V(omega1), V(f), V(omega2)) + # Thus aux = p*(Cartier(omega1), p-th_root(f), Cartier(omega2)) + aux_divided_by_p = superelliptic_cech(C, aux.omega0.omega.cartier(), aux.f.f.pth_root()) + print('aux_divided_by_p', aux_divided_by_p) + print('is regular', aux_divided_by_p.omega0.is_regular_on_U0(), aux_divided_by_p.omega8.is_regular_on_Uinfty()) + print('aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier()', aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier()) + return aux_divided_by_p else: - raise ValueError("aux.omega0.h2.function not in Rxy:", aux.omega0.h2.function) + print('aux.omega8.omega', aux.omega8.omega) + print('aux.omega8.h2', aux.omega8.h2) + print('second_patch(aux.omega8.h2.diffn()).is_regular_on_U0()', second_patch(aux.omega8.h2.diffn()).is_regular_on_U0()) + raise ValueError("aux.omega8.h2.expansion_at_infty().valuation() < 0:", aux.omega8.h2.expansion_at_infty()) def coordinates(self, basis = 0): C = self.curve @@ -113,4 +117,4 @@ class superelliptic_drw_cech: print(self.omega0.r().is_regular_on_U0(), self.omega8.r().is_regular_on_Uinfty(), self.omega0.frobenius().is_regular_on_U0(), self.omega8.frobenius().is_regular_on_Uinfty()) eq1 = self.omega0.r().is_regular_on_U0() and self.omega8.r().is_regular_on_Uinfty() eq2 = self.omega0.frobenius().is_regular_on_U0() and self.omega8.frobenius().is_regular_on_Uinfty() - return eq1 and eq2 + return eq1 and eq2 \ No newline at end of file